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United States
Department of
Agriculture
Forest Service
Pacific Northwest
Research Station
Research Note
PNW-RN-478
July 1988
Tables and Equations for
Estimating Volumes of Trees in
the Susitna River Basin, Alaska
Frederic R. Larson and Kenneth C. Winterberger
Abstract
Introduction
Scribner board-foot, merchantable cubic-foot, and total cubic-foot volume equations
were derived from fall, buck, and scale data for 441 trees at 78 locations in the
Susitna River basin, Alaska. Tree species included white and black spruce, 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.
Scribner board-foot, merchantable cubic-foot, and total cubic-foot volume equations
were derived from an analysis of fall, buck, and scale data obtained during a multi-
resource inventory of the Susitna River basin, Alaska (USDA, Soil Conservation Serv-
ice 1986). Board-foot 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. Merchant-
able cubic-foot volumes are presented for combinations of dbh and total tree height,
and for dbh and height to a 4-inch top. Total cubic-foot volumes are given for dbh
and total tree height only.
A total of 441 trees were used in the analysis: 244 white spruce (Picea glauca
(Moench) Voss), 43 black spruce (P. mariana (Mill.) B.S.P.), 97 paper birch (Betula
papyifera Marsh.), 14 quaking aspen (Populus tremuloides Michx.), and 43 black cot-
tonwood (P. trichocarpa Torr. & Gray). Data were collected from 78 locations in the
Susitna River basin, which is 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).
FREDERIC R. LARSON is research forester and KENNETH C.
WINTERBERGER is forester, Forestry Sciences Laboratory, 201 East
9th Avenue, Anchorage, Alaska 99501.
Figure 1—Part of the Susitna River basin, Alaska, where fall, buck,
and scale data were collected.
Methodology 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 in-
ventory plots. Al! tally trees greater than 5 inches dbh were destructively sampled.
Each sample tree was measured and marked at a 1-foot stump and at dbh. After fell-
ing and limbing, total height and height to a 6-inph and a 4-inch top were recorded.
The tree was bucked into 16.3-fo6t logs and at 6-inch and 4-inch tops. All cross-
sectional diameters inside bark were measured twice at right angles and averaged.
2
Discussion
Data from trees suitable for volume-table construction were used to build a data file
consisting of dbh, total height, height to 4-inch and 6-inch tops, total and merchant-
able cubic-foot volume, and Scribner board-foot volume. Trees with missing data, or
data obviously in error, were eliminated from the data base as were obviously
deformed and cull trees. 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.11f a log was too short or too long, a portion of the
next log was "added" or the log was "cut" to a standard length and a new diameter
was calculated; it was assumed that logs were circular in cross section with linear
taper between the existing end measurements. Board-foot volumes were not com-
puted for pieces shorter than 8 feet or if diameter inside bark at the small end was
less than 6 inches. Cubic-foot volumes were computed using Smalian's formula.
Board-foot volumes, Scribner rule, were computed by using the Girard and Bruce
rule of thumb (Dilworth 1968):
volume = (0.79 x diameter2 - 2.0 x diameter - 4.0) x (length/16.0) .
Plottings of volume over dbh2 x height indicated that cubic-foot volume was linearly
related to dbh2 x height and board-foot volume was curvilinearly related to dbh2 x
height. The independent variables tested therefore included dbh, dbh2, height (ht),
dbh2.x.ht, 1/dbh, 1/dbh2, and (dbh2ht)c.
Regression portions of the SPSSX statistical program package (SPSS 1983)2 were
used to run forward-stepwise analysis for linear expressions of the data. The term
(dbh2ht)c was fitted after transformation with logarithms; for example, In(BFV) = b0 +
1 x ln(dbh2ht). Both weighted and unweighted linear regressions were tested as
described by Furnival (1961) with various results. The logarithm transformation to
obtain an equation with (dbh2ht)c avoids the need of weights because it assumes
that the residuals are distributed normally about a log normal distribution function.
Analysis of covariance was used to test for significant differences in the data be-
tween white and black spruce and between paper birch and quaking aspen. In both
cases, the data were not significantly different and therefore were pooled.
The regression equation for each table is presented at the bottom of the table; it is
followed by the increased efficiency 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 indicates the limits of the data. The number of
trees in each diameter class by species is also presented.
1 Unpublished manual, 1981, "Forest Service Manual, title 2400, Timber
Management, Alaska Region Supplement 228," by U.S. Department of
Agriculture, Forest Service, Alaska Region, Juneau, Alaska 99802.
2 The use of trade, firm, or corporation names in this publication is for
the information and convenience of the reader. Such use does not
constitute an official endorsement or approval by the U.S. Department of
Agriculture of any product or service to the exclusion of others that may
be suitable.
3
Board-foot volumes for most species were lower than shown in all published tables
(Dippold and Farr 1971, Farr 1967, Gregory and Haack 1964, Haack 1963, Kerr and
Eleazer 1980) and unpublished tables3 for small-diameter classes. Greater board-foot
volumes are reported for spruce trees larger than 24 inches dbh in all published
tables except the Tyonek tables (Kerr and Eleazer 1980). The Tyonek tables show
that spruce volume is less than the volumes published in this report after the spruce
reach 10 inches dbh. Board-foot volumes for birch and aspen exceed published
values when trees exceed 16-18 inches dbh except in the Tyonek tables where, like
the spruce, more volume is reported at 10 inches dbh and above. Volumes for black
cottonwood were higher in lower classes, below 17 inches dbh, than are reported for
balsam poplar (Haack 1963) but slightly higher than Ryan's data for very large
classes (see footnote 3).
In our tables, board-foot volumes for trees whose height was measured to a mer-
chantable 6-inch top diameter were lower than Ryan's (see footnote 3) for white and
black spruce, lower than Ryan's for paper birch and quaking aspen less than 12
inches dbh, and lower than Ryan's for black cottonwood less than 19 inches dbh.
Our spruce merchantable cubic-foot volumes (that is, volumes to a 4-inch top
diameter inside bark [dib]) were nearly identical to those reported by Gregory and
Haack (1964) and Ryan (see footnote 3), and only slightly lower in large-diameter
classes than those reported by Haack (1963) and Dippold and Farr (1971). Merchant-
able cubic-foot volumes were greater than those reported by Kerr and Eleazer (1980)
for white and black spruce, birch, and aspen greater than 11 inches dbh. Birch and
aspen merchantable cubic-foot volumes were greater than those reported for Tyonek
(Kerr and Eleazer 1980) but, otherwise, not much different than those reported by
others cited. Black cottonwood merchantable cubic-foot volumes were nearly identical
to other reported data for this species except as reported by Gregory and Haack
(1964) for black cottonwood and balsam poplar {Populus balsamifera L.) where
reported volumes are greater in diameter classes above 16-17 inches dbh. Poplar
and cottonwood were combined by Gregory and Haack.
Merchantable cubic-foot volumes in tables for tree heights measured to a merchant-
able 4-inch top diameter inside bark were nearly identical to Ryan's (see footnote 3)
for spruce, birch, and aspen and only slightly lower than those for black cottonwood
in large-diameter classes.
Total cubic-foot volumes of the entire stem for spruce, paper birch and quaking
aspen were nearly equal to those reported by Gregory and Haack (1964) for small-
size classes but were slightly lower for larger classes. The total cubic-foot volume of
black cottonwood was slightly higher in our tables than in those of Gregory and
Haack (1964).
3 Unpublished office report, 1984, "Volume tables for the Susitna River
valley, Alaska," by Phyllis Ryan, State of Alaska, Department of Natural
Resources, 3601 C. Street, Anchorage, Alaska 99503.
4
Literature Cited Dilworth, J.R. 1968. Log scaling and timber cruising. Corvallis, OR: O.S.U. Book
Stores, Inc. 464 p.
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
Service, Pacific Northwest Forest and Range Experiment Station. 8 p.
Farr, Wilbur A. 1967. Board-foot tree volume tables and equations for white
spruce in interior Alaska. Res. Note PNW-59. Portland, OR: U.S. Department of
Agriculture, Forest Service, Pacific Northwest Forest and Range Experiment
Station. 4 p.
Furnival, George M. 1961. An index for comparing equations used in constructing
volume tables. Forest Science. 7: 337-341.
Gregory, Robert A.; Haack, Paul M. 1964. Equations and tables for estimating
cubic-foot volume of interior Alaska tree species. Res. Note NOR-6. Juneau, AK:
U.S. Department of Agriculture, Forest Service, Northern Forest Experiment
Station. 21 p.
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.
SPSS, Inc. 1983. SPSSX user's guide. New York: McGraw-Hill Book Company.
806 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.
5
Table 1- Board-foot volumes, Scribner line (1-foot stump to 6-inch top dib) given dbh and total height for white spruce and black spruce, Susitna River basin, AlaskaaTables a Regression: BFV = 0.000136 (d2h)1.40338 ; increased efficiency = 184 percent; standard error of estimate = 8.5 board feet or 21 percent of the mean volume. b For example, 9-inch class includes trees 8.6 to 9.5 inches in diameter c For example, 60-foot class includes trees 57.6 to 62.5 feet tall. d Number of trees; range of data is shaded. Includes 208 white spruce and 27 black spruce 6
Table 2—Board-foot volumes, Scribner rule (1-foot stump to 6-inch top dib) given dbh and total height for paper birch and quaking aspen, Susitna River basin, Alaskaa a Regression: BFV = 0.000081 * (d2h)1.48459 ; increased efficiency = 108 percent; standard error of estimate = 11.0 board feet or 24 percent of the mean volume. b For example, 9-inch class includes trees 8.6 to 9.5 inches in diameter c For example, 60-foot class includes trees 57.6 to 62.5 feet tall. d Number of trees; range of data is shaded. Includes 84 paper birch and 13 quaking aspen. 7
Table 3—Board-foot volume, Scribner rule (1-foot stump to 6-inch top dib) given dbh and total height for black cottonwood, Susitna River basin, Alaska8 a Weighted regression: BFV = -28.0674 * 0.00937 * d2h; increased efficiency = 147 percent; standard error of estimate = 27.3 board feet or 16 percent of the mean volume. b For example, 9-inch class includes trees 8.6 to 9-5 inches in diameter. c For example, 60-foot class includes trees 57.6 to 62.5 feet tall. d Number of trees; range of data is shaded. Includes 42 black cottonwood. 8
Table 4—Board-foot volumes, Scribner rule (1-foot stump to 6-inch top dib) given dbh and height to a usable top for white spruce and black spruce, Susitna River basin, Alaskaa a Regression: BFV = 0.005601 * (d2h)1.05619 ; increased efficiency = 171 percent; standard error of estimate = 6.4 board feet or 16 percent of the mean volume. b For example, 9-inch class includes trees 8.6 to 9.5 inches in diameter c For example, 60-foot class includes trees 57.6 to 62.5 feet tall. d Number of trees; range of data is shaded. Includes 208 white spruce and 27 black spruce. 9
Table. 5—Board-foot volumes, Scribner rule (1-foot stump to 6-inch top dib) given dbh and height to a usable top for paper birch and quacking aspen, Susitna River basin, Alaskaa a 2 1.02609 Regression: BFV = O.OO8764 0 (d h) ; increased efficiency = 119 percent; standard error of estimate = 8.3 board feet or 18 percent of the mean volume, b For example, 9-inch class includes trees 8.6 to 9.5 inches in diameter, c For example, 60-foot class includes trees 57.6 to 62.5 feet tall, d Number of trees; range of data is shaded. Includes 84 paper birch and 13 quaking aspen.
Table 6—Board-foot volume (1-foot stump to 6-inch top dib) given dbh and height to a usable top for black cottonwood, Susitna River basin, Alaska3 a Weighted regression: BFV = -2.91379 + 0.01094 • d2h; increased efficiency = 170 percent; standard error of estimate = 22.2 board feet or 13 percent of the mean volume, b For example, 9-inch class includes trees 8.6 to 9.5 inches in diameter, c For example, 60-foot class includes trees 57.6 to 62.5 feet tall, d Number of trees; range of data is shaded. Includes 42 black cottonwood. ...... DBH b (d) Inches 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 c Trees Height to a 6-inch top ~ib in feet (h) d measured 15 20 25 30 35 40 45 so 55 6o 65 70 75 80 85 Black 90 95 Cottonwood --------------------------------------------------Board-foot volume---------------------------------------------------Number--3.0 s.o 6.9 8.9 10.9 12.8 14.8 16.8 5.1 ftdfs'i£ 10.5 13.2 15.8 18.5 21.2 23.9 26.6 29.2 1 :..A ~,»._x, .. Jt{7{~f£~ 11.1 ·n-atf6;j 18.1 21.6 ~f~$1ff¥l 28.6 32.1 35.6 39.1 4 r' ' ~,... ........ ~ ....... '· ..:.l~. ¥. 10.4 14.8 19.2 23.7 28.1 32.5 37.0 4s.8 50.3 s4.7 59.1 1 13.5 19.0 24.4 29.9 35.4 40.8 46.3 57·3 62.7 68.2 73.7 16.9 23.6 30.2 36.8 43.4 ~:soHo\)" s6.7 ,..-~~,~~~~ 69.9 fi16~:5~~ 83.1 89.7 7 ft~w~f: . ..-!~ fl.;~~~};~ ~>..w: '"·· .... ~*-20.7 28.6 lff6:i*5r~ 44.3 52.2 60.1 68.0 75·9 {;'8~!~'. 91.6 99·5 107.4 115.2 123.1 131.0 2 . ·'t·~.'!<.,:t\ '~l~.;:'IO'v.;. 24.8 34.1 43.3 52.6 61.8 71 .. 0 80.3 89.5 98.8 108.0 117.3 126.5 135.8 145.0 154.2 163.5 172.7 29.2 40.0 50·7 61.4 72.1 82.9 93.6 104.3 115.0 r:t~~¥tf~1 136.5 ~ 168.6 179·3 190.1 200.8 3 , ....... 5..s7, ~·.:;, 46.3 58.6 ~!.1c)P'f~· 83.2 ~~Ji~.i 107.9 120.2 132.5 144 . 8 t{i!_K~~i 194.0 ~()'6~~ 218.6 230.9 6 t; ~~ t.~ .. t1 <. ,.;._ :·,~ ... ~~ 53.1 67.1 81.1 95·1 109.1 123.1 137.1 151.1 207.1 221.1 235.1 249.1 263.1 2 60.3 76.1 91.9 107·7 123.6 139.4 155.2 171.0 'i"(~~~· 234.2 250.0 !J.2fi5118-i 281.6 297.4 4 ,, 280.7 ~t-~'9~~-1/ ',1)f'G,;;ttl 333.8 2 138.9 156.6 174.3 192.0 ,; 262.9 l...ii: ~<~t': ... ~~ .... ?!. :1...:.-~::~t. .. ,.fl 155.1 174.8 194.6 214.3 273. 5 •j'2~f31i~3·; 313.0 332.8 352·5 372.3 2 194.0 215.9 237·8 ~f·~"'t*~,<$~ ~. ~~:A,;i:'$')" .~~ 347.2 369.0 390.9 412.8 2 .r3.2'3~;~~; 325. 3 238.3 262.4 286.6 310.7 334.8 358.9 383.0 407.2 431.3 ;~~fo~~J 1 1;;.6~;~ Iff ~\~ft2~f7:1t'~·(t 4~~ 261.8 288.3 314.8 341.3 ~3 ,7~r~'""'~9">>-'..:t;,. f,.,.~7 447.2 473.6 500.1 3 ,.t;,:-··:ft,tJ • ,..?~r~<~ •. '"""·~"'. ~le'--.... , • -s. s46.9 286.4 315.4 344.3 373·3 402.2 431.1 460.1 489.0 517.9 312.2 343.7 375.2 406.7 438.2 469.7 501.2 532.7 564.2 595.7 339.0 373.1 "146'7;.:;): 441.5 475.7 509.9 544.1 578.3 612.5 646.6 1 ..... ,s-, ...... k• .. :J' 366.9 4&3.8 440.8 477.8 514.8 551.7 588.7 625.7 662.7 699·7 395.8 435·7 475.6 515.5 555.4 595.2 635-1 675.0 714.9 754.7 Total 42
Table 7—Merchantable cubic-foot volume (1-foot stump to 4-inch top dib) given dbh and total height, Smalian's formula, for white spruce and black spruce, Susitna River basin, Alaskaa a , Weighted regression: CFV = -0.21849 * O.OOI89 ° d2h; increased efficiency = 136 percent; standard error of estimate = 1.4 cubic feet or 13 percent of the mean volume, b For example, 9-inch class includes trees 8.6 to 9.5 inches in diameter, c For example, 60-foot class includes trees 57.6 to 62.5 feet tall, d Number of trees; range of data is shaded. Includes 244 white spruce and 43 black spruce. OBH b (4) 20 25 30 35 110 c Total heisht in teet (h) 50 55 6o 70 75 80 90 lnchol -----------------------------------------Cubic-toot vo~u•e--------------------------------------------5 6 7 8 9 10 11 12 13 1/a 15 16 17 18 19 20 2J 22 23 211 25 26 27 0.7 .(t ... .1.6 2.2 2.8 3-6 5-5 6.6 7-8 6.6 7-9 9-4 10.9 12.5 14.3 16.2 16 .. 7 18.9 21.2 19.1 21.6 211.3 27-3 ..:2~.0 .. , 27-1 30.4 33-9 26.4 29.8 33-5 37-3 6.7 8.9 11.3 14.0 I ._ " "' oo .. -28.8 ;~'31.,;12.-YJJ. i .. 3~: ... 1 .. .,~ ' •"'"--,.;: 3 •• ~ • 32.6 35-3 )8.0. 40.7 . ( 36.5 39.6 ·•112':"f! • 115.7 54.o 58.1 59-2 63.8 69.8 76.0 82.5 89.2 96.2 51.0 s6.5 62.3 68.4 74.8 81.4 88.4 95.6 103.1 7-2 9-5 12.0 14.9 18. I 21.6 25-3 29.11 33.8 38-5 113.5 ·z.s•.s·• 511.11 60.3 66.s 73-0 79.8 86.9 94-3. 102.0 110.0 19.2 22.9 26.9 !.~3~~3 . • " .. 4 35-9 211.3 28.5 33-1 38.1 110,-9, 113.3 116.2, 118.9 51.8 :-54.-<J~ 57.8 61.2 64.0 67.8 70.6 74.8 77-5 82.1 84.8 89.8 92-3 97.8 100.2 106.1 108.4 114.8 116.9 123.8 Total Trees 4 measured b'hite Black spruce spruce --Number--7 1 19 9 12 9 26 8 40 5 34 3 22 II 31 1 14 2 14 1 8 8 4 II 1 244 4J
Table 8—Merchantable cubic-foot volume (1-foot stump to 4-inch top dib) given dbh and total height, Smalian's formula, for paper birch and quaking aspen, Susitna River basin, Alaskaa a 2 Weighted regression: CFV = -O.7120O + 0.00211 * d h; increased efficiency = 109 percent; standard error of estimate = 2.0 cubic feet or 16 percent of the mean volume, b For example, 9-inch class includes trees 8.6 to 9.5 inches in diameter, c For example, 60-foot class includes trees 57.6 to 62.5 feet tall, d Number of trees; range of data is shaded. Includes 97 paper birch and 14 quaking aspen.
Table 9—(Merchantable cubic-foot volume (1-foot stump to 4-inch top dib) given dbh and total height, Smalian's formula, for black cottonwood, Susitna River basin, Alaskaa a 2 Weighted regression: CFV = -1-39764 + 0.00188 ° d h; increased efficiency = 138 percent; standard error of estimate = 4.1 cubic feet or 11 percent of the mean volume. b For example, 9-inch class includes trees 8.6 to 9.5 inches in diameter. c For example, 60-foot class includes trees 57.6 to 62.5 feet tall, d Number of trees; range of data is shaded. Includes 43 black cottonwood.
Table 10—Merchantable cubic-foot volume (1-foot stump to 4-inch top dib) given dbh and height to a usable top, Smalian's formula, for white spruce and black spruce, Susitna River basin, Alaskaa a Weighted regression: CFV = 0.519^3 + 0.00243 * d h; increased efficiency = 117 percent; standard error of estimate = 1.3 cubic feet or 12 percent of the mean volume. b For example, 9-inch class includes trees 8.6 to 9-5 inches in diameter. c For example, 60-foot class includes trees 57.6 to 62.5 feet tall. d Number of trees; range of data is shaded. Includes 244 white spruce and 43 black spruce.
Table 11—Merchantable cubic-foot volume (1-foot stump to 4-inch top dib) given dbh and height to a usable top, Smalian's formula, for paper birch and quaking aspen, Susitna River basin, Alaskaa a Weighted regression: CFV = O.A786O + 0.00278 0 d2 h; increased efficiency = 106 percent; standard error of estimate =1.9 cubic feet or 15 percent of the mean volume. b For example, 9-inch class includes trees 8.6 to 9.5 inches in diameter. c For example. 60-foot class includes trees 57-6 to 62.5 feet tall. d Number of trees; range of data is shaded. Includes 97 paper birch and 14 quaking aspen. ..... 0> DBH b (d) Inches 5 6 7 8 9 19 11 12 13 14 15 16 17 18 19 20 21 22 Height to a 4-inch top dib in feetc 5 10 15 20 25 30 35 40 45 so 55 60 65 70 ---------------------------------------Cubic-foot volume---------------------------------------.8 1.0 1.2 1.4 1.6 1.9 1.8 2.3 2.7 3·3 4.6 s.s 6.s 7.5 8.7 6.0 7.2 a.s 9·9 11.4 18.3 20.6 23.0 25.6 28.3 21.8 24.6 27·5 J0.6 33.8 25.4 28.6 ~Si"i'Wk ~!~~~~~ 35.6 39.4 3·3 4.5 28.9 "<i}.iV:~. e.~:~;{ J6.s 40.6 4s.o 3.6 5·0 6.6 32·5 36.6 41.0 45.6 50.5 5·5 7.3 36.1 llb1161~ U'l=~+t:·~~~ 4s.5 50.7 56.1 55·6 61.8 61.0 67.8 11.2 14.0 17.2 15.1 18.5 22.3 26.s 31.0 35·9 19.9 24.0 28.5 33.4 38.6 41.1 44.3 39.6 44.7 50.0 55·7 ·~ti1~~~ .<;; ~ ... ~'"~i:' ·l"f 43.2 48.7 54.s 60.7 67.2 46.7 52.7 59.0 65.7 72.8 67·9 74.0 80.2 74·5 81.2 87.9 50·3 56.7 63.5 70.7 78.3 Total Trees d 11easured Paper Quaking birch aspen --Number--3 5 8 16 5 16 12 14 7 3 4 2 1 1 97 1 1 4 2 2 3 14
Table 12—Merchantable cubic-foot volume (1-foot stump to 4-inch top dib) given dbh and height to a usable top, Smalian's formula, for black cottonwood, Susitna River basin, Alaskaa a Weighted regression: CFV = 1.9987 + 0.00204 * d2 h; increased efficiency = 131 percent; standard error of estimate = 4.1 cubic feet or 11 percent of the mean volume. b For example, 9-inch class includes trees 8.6 to 9.5 inches in diameter. c For example, 60-foot class includes trees 57.6 to 62.5 feet tall. d Number of trees; range of data is shaded. Includes 43 black cottonwood.
Table 13 –Total cubic-foot volume (1-foot stump to tree tip) given dbh and total tree height, Smalian's formula, for white spruce and black spruce, "Susitna" River basin, Alaskaa a Weighted regression: CFV = 0.65559 + 0.00191 ° d h; increased efficiency = 137 percent; standard error of estimate = 1.4 cubic feet or 11 percent of the mean volume. b For example, 9-inch class includes trees 8.6 to 9-5 inches in diameter. c For example, 60-foot class includes trees 57-6 to 62.5 feet tall. d Number of trees; range of data is shaded. Includes 2kk white spruce and 43 black spruce.
Table 14—Total cubic-foot volume (1-foot stump to tree tip) given dbh and total tree height, Smalian's formula, for paper birch and quaking aspen, Susitna River basin, Alaskaa a Weighted regression: CFV = O.6M56 + 0.00206 • d2h; increased efficiency = 113 percent; standard error of estimate =1.8 cubic feet or 13 percent of the mean volume, b For example, 9-inch class includes trees 8.6 to 9.5 inches in diameter, c For example, 60-foot class includes trees 57.6 to 62.5 feet tall, d Number of trees; range of data is shaded. Includes 97 paper birch and 14 quaking aspen.
Table 15—Total cubic-foot volume (1-foot stump to tree tip) given dbh and total tree height, Smalian's formula, for black cottonwood, Susitna River basin Alaska a Weighted regression: CFV = 0.98640 +0.00181 ° d2h; increased efficiency = 138 percent; standard error of estimate = k.2 cubic feet or 11 percent of the mean volume. b For example, 9-inch class includes trees 8.6 to 9.5 inches in diameter. c For example, 60-foot class includes trees 57.6 to 62.5 feet tall. d Number of trees; range of data is shaded. Includes 43 black cottonwood.