Made in the United States of America
Reprinted from Forest Science
Vol. 21, No. 4 December 1975
pp. 365-370
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Out..of.·Roundness in Douglas..fir Stems
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Out-of-roundness
806
that in upper stem positions.
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trees felled and bucked according to current
)
Out-of-roundness (OOR
at stump height was greater than
Orientation of longest diameter (OLD) on gentle slopes
of slope. No such significant, or even apparent, tendencies were found on moderate or
Because OLD was random in most circumstances,
large-scale
cruises
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The bias in volume estimates of individual trees, however, can be appreciable.
menziesii.
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Pseudotsuga
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that observers had to go uphill from subject �
trees to avoid overly large vertical angles.
Obviously, the amount of bias will depend
on both OLD and amount of OOR.
This bias was studied in data collected
for new log grading rules for coastal
Douglas-fir (Pseudotsuga menzicsii (Mirb.)
Franco var. menziesii). The data and ru1es
(Lane and others 1973) are intended for
grading logs in standing trees, but data
such as length and direction of longest
diameters were also collected.
With these data, I hoped to answer these
questions about cross-section OOR:
1. Is OOR related to factors such as
diameter breast high ( dbh) and height of
tree, degree of slope, and amount of tree
lean?
2. Is OLD related to other directional
variables such as aspect, direction of tree
lean, shape of crown, or any particular
azimuth(s)?
3. Do OOR and OLD differ at various
relative heights in trees?
It is important to note that the available
data do not include OOR measurements
The author is Mensurationist, Pacific North­
west
Forest
USDA
and
Forest
Range
Service,
Experiment
Olympia,
Station,
,}�,g§h.
The
author thanks David Bruce and Ca�;ryanq�, V�n­
coevering for assistance with statistical analyses.
Manuscript received September
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OPTICAL CALIPERS and rangefinder den­
drometers permit upper-stem measurements
on trees without climbing or felling. Such
dendrometer measurements can provide
tree volumes, form factors, and other
tree characteristics. Dendrometer measure­
ments lead to direct tree volume estimates,
bypassing local or standard volume tables
and their possible biases. When coupled
with a suitable sampling plan for deciding
which trees to measure, dendrometer cruises
offer increased precision over other types
of standing tree cruises (Grosenbaugh
1965, Hazard and Berger 1972).
One possible difficu1ty in using dendrom­
eter measurements to get tree volume esti­
mates is their inability to detect, or com­
pensate for, out-of-roundness (OOR)
when stems are viewed from only one direc­
tion. In this study, OOR was defined as
the quotient of the difference in length be­
tween the longest diameter of a stem cross
section and the diameter at right angles to
it, divided by this shorter diameter. Neither
diameter necessarily passed through the
pith. If there happened to be a consistent
relationship between orientation of longest
diameter (OLD) in azimuth degrees and
that of tree to instrument direction, bias in
volume estimates would resu1t. This would
happen if, for instance, the longest diam­
eters were oriented in the same direction
as slope, and if slopes were steep enough
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Forest Sci. 21:365-370.
Additional key words. Stem diameter measurement, stem cross-section area,
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using optical dendrometry for upper-stem measurements should be biased very little by
OOR.
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showed significant, but slight, tendencies toward north and south directions and direction
steep slopes.
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(stem circumference not circular) of Douglas-fir stems
was measured on cross sections of
merchantability standards.
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RICHARD L. WILLIAMSON
Abstract.
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30, 1974.
volume 21, number 4, 1975 I 365
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at breast height. Basal OOR measurements
are those at stump height.
Data Collection and Preparation
Trees were selected from 72 sample areas
distributed throughout northern California
and western Oregon and Washington to ob­
tain a wide range of tree size and quality
in coastal Douglas-fir sawtimber. Tree
size, stem quality, and site index were the
principal stratifications used in selecting
sample trees. The sample areas were also
located to sample the environmental factors
of forest type, stand density, elevation,
aspect, and geographic location.
Before trees were felled, a mark was
made on the north side of each trunk, and
a vertical projection of the crown sketched.
This yielded information on azimuth and
distance of crown center from center of
stump and orientation of the longest crown
diameter in a horizontal plane. Diameter
breast high was measured to the nearest
0.1 inch (0.25 em) with a diameter tape.
Basal area of the surrounding stand was
estimated and tree lean was measured to
the nearest degree. Direction of lean and
aspect azimuth were measured to the
nearest 45 o. After each tree was felled, an
orientation line was painted the full length
of the merchantable part of the bole and
on top of the trunk as it lay. The direction
this orientation line would face if the tree
were standing was determined. Logs were
bucked to achieve maximum value of end­
product; thus, they were of variable length.
Log-end measurements were made in
mill yards. At each end of each log, the
longest diameter and diameter at right
angles to the longest were measured to the
nearest 0. 1 inch (0.25 em). Neither diam­
eter necessarily passed through the pith.
The angle formed by the longest diameter
and the diameter passing through the
orientation line and through the approxi­
mate geometric center of the section was
recorded and used to calculate azimuth of
OLD to the nearest 5 degrees. Azimuth of
the orientation line was unknown to the
people making these log-end measure­
ments.
The 806 trees available for analysis of
366 I Forest Science
OOR averaged 36 inches (91
(ranging from 10 to 78 inches,
198 em) and 153 feet (47 m)
(ranging from 68 to 258 feet,
79 m).
em) dbh
or 25 to
in height
or 2 1 to
Analys�s, Results, and Discussion
OOR at Stump Height-Magnitude. The
dependent variable (OOR) ranged between
0 and 0.644 with mean and standard devia­
tion of 0. 123 and 0.088. Numerous step­
wise regressions of pooled data from all
sampling areas yielded no combination of
significant independent variables (includ­
ing slope, aspect, basal area, lean, and
crown characteristics) which accounted for
more than 4 percent of total variation in
OOR. Even after data were sorted into
three slope classes (0°-14 o, 15°-29°,
30°+ ), maximum variation accounted for
in any slope class was only 10 percent.
I sorted data into slope classes because I
expected more OOR on steep slopes and
thought a possible lack of OOR on gentler
slopes might desensitize analysis when all
data were pooled. Average basal OOR�
however, was significantly {p < 0.05)
greater (0. 135) in the 0°-14° slope class
than in either the 15 -29° or 30°+ classes
·(0.114 and 0.117, respectively). This re­
sult may be hard to explain because of the
commonly observed increase of eccentricity
of pith with increasing slope. However,
trees with eccentric pith are not necessarily
out-of-round (Pawsey 1966).
Throughout all multiple regression trials,
consistently significant variables were those
including dbh. On the average, the bigger
the dbh, the greater the OOR. This finding
is consistent with other work (Muller 1958).
Over all slope classes, I was able to
account for only 4 percent of the variation
in OOR. Other areas for further study of
OOR are its relationships to detailed stand
and crown structures surrounding subject
trees, and to direction of prevailing winds.
Although prevailing winds may control
amount of OOR and OLD, these winds
may become randomly oriented duejo hilly
or mountainous terrain. Almost au.;;fih.�e .
data were collected in such terrain.
o
TABLE 1. Means standard deviations and sample sizes (n) for basal azimuth difference
between aspect and longest diameter (DEV), by octants of aspect, for trees in the 2°-14°
slope class.
Aspect
Statistic
Mean, degrees
oo
270°
3 15°
46
44
44
26
28
31
16
85
17
41
18
45°
90°
135°
38
55
30
47
42
30
23
28
24
59
30
14
11
. 180°
225°
(expected, 45 o )
Standard deviation, degrees
(expected, 26°)
11
Orientation. Analyses of basal OLD tested
the hypothesis that this orientation was
random, that is, that OLD could occur in
any direction with the same probability that
it could occur in any other direction. I used
three methods of testing.
First, visual inspection of plottings of
OLD and of the angular deviation (DEV)
of OLD from aspect azimuth revealed no
coqsistent relationship of OLD with com­
pass direction or with aspect azimuth. Since
one has a choice of two directions in de­
fining OLD, each 180° from the other,
I arbitrarily chose the direction that was
within ±goo of slope direction. Since OLD
was calculated to the nearest 5 degrees,
DEV was also rounded to the nearest 5
degrees.
The second method involved segregating
basal OLD, by slope classes, into equal
subdivisions (15°) of the compass semi­
circle. Means and standard deviations for
basal OLD were reasonably close to the
values expected if counts were distributed
uniformly in the oo to 180° range. How­
ever, a chi-square test of goodness of fit
for each slope class showed that, for trees
on gentle ground, there was a slight but
significant (p < 0.05) tendency for OLD
to occur in approximately north-south di­
rections. Basal OLD apparently occurred
randomly on moderate and steep slopes.
The third method involved analysis of
DEV. DEV was expressed on an absolute
(sign deleted) basis; thus, it had a possible
range of oo to goo. Means and standard
deviations of DEV were close to the values
expected if DEV occurred at random
(Table 1). However, DEV was categorized
into 10° cells, and chi-square tests, by slope
classes, showed a moderate but highly sig­
nificant (p � 0.01) tendency on gentle ter­
rain for OLD to lie in the direction of
slope. DEV, in common with OLD, is ap­
parently random in the 15°-2go and 30°+
slope classes.
Similar results were obtained when angle
between OLD and direction of tree lean
was analyzed the same way. For trees on
gentle terrain, there is a moderate ann-sig­
nificant tendency for OLD· to lie in the
direction of tree lean. No such tendency
is evident on moderate and steep slopes.
The significant tendency for OLD to
agree with slope and lean directions in the
2 o-14 o slope class is not likely important.
DEV means and standard deviations on
each class of aspect appear reasonably close
to values expected for a uniform (listribu­
tion (45° and 26° , respectively) on all
octants (0°, 45°, goo, and so on) of
aspect, except east (goo) and northwest
(315 °) (Table 1). These most severe de­
partures from expected values occur with
small sample sizes and are not statistically
significant (p > 0.05).
OOR Above Stump Level-Magnitude.
The amount of OOR in portions of trees
from the top of the first log through go
percent of total height (measured from
ground level) averages about half of
average OOR at stump height (Table 2).
Average mean and standard deviation for
OOR in these upper portion��e 0.0615
�h
and 0.0477, respectively.
·
•
volume 21, number 4, 1975 I 367
TABLE 2. Average out-of-round (OOR), azimuth difference between aspect and longest
diameter (DEV), and orientation of longest diameter (OLD), by slope classes, for stump
height and for positions above stump height.
Variable
Slope
class
D EV
OOR
��--
Basal
U pper
OLD
Basal
Upper
Basal
Upper
11
Degrees Degrees
Degrees
Degrees
0°-14°
0.135
0.0604
45.4
43.3
92.4
100.0
295
15°-29°
.114
.0578
44.6
45.8
89.5
97.0
247
30°+
.117
.0663
44.5
42.7
90.8
90.7
264
All classes
.123
.0615
44.9
43.9
90.9
96.0
806
Section data above stump level were mea­
sured on ends of logs bucked according to
current merchantability standards practiced
at the mill for which the logs were destined.
Section data were sorted into relative height
classes, with each class 1 0 percent of total
height. Each relative height class contained
sections from different sets of trees be­
cause of the chance location of log buck­
ing points. A separate one-way analysis of
variance was made for each relative height
class, except 0-10 and 91-100, to test for
significant differences between average
OOR by slope classes. These latter classes
were judged to have insufficient numbers
of observations to yield reliable averages.
These tests were inconclusive-a few
with high significance (greatest OOR on
steep slopes), but the rest insignificant
(p ;? 0.20).
Regardless of relative position in trees,
OOR varies little between slope classes, and
the minor occurrences of statistical signifi­
cance may well be happenstance.
Orientation. Overall average and stan­
dard deviation (90.9o and 54o, respec­
tively) for upper stem OLD closely ap­
proach expected values for a uniform dis­
tribution. The same holds true for DEV
(mean= 44.9, standard deviation= 28.3).
Longest diameter orientation and DEV
above stump level were analyzed by chi­
square tests similar to those for stump level
data. Separate chi-square analyses were
done for each relative height class, except
0-10 and 91-100, and for each slope class.
368 I Forest Science
Significance occurred primarily for trees
on gentle ground and in the upper portions
of trees, where effects on merchantable
volume would be minimal. Where signifi­
cant, the basic data consistently show a
moderate tendency for OLD to lie in car­
dinal directions, principally north-south,
and in the direction of slope. This agrees
with basal OLD. And, as with basal OLD,
these tendencies are not likely to be im­
portant since means and standard deviL
tions for upper stem OLD and DEV are
reasonably close to expected 1values, that
is, orientation appears to be a nearly ran­
dom occurrence.
OOR Influences on Tree Volume Esti­
mates. If OLD were c�nsistent throughout
tree lengths, the worst cases of bias in
volume estimation with an optical den­
drometer should be when measurement is
from a direction parallel or perpendicular
to OLD at stump height.
To gain insight into the possible extent
of this bias, I calculated the volume of
each tree in four ways as viewed ( 1) from
a direction parallel to basal OLD, (2) from
a perpendicular direction, (3) from 45o,
and ( 4) from 13 5o.
Individual log volumes in each case were
calculated with Smalian's formula. For the
parallel direction, apparent diameter for
determining a sectional area above stump
level was determined by:
( 1) multiplying the difference between
long and short diameters of that section by
the cosine of the angle between'"''LD at
-,
stump height and OLD of the section: '
(2) adding the product of (1) to the
short diameter of the section.
Apparent diameter for the perpendicular
direction was determined by a similar pro­
cedure. These steps give correct caliper
values for longest diameter and diameter
at right angles to the longest and allocate
the difference smoothly for other view
angles. Because tree sections are irregular,
no single function will be exact. This
procedure should yield the maximum range
in estimation of volume per tree if OLD is
consistent within trees.
Finally, volume ratio-parallel over per­
pendicular lines of sight-was calculated
for each entire tree, and for the butt log
and upper portion above butt log separately.
If OLD occurs randomly, average ratio for
upper portions of trees should be nearly
1.0. Average volume ratios and average
stump and top of butt log parallel: per­
pendicular basal area ratios are:
Section
of
tree
Basal
area
Volume
Mean
Standard
deviation
Stump
Top of
butt log
0.81
0.11
0.97
0.08
Butt log
Upper
Entire
0.86
0.98
0.92
0.08
0.06
0.06
The mean basal area ratio for tops of butt
logs shows almost no agreement with mean
stump ratio and indicates almost random
OLD at that position. Likewise, relation­
ship between stump basal area ratios and
tree volume ratios, though statistically
highly significant (p � 0.01), is very weak
(r2 = 0.0102). Volume ratios for individ­
ual entire trees ranged from 0.70 to 1.09,
and, for upper portions of trees, from 0.76
to 1.21. Since these ratios are derived from
extremes, and true volume probably lies
about midway between extremes, maximum
deviations of dendrometer estimates from
true volume probably lie within 10 to 12
percent of true volume.
Much of the butt log bias in volume
estimation of individual trees can be elimi­
nated by using diameter tape measurements
at breast height and for lower positions if
required. One may wonder, however, about
the relative advantages of dendrometer and
D-tape when many trees are to be mea­
sured. Dendrometry from one position is
approximately equivalent to calipering from
one direction; If this direction is assumed
to be randomly oriented, calipering will re­
sult, in average positive bias in cross-sec­
tional area estimation of 0 to 3.4 percent,
depending on the geometric shape as­
sumed for the cross-section (Matern 1956).
This bias is approximately equivalent to
that from diameter-tape measurements, so
the choice between diameter-tape and opti­
cal dendrometer should probably depend
on the precision of each. Diameter-tape
measurements are much more consistent
than measurements made by calipering in
two directions ( McArdle 1928) and would
logically be even more consistent than
calipering in one direction. The greater
precision of the diameter tape will lead to
greater sampling efficiency.
For the two measurement directions of
45° and 135° to basal OLD, volume and
basal area. ratios relative to perpendicular
direction values are almost identical:
Portion
of
tree
Basal
area
Volume
;·.-· .
Mean
Standard
deviation
Stump
Top of
butt log
0.94
0.04
0.99
0.05
Butt log
Upper
Entire
0.96
0.99
0.97
0.03
.0.04
0.03
All the above indicate nearly random
orientation of upper stem OLD and basal
OLD, and little, if any, relation between
them. In addition, where cardinal or slope
direction tendencies do seem to occur­
on gentle terrain---dendrometer users may
place themselves to have the best views
possible of subject trees. This placement
is likely to be in random directions from
subject trees. Thus, stand volume estimates
by dendrometry should have small average
bias due to OOR. However, the two tabu­
lations show that errors in indi-vdQual tree
estimates can be large.
volume 21, number 4, 1975 I 369
Conclusions
Out-of-roundness generally increases with
tree size but is little affected by slope of
ground, amount of tree lean, or density of
the surrounding stand. OOR, from the top
of the butt log on up the tree, averages only
about half that at stump level.
OLD does not appear to depend on
orientation or position of crown. There is
a slight tendency for the longest diameter
to be oriented north-south, in direction of
slope, and in direction of tree lean on
ground with gentle slopes. On gentle ter­
rain, dendrometer users may place them­
selves so as to have the best views of subject
trees possible. This placement is liable to
have a random orientation with respect to
cross-section OLD and direction of slope.
On steep ground, where dendrometer users
must go uphill from subject trees to avoid
large vertical angles, OLD appears to be a
random occurrence and no appreciable bias
in volume estimates should result from
OOR.
Evaluation of tree volumes derived as
though viewed from various directions
indicate that average stand volume biases
due to OOR will be negligible (about 2 or
3 percent) under any circumstances.
Volume bias of individual trees can be
large, however.
Literature Cited
GROSENBAUGH, 'L. R.
1965. Three-pee sampling
theory and program "THRP" for computer
gtlneration of selection criteria.
S�rv Res Pap PSW-21, 53 p.
Forest & Range Exp Stn, Berkeley, Calif.
H�ZARD, JoHN W., and JoHN M. BERGER.
1972.
·Volume tables vs. dendrometers for forest sur­
veys. J For 70:216-2 19.
LANE, PAUL H., RICHARD 0. WooDFIN, JR., JOHN
W. HENLEY,
and MARLIN
E.
PLANK.
1973.
New timber cruising grades for coast Douglas­
fir.
USDA Forest Serv Res Pap PNW-151,
12 p. Pac Northwest Forest & Range Exp Stn,
Portland, Oreg.
McARDLE, RICHARD
E.
1928. Relative accuracy
of calipers and diameter tape in measuring
Douglas fir trees. J For 26:338-346.
MATERN, BERTIL. 1956. On the geometry of the
cross-section of a stem. Medd Fran Stat Skogs­
forsk 46(1 1), 28 p.
MULLER, G.
sectional
1958.
shape
Investigations on the cross­
of
tree
trunks.
Forstwiss
Centralbl 77( 11/12) :374-381.
PAWSEY, C. K. 1966.
Lean and-�ccentricity in
Pinus radiata (D. Don) in the southeast of
South Australia. Aust For Res 2(3):22-35.
PURCHASED BY THE FOREST SERVICE, U.S. DEPARTMENT OF AGRICULTURE,
370 I Forest Science
USDA For
Pac Southwest
for
officia�u.�e.,