0.31
with a range of -0.70 to 0.94 and
a standard deviation of 0.31. A linear
regression of tarif number on diameter
was also fit for each plot of the form:
Effects of the Tarif Number/
Diameter Relationship on
Volume and
Height Estimates
T2
Gary W. Clendenen, USDA Forest Service, Pacific Northwest
Research Station, Forestry Sciences Laboratory,
Olympia, WA 98502
ABSTRACT. Volume estimates using the
tarif system often assume a single mean
tarif number for an even-aged stand. Con­
sistent trends of tarif number with dbh
within plots were found in a set of 67 plots
in western Oregon and Washington. Ef­
fects of these trends on plot and diameter
class volume estimates, and on heights es­
timated from these volumes, were exam­
ined. Total plot volume estimates were ap­
parently not biased, but substantial biases
were found in estimates of volumes and
heights by dbh ,class. Height samples
should be represlitative of the range of di­
ameters, adequate to detect trends in tarif
number, and adequate to support alterna­
tive methods of Jolume and height estima­
tion.
f
West.
f. Appl.
For. 5(1):9-12.
The Tarif system of volume estima­
tion was introduced to American for­
estry in 1963 with publication of Com­
prehensive Tree-Volume Tarif Tables by
Turnbull et al. (1963). The tarif system
was further described and extended
by T u r n b u l l and Hoyer (1965),
Brackett (1973), and Chambers and
Jenkins (1976). The tarif system is
often used for volume estimation, par­
ticularly when height samples are in­
adequate for deriving conventional
height/diameter equations. Individual
tree tarif numbers are averaged to es­
timate the tarif number for the stand
or particular stand component. This
procedure assumes that the tarif
number is not related to dbh for the
stand components of interest. Also,
heights can be assigned to trees not
m e a s u r e d in the f i e l d by using
volumes estimated with the tarif
system and rearranging a standard
volume equation to give estimates of
tree height.
This paper reports a case study of
the effects on volume estimates and
heights estimated from these volumes
when this constant tarif assumption is
not met.
METHODS
Tree measurements were originally
assembled on 67 plots in a study of the
effects of burning slash after logging
on the growth of young, even-aged
stands in western Oregon and Wash­
ington (Miller et al. 1986). Average
breast height ages for trees on these
plots ranged from 14 to 33 years and
site index (King 1966) ranged from 71
to 130 with a mean of 105. During
analysis of the data, it became ap­
parent that tarif was positively corre­
lated with dbh on many plots. This vi­
olated a basic assumption of the tarif
system-that in even-aged stands,
tarif number is constant across dbh
within a given stand-and raised a
question about the applicability of the
tarif system to this and similar data
sets.
Tarif numbers (T) were estimated
for each tree by using volume esti­
mates (V) from the volume equation
for young growth Douglas-fir b y
Bruce and DeMars (1974) and equa­
tions given by Brackett (1973, p. 7).
Mean tarif (Tl) was computed for each
of the 67 plots. The mean slope was
=
b0 + b1
*
dbh.
(1)
The slope coefficient, b1, was tested
and found to be significantly different
(P < 0. 100) from zero on 32 plots
(48%). All these 32 plots had positive
slope coefficients. In fact, 58 of the 66
plots with Douglas-fir (Pseudotsuga
menziesii) present had positive slopes
(Figure 1). The assumption of a con­
stant tarif number for all diameters
within plots is clearly untenable for
these data.
Use of a single mean tarif number
when tarif number is actually a func­
tion of dbh must introduce error in
volume estimates. Two plots with
more than 95% Douglas-fir by basal
area were selected from the 66 plots
with positive slopes, as examples of
the effects of the tarif number/dbh re­
lation on volumes and on heights esti­
mated from these volumes.
Plot A had the most significant
slope coefficient (b1
0.73) with a t­
statistic of 6.18 (P < 0.001); plot B had­
the least significant slope <::_ e ficient
(b1
0.07) with a t-statistit· of 0.44 (P
> 0.500). Plot A had 84 Douglas-fir
larger than 2.0 in. dbh, of which 27
were measured for total height. Plot B
had 123 Douglas-fir larger than 2.0 in.
dbh, of which 25 were measured for
total height. Only Douglas-fir trees
larger than 2.0 in. dbh were used.
Other selected stand statistics for each
plot are given in Table 1. Height trees
on both plots were selected across the
range of diameters.
Total stem cubic-foot volumes, in­
cluding stump and tip (V1 and V2),
were computed for each tree on each
plot by using the two estimates of tarif
(Tl and T2). Scribner board-foot
=
=
12 �------,
10
8
6
LL
0
0:4
w
ID
:E
:::> 2
z
-0.6
-0.4
·0.2
0
0.2
0.4
0.6
0.8
1.0
SLOPE COEFFICIENT CLASS
Fig. 1. Number of plots by tarif equation slope class.
WJAF 5(1)1990
Reprinted from the Western Journal of Applied Forestry, Vol. 5, No. 1, January 1990.
9
Table 1. Plot statistics.1
Plot B
Plot A Plot size in acres
Age
Site index
Number of trees per acre
Quadratic mean diameter
Arithmetic mean diameter
Mean tarif
Percent Douglas-fir by basal area
Total stem cubic-feet per acre
Scribner board-feet per acre,
16-ft logs, to a 6-in top 0.45
27
92
187
7.4
7.0
22.1
98.4
1113
0.25
23 117 492 6.6
5.7
24.1
96.6
2544
2384
6640
1 Volumes computed using tarif adjusted for dbh.
Table 2. Individual tree summary of results for Plot A and Plot B.
Plot B
Differences
Plot A
Differences
Differences
Max.
Mean
Max.
Mean
T1 minus n
V1 minus V2
51 minus 52
H1 minus H2
5.05
-1.61
-9.38
5.60
1.59
0.09
-0.49
2.38
0.53
-0.47
-3.79
-0.90
0.28
0.00
-0.16
0.33
variables:
H = total tree height in feet H1 = Has a function of T1 H2 = Has a function of T2 5 = Scribner board-foot volume, 16-ft logs, to 6-in. top
51 = 5as a function of T1
52 = 5 as a function of T2
T1 = mean tarif number
T2 = tarif number fit as a linear function of dbh
V = cubic-foot volume including stump and tip V1 = Vas a function of T1 V2 = Vas a fu ction of T2 1
,
30
I
T 1 =MEAN TARIF NUMBER
T2=TARIF NUMBER ADJUSTED FOR DBH
25
T2
-- PLOT A
MEAN TARIF
----- PLOT A ADJUSTED TARIF
-·-·-·
PLOT B MEAN TARIF
PLOT
B ADJUSTED TARIF
15 �--�--�--��6
7
8
9
10
11
12
4
5
3
13
14
15
2
DBH CLASS {INCHES)
Fig. 2. Mean tarif and tarif adjusted for diameter.
10
WJAF 5(1)1990
H1
H2
.
DISCUSSION
'
volumes, 16-ft logs, to a 6-in. top (51
and 52) were computed in the same
way.
Total height was estimated for each
tree on each plot by solving the
volume equation (Bruce and DeMars,
1974) for height and using the mea­
sured diameters and estimated
volumes corresponding to the two
tarif numbers (Tl and T2). These esti­
mated heights (H1 and H2) were fit as functions of dbh for comparison pur­
poses as follows: cant trend in tarif number across dbh exists as on plot A, there is no prac­
tical difference in total volume per acre, both cubic and Scribner, be­
tween the two tarif-based methods of estimating volume. Large differences between tarif esti­
mates by dbh class on plot A and
small differences on plot B are evident
in Figure 2. Plot A shows 2 8% more
total stem cubic-foot volume for small
/diameters and 8% less total stem
;, cubic-foot volume for large diameters
when the mean tarif number is used
instead of the tarif number adjusted
for dbh (Figure 3); however, these dif­
ferences were of no practical impor­
tance in total stem volume per acre es­
timates by dbh class on plot B (Figure
4). Differences in Scribner board-foot
volumes are even greater on plot A,
ranging from 16% for 6-in. trees to
-14% for 11 in. trees (Figure 3).
Volume differences on each plot are a
direct reflection of the differences in
tarif number shown in Figure 2.
There is a large difference in tarif
based estimates of tree height (35% for
small dbh trees) on plot A where a sig­
nificant trend in tarif across dbh exists
and a small difference (generally less
than 5%) on plot B where no signifi&..­
cant trend across dbh exist (Figure 5).
=
=
f(V1,D)
4. 5 + EXP(b0
+ b1 * D ** b2),
(2)
=
f(V2,D)
4. 5 + EXP(b0
(3)
+ b1 * D ** b2),
=
RESULTS
Plot A showed apparent differ­
ences, among dbh class, between T1
and T2, V1 and V2, 51 and 52, and H1
and H2. Plot B had no practical differ­
ences among any of the comparisons
made (Table 2). Even when a signifi­
On most plots, the underlying as­
sumption of constant tarif across the
range of diameters was not met. In­
stead, a consistent trend of increasing
tarif number with increasing diameter
was found. Such a trend would
seldom be detectable with the limited
height samples commonly used in ap­
plications of the tarif system. As in
this study, Rustagi and Alegria (1981)
also found that tarif number and dbh
were not independent on several plots
they examined at Pack Forest, WA.
If tarif number is related to diam­
eter, and height samples are confined
to a few large trees (a common prac­
tice among users of the tarif system),
then estimates of mean tarif number
will be biased, and estimates of both
total volume and volume by indi­
vidual diameter classes will also be
biased.
Turnbull et a!. (1963) specify that
trees should be sampled for tarif
numbers from the group or �QJJ.PS of
interest across the entire range of,clJ-,
ameters present in the group, that a
minimum of six trees should be sam­
pled on a given plot, and at least 20
trees should be sampled within each
group of interest for the stand. Six
trees are probably adequate if similar plots are to be combined into a stand estimate, but it is not sufficient to de­
tect tarif/dbh trends for individual
plots. If individual plots must stand
alone in an analysis (often the case in
_
• SCRIBNER
fillll CUBIC
V1>V2
V1=VOLUME ESTIMATED FROM MEAN TARIF
V2=VOLUME ESTIMATED FROM TARIF ADJUSTED FOR DBH
V1 < V2
2
3
4
5
6
7
8
9
10 11 12
DBH CLASS {INCHES)
13 14 15
Fig. 3. Percent difference, by dbh class, on plot A between volume estimated from mean
tarif vs. volume estimated from tarif adjusted for dbh for total stem cubic-foot volume and
Scribner board-foot, 16 ft logs, to a 6-in. top.
30.--------------------------------25
lliU CUBIC
V1>V2
w20
----.
• SCRIBNER
u
15
a:
lJJ
u..
u.. 10 '
1(
Ci
5
o
u
, fiiJL
V1=VOLUME ESTIMATED FROM MEAN TARIF
V2=VOLUME ESTIMATED FROM TARIF ADJUSTED FOR DBH
171· rm. =·-=-
-
·
....
ffi
·5
CL _, .
., ..
V1 < V2
-10
·15+--.--.--�-.--.�
2 3 4 5 6 7 8 9 10 11 12 13 14 15
DBH CLASS
Fig. 4. Percent difference, by dbh class, on plot B between volume estimated from mean
tarif vs. volume estimated from tarif adjusted for dbh for total stem cubic-foot volume and
Scribner board-foot, 16 ft logs, to a 6-in. top.
research), and anything more than
total volume is wanted, then a larger
sample is needed.
Berry and Wiant (1967) and Rustagi
and Alegria (1981) suggest using a
prism sample for tarif tree selection,
thereby weighting the selection to­
ward the larger trees. The most effi­
cient metliod of selecting the trees to
be sampled will depend on how the
,data is to be analyzed, but it is essen­
/tial that the requirement for sampling
across the entire dbh range be ob­
served.
If height samples are distributed
across the range of diameters, as spec­
ified in the original instructions of
Turnbull et al. (1963), any bias in total
volume per acre estimates introduced
by use of a single mean tarif number is
probably of little practical importance.
A trend of tarif number with diameter,
however, will result in substantial and
potentially important biases in esti­
mates of cubic-foot and board-foot
volume by diameter classes (as illus­
trated by plot A). These biases are
more pronounced for estimates of
board-foot volume, because board­
foot to cubic-foot volume ratios in­
crease with diameter.
Heights can be assigned to trees notmeas ured i n the field1by using
volumes estimated with the tarif
system and rearranging a standard
volume equation to give estimates of
tree height. This procedure is some­
times used for purposes such as esti­
mating top heights on remeasured
plots when height samples for a given
measurement date are missing or in­
adequate and when tarif numbers by
plot are smoothed over time to pro­
vide interpolated values. Biases sim­
ilar to those for volume estimates can
be expected in estimates of dominant
height or top height derived from a
single-plot mean tarif number.
RECOMMENDATIONS
40
w
()
z
w
a:
w
()
a:
w
a.
PLOT A
PLOT B
30
25
20
H1=HEIGHT ESTIMATED FROM MEAN TARIF
H2=HEIGHT ESTIMATED FROM TARIF ADJUSTED FOR DBH
!:!:
15
c
!z
•
l£ll
H1> H2
35
10
5
0
5
10
2
3
4
5
7
8
9
10 11 12 13 14 15
DBH CLASS {INCHES)
6
Fig. 5. Percent difference, by dbh class, between height estimated from mean tarif vs.
height estimated from tarif adjusted for dbh.
It is therefore recommended that
height samples for tarif estimation
should be distributed across the full
range of diameters of interest for
volume computations. These samples
should be sufficient to allow a sensi­
tive test of the slope coefficient in the
regression of tarif number on diam­
eter. If the slope coefficient differs sig­
nificantly from zero and thert'f1s-1n­
terest in any tarif-derived stand s1'a""'
tistic other than total stand volume,
then either a separate tarif number
should be used for each diameter class
as calculated from the tarif/diameter
regression, or alternatively, height/di­
ameter or volume/diameter curves can
be used.
D
LITERATURE CITED
BRACKETT, M. 1973. Notes on tarif tree volume computation. State of Washington, Dep. WJAF 5(1)1990
11
Natur. Resour., Olympia, WA. Resour.
Manage. Rep. 24. 26 p.
BRUCE, D., AND D. J. DEMARS. 1974. Volume
equations for second-growth Douglas-fir.
USDA For. Serv. Res. Note PNW-239. 5 p.
CHAMBERS, C. J., AND D. F. JENKINS. 1976. Com­
prehensive log scale tree-volume tarif tables for
Douglas-fir. State of Washington, Dep. Natur.
Resour., Olympia, WA. 138 p.
KING, J. E. 1966. Site index curves for Douglas-fir
in the pacific northwest. Weyerhauser For.
Res. Cent., Centralia, WA. For. Pap. No. 8.
49 p.
MILLER, R. E., R. E. BIGLEY, AND S. N. LITTLE.
1986. The effects of slash burning on stand es­
tablishment and stand volume growth. Un­
publ. study plan on file at For. Sci. Lab. ,
Olympia, WA.
RUSTAGI, K. P., AND J. ALEGRIA. 1981. The tarif
system: An evaluation. Unpubl. manuscript on
Purehosed by the Forest Service
U.S. Department of Agriculture,
for official use
12
WJAF 5(1)1990
file at Coli. of For. Resour. , Univ. of Wash­
ington, Seattle. 11 p.
TURNBULL, K. J. , AND G. E. HoYER. 1965. Con­
struction and analysis of comprehensive tree­
volume tarif tables. State of Washington, Dep.
Natur. Resour. , Olympia, WA. Resour.
Manage. Rep. 8. 64 p.
TURNBULL, K. J., G. R. LITTLE, AND G. E. HoYER.
1963. Comprehensive tree-volume tarif tables.
State of Washington, Dep. Natur. Resour.
Olympia, Wash. 127 p.