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GROSS CUBIC-VOLUME EQUATIONS
AND TABLES, OUTSIDE BARK,
FOR PINYON AND JUNIPER TREES
IN NORTHERN NEW MEXICO

Gary W. Clendenen

USDA Forest Service Research Paper INT-228
INTERMOUNTAIN FOREST AND RANGE EXPERIMENT STATION
FOREST SERVICE, U.S. DEPARTMENT OF AGRICULTURE

THE AUTHOR

GARY W. CLENDENEN, formerly Associate Mensurationist with the
Renewable Resources Evaluation Research work unit, Ogden,
Utah, is now Associate Mensurationist with the Forestry Sciences
Laboratory, Olympia, Washington.

RESEARCH SUMMARY

Presents cubic-volume equations and tables for estimating gross cubic
volume outside bark of individual pinyon and juniper trees in northern New
Mexico; also shows procedures used in building mathematical models.

USDA Forest Service

Research Paper INT-228
May 1979

\\
GROSS CUBIC-VOLUME EQUATIONS...
FOR PINYON AND JUNIPER TREES » <
IN NORTHERN NEW MEXICO

Gary W. Clendenen

INTERMOUNTAIN FOREST AND RANGE EXPERIMENT STATION
Forest Service
U.S. Department of Agriculture
Ogden, Utah 84401

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CONTENTS

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INTRODUCTION

Pinyon and juniper trees are commonly small and scrubby, have rapid taper and a
bushy appearance. These characteristics, which are different from those of tree species
conventionally managed for production of sawlogs, give both the private landowner and
the public forester some unusual problems in estimating wood volume. Few volume tables
have ever been published, and volume equations are virtually nonexistent. Howell and
Lexen published some tables in the late 1930's and early 1940's (Howell and Lexen 1939;
Howell 1940 and 1941) and Moessner later published an aerial photo volume table (1962).
All these tables were published within one cover by Barger and Ffolliot (1972).

DATA COLLECTION

The lack of adequate equations or tables for estimating cubic volumes of pinyon
and juniper plus the interest of personnel on the Carson National: Forest in New Mexico
in assessing the current situation in their pinyon and juniper resources resulted in
plans for a cooperative study. Participants were the Intermountain Forest and Range
Experiment Station's Renewable Resources Evaluation work unit, the Carson National
Forest, and the Southwestern Region of the Forest Service. The data used to develop
the cubic volume equations presented here were collected on the Carson National Forest
as part of this cooperative study. Independent variables collected and used in the
data analysis were:

Species
Basal diameter outside bark--diameter at ground line
Total tree height
Number of 3-in (7.62 cm) and larger forks anywhere on the stem where both
stems coming out of the fork were 3 in or larger diameter outside the bark

5. Number of stems 3-in (7.62 cm) diameter and larger outside the bark and
originating within the first 12 in (30.43 cm) above ground line.

PWNrF

The two independent variables measured for use in determining cubic-foot volume of
each sample tree were: (1) the number of segments in each tree by 2-ft (0.61 m) length
classes, and (2) 2-in (5.08 cm) midpoint diameter classes (2 to 8 ft, or 0.61 to 2.44 m).
The midpoint diameter classes were even 2-in (5.08 cm) classes; 2-in (5.08 cm) diameters
were the smallest. If any segment (except for the 2-ft length class) had more than
2 in of taper, it was divided into two or more segments such that maximum taper within
a segment could not exceed 2 in (5.08 cm).

Of the several species of pinyons and junipers native to the Rocky Mountain West,
only three were encountered in this study: pinyon (Pinus edulis:Engelm.) and Rocky
Mountain and Utah junipers (Juntperus scopulorum Sarg. and J. osteosperma'|Torr.]
Little). Of the total of 2,318 trees measured, 1,559 were pinyons and 759 were junipers.
The trees were selected from 96 field plots randomly scattered about the Carson National
Forest.

DATA ANALYSIS

Using diameter and length class, the cubic volume was calculated for each segment
in each sample tree assuming the segment was a cylinder having diameter equal to the
segment midpoint diameter and length equal to the segment length class (Huber's formula).

The segment cubic volumes were then summarized by diameter class to provide estimates of
cubic volume for each tree by six different top diameters--1 in through 11+ in (2.54 cm-
27.94 cm) by 2-in (approximately 5 cm) odd increments. Cubic volume, so calculated, was
used as the dependent variable for regression analyses.

A combinatorial screening approach (Grosenbaugh 1967) was used initially to deter-
mine which combination of pertinent transforms of all independent variables gave the best
estimate of cubic volume. The results indicated basal diameter and total height to be
the best predictors of cubic volume for pinyon. Basal diameter, height, and number of
forks provided the "best" correlation with juniper volume. Substituting number of stems
for number of forks gave a slightly smaller correlation; however, number of stems was
selected for the final juniper volume model because number of stems is more easily and
accurately determined in the field.

After these independent variables were selected, the data were summarized by
species for each minimum top diameter limit. For pinyon, mean cubic volume was computed
for each 2-in (approximately 5 cm) basal diameter class and each 5-ft (1.5 m) height
class. For juniper, mean cubic volume was computed for each 2-in (5 cm) basal diameter
class, 5-ft (1.5 m) height class, and number-of-stems class. These mean cubic volumes
were then used to develop a refined volume model that was finally fitted to all indi-
vidual tree volumes by linear least squares techniques.

The following constraints were applied to the volume models:

1. Volume should increase over height and must pass through zero cubic volume
when height equals zero.

2. Volume should increase over basal diameter and must pass through zero cubic
volume when basal diameter equals minimum top diameter limit.

3. Volume must approach zero cubic volume as number of stems increases.
4. Volume must decrease with increasing minimum top diameter limit.

5. The minimum top diameter components must not cross.

6. The number of stem components of model must not cross.

An initial plotting of the data indicated volume increased linearly over height
and was concave upward over basal diameter.

The first constraint is satisfied by a model of the form Y = bH where pb is ex-
pressed as a function of basal diameter, number of stems, and minimum top diameter
limit. Minimum top diameter limits of 9 in (22.86 cm) and 11 in (27.94 cm) were dropped
from the analysis because inadequate sample sizes resulted in inconsistent trends. The
final model was then developed using minimum top diameter limits of 1, 3, 5, and 7 in
(25548, Peee, W505 eincl Uo VS CM)\6

The first step in the model building process was to fit a weighted linear equation
of the basic model form through the origin with height as the independent variable and
cubic volume as the dependent variable. This was done for each species, 2-in (5 cm)
basal diameter class, minimum top diameter limit, and in the case of juniper, each
number-of-stem class up to six. Beyond six stems, the data base was insufficient to
determine consistent trends. The weights used were the number of observations contrib-
uting to each mean volume.

Next, the resulting slopes (b coefficients) were plotted over basal diameter minus
minimum top diameter limit. Basal diameter minus minimum top diameter limit was used
because of the second constraint mentioned previously. Matchacurve techniques (Jensen
1964, Jensen and Homeyer 1970, 1971, Jensen 1973, 1976) were used to describe the trends
of the slopes in relation to basal diameter minus minimum top diameter for each minimum
top diameter class. For pinyon, the power function of the form

Y= ax”

was a satisfactory descriptor with a and ” to be a function of minimum top diameter
alone. For juniper, a single power function did not provide enough upward curvature

for the larger basal diameters; therefore, a multiple component model having the follow-
ing form was used:

a Ged & Gk?
where the AnxX”2 component becomes essentially zero for small diameters.

As in step 1, each model component was fitted through the origin by weighted
(number of observations) least squares techniques.

For juniper, the slopes were also a function of number of stems. The number-of-
stems effect was allowed to asymptote toward zero at 20 stems.

Appropriate power functions for the minimum top diameter limit effect were then
determined. The same procedure as used in step 2 was employed, except this time the
independent variable was minimum top diameter limit.

The components were combined for each model and the latter were each fitted to
their respective data set by least squares techniques. The simple linear model,
Y = b (model), was used, forcing the model through the origin. The resulting coeffi-
cients were very close to 1, indicating that the models as developed fitted the overall
data trends very well.

Next the residuals were plotted over estimated volume. The plotted residuals
showed increasing residuals with increasing estimated volume, indicating a need to
weight the estimate of Db in the final models. Draper and Smith (1966) and Cunia (1964)
recommend weighting the dependent variable by the reciprocal of the variance where
variance is unequal. An estimate of the variance can be obtained from the residuals
squared.

The next step was to screen possible variables for correlation with residuals
squared. The LOG of the residuals squared was screened against all possible combina-
tions of the LOG's of the following variables:

Estimated cubic volume

Basal diameter minus minimum top diameter limit
Minimum top diameter limit

Height

Number of stems (juniper only).

nNRWNF

The screen indicated the estimated cubic volume was the simplest, best overall
predictor of residuals squared.

A LOG model of the following form was fitted to arrive at a preliminary estimate
of variance as a function of estimated cubic volume:

HOeKGr = QE) ae 6 HOGA

where:
(QL 130) = estimated variance, residuals squared
Y = field measured cubic volume
Y = estimated cubic volume from previous regression.

Substituting V for (Y - Y)* and taking the antilog yielded:
V = ay.

Therefore, the estimated weight was:

a

W

ale

av

Since a is a constant, it was dropped from the weight without affecting the relationship
between the weights over estimated cubic volume. Dropping the constant yielded:

eat yd

W= Cpe

After the initial estimate of the weight was determined, the model was fitted using
weighted least squares techniques. From the weighted model, a new estimate of variance
and corresponding weight was obtained by again fitting a LOG model. Having obtained a
new b value for the estimated weight, a new weighted regression was computed. The
fourth iteration of this process yielded weights and regression coefficients essentially
the same as the third iteration; this indicated the weights had stabilized and an
appropriate weight had been found. The final weight used for the weighted regression
was:

as z
where:
Y = estimated cubic volume from previous iteration
b=

1.43 for pinyon and 1.40 for juniper

Next another plot of the residuals was made over estimated cubic volume. The
residuals were weighted by the square root of the weight used for the final weighted
regression. The plot showed that the residuals:

Appeared in a horizontal band

Appeared balanced overall

Appeared unbalanced close to the origin

Appeared unbalanced for large estimated cubic volumes

For juniper only, had a conspicuous absence of positive residuals at 15 ft
(0.42 m ) offset by an absence of negative residuals at 25 ft (0.71 mM).

Cac CY St

Items 1 and 2 indicate appropriate weights were used. Items 3 and 4 indicate an
intercept value should be included in the model. Item 5 indicates that two segments of
the juniper model do not fit the data trends, but the lack of fit in one segment is off-
set by a corresponding lack of fit in another. Another examination of the means used
to derive the original model revealed that to correct for the lack of fit in the two
areas would result in an unrealistic model form. Therefore, the original model form
was retained.

As a result of items 3 and 4, a new weighted regression was computed, this time
with an intercept. The resulting intercepts were small [0.03 ft? (0.0008 m°) for both
pinyon and juniper], and the slope corrections were not unreasonable. A plot of the
weighted residuals about the models with intercepts revealed that items 1 and 2 had
been unchanged, items 3 and 4 had been corrected, and item 5 for juniper had been im-
proved. Therefore, the weighted models with intercept values were accepted as the best
linear unbiased estimators of cubic volume.

The final equations which follow have the foliowing use restrictions:

1. The minimum top diameter limits must be in the range of 1 to 7 in (2.5 to
17 318 (em).

2. The number of stems cannot exceed 20.

3. The cubic volume predicted is total volume from ground line to point of
minimum top diameter including bark and limbs.

4, The equations are considered representative of pinyon, Utah juniper, and Rocky
Mountain juniper in northern New Mexico. Use elsewhere should be accompanied by suit-
able checks of applicability.

The pinyon cubic volume equation is:

V=c + bx'H
where:
e (English units) = 0.02768
e@ (metric units) = 0.0007838

X (English units) = D - 7D
De =eED,
2.54

D = basal diameter (at ground line) in inches for English units or centimeters
for metric units

X (metric units) =

se
I

total tree height in feet for English units or meters for metric units

TD = minimum top diameter limit in inches for English units or centimeters
for metric units

0.08789 - 0.03675(11.0 - 7D)°-3°

b (English units)

0.0081652 - 0.0024637(27.94 - 7TD)°%-3°

b (metric units )
n (English units) = 1.1 + 0.007(11.0 - 7D)?-°

nm (metric units) = 1.1 + 0.001085(27.94 - TD)?-°

V = gross cubic volume outside bark to the specified minimum top diameter

limit including stump and limbs in cubic feet for English units or cubic
meters for metric units.

Figure 1 illustrates the pinyon l-inch top diameter volume surface showing the
means used for model development plotted and connected to the surface by a vertical
line. Note that more than 95 percent of the total data set was less than 14 in basal
diameter.

150
130

=
VOLUME (FT*)

BASAL DIAMETER (IN)

Figure 1.--Pinyon gross cubte-foot volume outstde bark tneluding stump and limbs to
1-inch minimum top diameter limit showing differences between observation means and
corresponding predicted values.

The juniper cubic volume equation is

Vee « GigE

where:
e (English units) = 0.03066
e (metric units) = 0.0008682
20.0 - STEMS
G2

TORO
mn (English units) = 2.25 + 0.38130(7D - 1.0)

3

(metric units) = 2.25 + 0.15012(7D - 2.54)

X (English units) = 0.00491(D - 7D)1-8 + 1.50147£-08(D - 7D)°-°

X (metric units) = 0.0000852(D - 7D)!-8 + 1.3194#-11(D - 7D)°-°

STEMS = number of stems 3 in (7.62 cm) diameter and larger originating

within first 12 in (0.3 m) above ground line. Trees less than
3 in (7.62 cm) basal diameter are considered single stemmed.

6

b (English units) = 1.08100 + 0.06263(7D - 1.0)
b (metric units) = 1.08100 + 0.0246575(7D - 2.54)

D = basal diameter (at ground line) in inches for English units or
centimeters metric units

H = total tree height in feet for English units or meters for metric units

TD = minimum top diameter limit in inches for English units or centimeters
for metric units

V = gross cubic volume outside bark to the specified minimum top diameter
limit including stump and limbs in cubic feet for English units or cubic
meters for metric units.

Figure 2 illustrates the juniper l-in top diameter volume surface for single-
stemmed trees showing the means used for model development plotted and connected to
the surface by a vertical line. Note that more than 90 percent of the total data set
was less than 14 inches basal diameter.

150

VOLUME (FT *)

BASAL DIAMETER (IN)

Figure 2.--Juntper gross-cubic volume outstde bark ineluding stump and limbs to 1-inch
minimum top diameter limit for stngle stemmed trees showing differences between
observatton means and corresponding predicted values.

Figure 3 illustrates the top diameter effect for pinyon, and figure 4 illustrates
the top diameter effect for single-stemmed juniper. Figure 5 illustrates the number-
of-stems effect for juniper to a l-in top diameter.

=
VOLUME FT (FT°)

2 6 10 14 18 22 26 30
BASAL DIAMETER (IN)

Figure 3.--Pinyon gross cubic-foot volume outstde bark tneluding stump and limbs to
l-ineh, 2-tneh, 4-itnch, 6-tnch, and 7-tnch top diameter limits.

150
130
110

VOLUME (FT?)

Cesena Ome aS e260 30
BASAL DIAMETER (IN)

Figure 4.--Juntper gross cubtc-foot volume outside bark ineluding stump and limbs to
1-ineh, 2-inch, 4-ineh, and 7-inch mintmum top diameter limit for stngle stemmed
trees.

VOLUME (FT°)

2 6 10 14 18 22 26 30
BASAL DIAMETER (IN)

Figure 5.--Juniper gross cubtc-foot volume outside bark ineluding stump and limbs to
1-inch mintmum top diameter for 1, 2, 3, 4, 5, 10, and 15 stemmed trees.

APPLICATION

The volume equations presented here are too complex to be solved easily with a
desk calculator; therefore, two computer subroutines for computing individual tree
volumes were written (English and metric units) and are included in Appendix I. The
subroutines compute volumes in cubic feet with English unit input and cubic meters
with metric unit input.

For desk calculator computation of tree volumes, tables 1 through 10 (in Appendix
II) can be used. Tables 1 and 3 are in English units for pinyon and tables 5, 7, and
9 are in English units for juniper. Tables 2 and 4 are in metric units for pinyon and
tables 6, 8, and 10 are in metric units for juniper.

To compute cubic-foot volume for a pinyon tree, first find the volume to a 1l-in
minimum top diameter for the tree in table 1. Then in table 3 find the appropriate
proportion for the basal diameter of the tree and the desired minimum top diameter limit.
Multiply the table 1 value by the table 3 value to obtain the cubic-foot volume of the
tree to the desired minimum top diameter limit. Metric volume is obtained by the same
procedure except that tables 2 and 4 are used instead of tables 1 and 3.

To compute cubic-foot volume for a juniper tree, first find the volume of a single-
stemmed tree to a l-in minimum top diameter in table 5. Second, in table 7 find the
appropriate proportion for the basal diameter of the tree and the desired minimum top
diameter limit. Finally, in table 9 find the appropriate proportion for the number of
stems and the desired minimum top diameter limit. Multiply the values obtained from
tables 5, 7, and 9 together to obtain the cubic-foot volume of the tree to the desired
minimum top diameter limit. Metric volume is obtained by the same procedure except
that tables 6, 8, and 10 are used instead of tables 5, 7, and 9.

Example: Assume a pinyon tree 10-in basal diameter and 30 ft tall. Determine
the cubic-foot volume of this tree to a 4-in minimum top diameter limit. From table 1,
themvalwensnS2ucubicwfeet ais mead. »From) tabile) 3, the proportion 0/3692 1s read. \ The
cubic-foot volume of this tree to a 4-in top is then 6.1 ft (8.82 X 0.692).

Example: Assume a juniper tree 12-in basal diameter, 20 ft tall, and having three
stems originating within the first 12 in above ground line. Determine the cubic-foot
volume of this tree to a 4-in minimum top diameter limit. From table 5,the value 8.034
is read. From table 7, the proportion 0.659 is read. From table 9, the proportion

0.686 is read. The cubic-foot volume of this tree to a 4-in top is then 3.63 ft
(8.034 X 0.659 X 0.686).

CONCLUSIONS

The equations, computer subroutines, and tables presented in this paper are
applicable throughout northern New Mexico for volume estimation in the pinyon-juniper
type. Use outside of northern New Mexico should be accompanied by appropriate field
checks.

10

PUBLICATIONS CITED

Barger, Roland L., and Peter F. Ffolliott.

1972. Physical characteristics and utilization of major woodland tree species in
Arizona. USDA For. Serv. Res. Pap. RM-83, 80 p. Rocky Mtn. For. and Range Exp.
Stniy,, Kone Coltinsie Colo.

Gunwaluely.
1964. Weighted least squares method and construction of volume tables. For. Sci.
10(2) :180-191.
Draper, N. R., and H. Smith.
1966. Applied regression analysis. 407 p. John Wiley and Sons, Inc., New York.
Grosenbaugh, L. R.

1967. REX--FORTRAN-4 SYSTEM for combinatorial screening or conventional analysis of
multivariate regressions. USDA For. Serv. Res. Pap. PSW-44, 47 p. Pacific South-
west For. and Range Exp. Stn., Berkeley, Calif.

Howell, Joseph, Jr.
1940. Pinyon and juniper--a preliminary study of volume, growth, and yield. USDA
Soal (Conserv (Reg. 8 Bul 717 For. Serve 120590) pee Albuquerque: NemMexs.
Howell, Joseph, Jr. :
1941. Pinyon and juniper woodlands of the Southwest. J. For. 39:542-545.
Howell, Joseph, Jr., and Bert R. Lexen:.

1939. Fuelwood volume tables for Rocky Mountain red cedar (Juntperus scopulorum
Sarg.). USDA For. Serv. Res. Note SW-68, 4 p. Southwest For. and Range Exp. Stn.,
Tucson, Ariz.

Jensen, Chester E.

1964. Algebraic description of forms in space. 57 p. USDA For. Serv., Cent. States

For. Exp. Stn., Columbus, Ohio.
Jensen, Chester E.

1973. Matchacurve-3: Multiple-component and multidimensional mathematical models for
natural resource studies. USDA For. Serv. Res. Pap. INT-146, 42 p. Intermt. For.
and Range Exp. Stn., Ogden, Utah.

Jensen, Chester E.

1976. Matchacurve-4: Segmented mathematical descriptors for asymmetric curve forms.
USDA For. Serv. Res. Pap. INIT-1825 16 p.) Intermt.. For.) andsRange Exprmocites
Ogden, Utah.

Jensen, Chester E., and Jack W. Homeyer.

1970. Matchacurve-1 for algebraic transforms to describe sigmoid- or bell-shaped

curves. 22 p. USDA For. Serv., Intermt. For. and Range Exp. Stn., Ogden; Utah:
Jensen, Chester E., and Jack W. Homeyer.

1971. Matchacurve-2 for algebraic transforms to describe curves of the class Nee
USDA For. Serv. Res. Pap. INT-106, 39 p. Intermt. For. and Range Exp. Stn;
Ogden, Utah.

Moessner, Karl E.

1962. Preliminary aerial volume tables for pinyon-juniper stands. USDA For. Serv.

Res. Pap. INT-69, 12 p. Intermt. For. and Range Exp. Stn., Ogden, Utah.

Il

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APPENDIX I

SUBROUTINE PJVOL(BD,TD,STEMS,HT, ISPEC,V)

REEKEK

* THIS SUBROUTINE COMPUTES GROSS CUBIC-FOOT VOLUME FOR INDIVIDUAL
* PINYON AND JUNIPER TREES.

REQUIRED INPUTS --
* 1. DIAMETER AT GROUND LINE
* 2. MINIMUM TOP DIAMETER LIMIT
= 3. NUMBER OF 3-INCH AND LARGER STEMS ORIGINATING WITHIN
* FIRST 12 INCHES ABOVE GROUND LINE FOR JUNIPER ONLY
i 4. TOTAL TREE HEIGHT
uy 5. SPECIES INDEX OF 1 FOR PINYON AND 2 FOR JUNIPER

D = BD - TD
IF(TD.LT.1.0.OR.TD.GT.7.0.0R.STEMS.LT.0.0.AND. ISPEC.EQ.2.OR.STEMS.
1 GT.20.0.AND.ISPEC.EQ.2.0R.HT.LT.0.0.0R.D.LT.0) GO TO 20

IF (ISPEC.EQ.2) GO TO 10

IF(ISPEC.NE.1) RETURN

KREREKK

* PINYON

REKKK

We (G0) = Jose © Gul) Stmp)es 8s) 3 M@eaGigh & 007 2 GN. =
1 TD)**2.0)) * HT + .02768
RETURN

KEKKK

* JUNIPER

KKEKKK

10 IF(STEMS.LE.1.0) STEMS = 1.000000
Vi-=) (C(20s = STEMS) 1/2 19.) * (2925) S81) DD) ep) Sal OSO One:
1 .06263 * (TD - 1.)) * ((.00491 * D**1.8) + (1.50147E-08 * D
2 ** 5.0))) * HT + .030664
RETURN
20 V = 0.0
RETURN
END

LS)

(RVR) CY Ge) Gl (RY) (ee) (RRC) (2) (2)

ALI Qria

(RY Ree) eh Ge)

SUBROUTINE PJVOL(BD,TD,STEMS,HT, ISPEC,V)

KRKKKK

* THIS SUBROUTINE COMPUTES GROSS CUBIC-METER VOLUME FOR INDIVIDUAL
* PINYON AND JUNIPER TREES.

* REQUIRED INPUTS --

- 1. DIAMETER AT GROUND LINE

2. MINIMUM TOP DIAMETER LIMIT

td 3. NUMBER OF 3-INCH AND LARGER STEMS ORIGINATING WITHIN
x FIRST 12 INCHES ABOVE GROUND LINE FOR JUNIPER ONLY

sg 4. TOTAL TREE HEIGHT

td 5. SPECIES INDEX OF 1 FOR PINYON AND 2 FOR JUNIPER

D = (BD - TD) / 2.54

IF(ISPEC.EQ.2) D = D * 2.54

IF (TD.LT.2.5.0R.TD.GT.15..OR.STEMS.LT.0.0.AND.ISPEC.EQ.2.OR. STEMS.
1 GT.20.0.AND.ISPEC.EQ.2.OR.HT.LT.0.0.0R.D.LT.0) GO TO 20
IF(ISPEC.EQ.2) GO TO 10

IF (ISPEC.NE.1) RETURN

KKEKK

* PINYON

KKKKK

V = (.0081652 - .0024637 * (27.94 - TD)**.35) * (D**(1.1 + .001085
1 * (27.94 - TD)**2.0)) * HT + .0007838
RETURN

REKKKK

* JUNIPER

kKkKKKK

10 IF(STEMS.LE.1.0) STEMS = 1.000000

V = (((20.0 - STEMS) / 19.0)**(2.25 +.15012 * (TD - 2.54)) * (1.0
181 + .0246575 * (TD - 2.54)) * ((8.52E-05 * D**1.8) + (1.3194E-11
2 * D**5.0))) * HT + .0008682

RETURN

20 V = 0.0

RETURN
END

14

APPENDIX II

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16

Table 3.--Pinyon gross cubte-foot volume proportton of
1-ineh mintmum top dtameter limit

es Minimum top diameter limit (inches)
lameter
(inches) : al : 2 : 3 : 4 : 5 : 6 : 7
2
4
6
8
10
2
14
16
18
20
22
24
26
28
30
32
34
36
38
40
Table 4.--Pinyon gross cubtc-meter volume proportton of
2.5 centimeter mintmum top dtameter limit
Basal Boe : Arma 6
j Minimum top diameter limit (centimeters)
diameter
(centimeters) ; Aes) : 5.0 : 10.0 : 15.0
2.5 1.00000 (6) O 0)
5.0 1.00000 0 (0)
10.0 1.00000 0.67600 (0)
15510 1.00000 - 85278
20.0 1.00000 -91509
25.0 1.00000 -94118 -69524
30.0 1.00000 -95158 - 73448 - 54803
35.0 1.00000 -95505 - 75083 - 58607
40.0 1.00000 - 95465 - 75559 - 60266
45.0 1.00000 - 95230 - 75392 -60744
50.0 1.00000 - 94892 - 74867 - 60563
55510 1.00000 - 94479 - 74144 - 60006
60.0 1.00000 - 94036 - 73314 -59228
65.0 1.00000 -93577
70.0 1.00000 - 93118 - 71519 -57372
75.0 1.00000 -92655 - 70609 - 56389
80.0 1.00000 - 92203 -69711 - 55406
85.0 1.00000 -91757 - 68830 - 54432
90.0 1.00000 - 91324 -67974 -53481
95.0 1.00000 -90901 -67143 -52557
100.0 1.00000 - 90489 - 66340 - 51662

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Table 7.--Juntper gross cubtc-foot volume proportion of 1-inch
mintmum top diameter limit for stngle stemmed trees

Baber : Minimum top diameter limit (inches)
diameter :
(inches) : al : 2 : 3 : 4 : 5 : 6 : 7

2

4 OR Sa47

6 5 Ko) 0.230 0.074

8 -802 - 430 50) 0.138 0.044
10 ~855 565 -428 - 300 188
F2 -890 -659 544 -432 325
14 -914 -728 -631 534 439
16 aeeut 6 US) -697 614 3530
18 -944 -818 749 -677 - 604
20 -954 -728 - 663
22 -962 - 768 5 a
24 - 968 - 800

26 973 826
28 -977

30 1.000 - 980 956 928 898 864 829
32 1.000 - 982 -961 - 936 -908 -878 845
34 1.000 984 -964 ~942 916 - 888 859
36 1.000 985 967 946 923 897 - 869
38 1.000 - 987 -970 -950 928 904 -878
40 1.000 - 988 -972 953 -932 -909 . 884

Table 8.--Juntper gross cubic-meter volume proportion of 2.5 centimeter
mintmum top diameter limit for single stemmed trees

Basal g aan : ie A
Anewoter : Minimum top diameter limit (centimeters)
(centimeters) : Bod : 510 : 10.0 : 530
iD 1.00000 )
5210 1.00000 0
10.0 1.00000 0.51891
15.0 1.00000 - 70932 0.23051
20.0 1.00000 - 80120 - 42956
25.0 1.00000 - 85445 - 56423
30.0 1.00000 - 88916 - 65827
35710 1.00000 VOLS . 72624
40.0 1.00000 - 93069 - 77743
45.0 1.00000 - 94372 - 81655
50.0 1.00000 - 95381 - 84713
5550) 1.00000 - 96161 ~87121
60.0 1.00000 - 96777 - 89041
65.0 1.00000 -97264 - 90566
70.0 1.00000 -97644 - 91787
7550 1.00000 ~9795i - 92762 - 86366
80.0 1.00000 - 98193 793538 - 87742
85.0 1.00000 - 98382 -94155 - 88841
90.0 1.00000 - 98534 - 94648 - 89720
95.0 1.00000 - 98656 - 95041 - 90424
100.0 1.00000 - 98756 - 95359 - 90992

20

Table 9.--Juniper gross cubte-foot volume proportton of single
stemmed trees for multiple stemmed trees

pees Minimum top diameter limit (inches)
stems al g 2 3 : 4 : 5 6 7
al 1.000 1.000 1.000
2 - 850 - 832 815
3 5 Haus) - 686 -657
4 - 596 -558 523
5 -491 - 448 -410
6 3399 A S55) - 316
U - 319 -276 -239
8 - 250 -210 -176
9 - 292 COST wh93 - 156 alii - 103 - 084
10 6 9 2145 Al Lis) - 089 - 069 -054
er - 186 - 140 Sal(o}s) -079 - 060 045 -034
12 - 143 - 103 -074 2053 - 038 -027 -020
13 - 106 HOM - 049 Q34 Q -016 -O1l
14 O75 - 048 -O31 -020 013 -008 -005
U5 -050 -030 -018 -O1l - 006 -004 -002
16 -030 OM, -009 005 -003 - 002 -OO1
Ly); -016 -008 -004 -002 -OO1 - 000 - 000
18 - 006 -003 -O001 - 000 - 000 - 000 - 000
19 -OO1 - 000 - 000 - 000 - 000 - 000 - 000
20 - 000 - 000 - 000 - 000 - 000 - 000 - 000
Table 10.--Juntper gross cubic meter volume proportion of single
stemmed trees for multtple stemmed trees
eee i Minimum top diameter limit (centimeters)
stems g 25) g 5.0 10.0 15.0
ab 1.00000 1.00000 1.00000 1.00000
2 - 88576 - 86797 - 83346 - 80033
3 - 77916 - 74730 -68745 - 63242
4 - 68008 - 63760 - 56045 - 49265
5 - 58839 - 53845 - 45093 -37765
6 - 50403 - 44946 ~35741 - 28424
7 - 42682 - 37018 - 27846
8 - 35667 - 30019 - 21266
9 - 29343 - 23904 - 15865 - 10532
10 - 23696 - 18626 alike lil -07116
aLIE - 18709 - 14138 - 08075 - 04615
12 - 14367 - 10388 -05434 - 02846
als} - 10651 - 07326 - 03470 - 01648
14 -07540 - 04897 -02070 - 00880
5 - 05013 - 03043 -01126 - 00423
16 - 03044 -01702 - 00538 -00178
aly - 01602 - 00808 -00213 -00065
18 - 00653 - 00288 - 00065 -00024
19 -00149 -00058 -00019 -00015
20 -00014 -00014 -00014 -00015

vy U.S. GOVERNMENT PRINTING OFFICE: 1979—677-019/84 REG. 8 D i

Clendenen, Gary W.
1979. Gross cubic-volume equations...for pinyon and juniper trees in
northern New Mexico. USDA For. Serv. Res. Pap. INT-228, 21 p.
Intermt. For. and Range Exp. Stn., Ogden, Utah 84401.

Presents cubic-volume equations and tables for estimating gross cubic
volume outside bark of individual pinyon and juniper trees in northern New
Mexico; also shows procedures used in building mathematical model.

KEYWORDS: gross cubic-volume, equations, pinyon, juniper, mathematical
models.

Clendenen, Gary W.
1979. Gross cubic-volume equations...for pinyon and juniper trees in
northern New Mexico. USDA For. Serv. Res. Pap. INT-228, 21 p.
Intermt. For. and Range Exp. Stn., Ogden, Utah 84401.

Presents cubic-volume equations and tables for estimating gross cubic
volume outside bark of individual pinyon and juniper trees in northern New
Mexico; also shows procedures used in building mathematical model.

KEYWORDS: gross cubic-volume, equations, pinyon, juniper, mathematical
models.

Headquarters for the Intermountain Forest and
Range Experiment Station are in Ogden, Utah.
Field programs and research work units are
maintained in:
Billings, Montana
Boise, Idaho
Bozeman, Montana (in cooperation with
Montana State University)
Logan, Utah (in cooperation with Utah State
University)
Missoula, Montana (in cooperation with
University of Montana)
Moscow, Idaho (in cooperation with the
University of Idaho)
Provo, Utah (in cooperation with Brigham
Young University)
Reno, Nevada (in cooperation with the
University of Nevada)

we We