_
U!rpte_dtmSuta_te:'
Forest
NSeor_ihCcentra I
_t°ate°tnExperiment
Research
Paper N0-242
_
Weight and Volume
Equations and
Tables for Red Mal)le
inthe
T. R. Crow and G. G. Erdmann
La
ke
States
Crow, T. R.; Erdmann,
G. G.
Weight and volume equations and tables for red maple in the Lake
States. Res. Pap. NC-242. St. Paul, MN: U.S. Department
of Agriculture, Forest Service, North Central Forest Experiment
Station;
1983. 14 p.
Weight and volume information
based on regional sampling are
provided for red maple in the Lake States. Both green weight and
dry weight values are presented for biomass. Volume equations predict total stem volume, volume to 8-inch top, and volume to 4-inch
top, inside and outside bark.
KEY WORDS: Acer rubrum, biomass, total tree weight, component
weight, stand weight, stem volume.
North Central Forest Experiment
Station
Forest Service--U.S.
Department of Agriculture
1992 Folwell Avenue
St. Paul, Minnesota
55108
Manuscript
approved for publication
February 14, 1983
December,
1983
WEIGHT AND VOLUME EQUATIONS AND TABLES
FOR RED MAPLE IN THE LAKE STATES
T. R Crow, Research Ecologist,
Rhinelander,
Wisconsin,
and G. G. Erdmann,
Silviculturist
Marquette,
Michigan
Red maple (Acer rubrum L.)is a common component of second-growth
forests in the Lake States.
In Michigan's
Upper Peninsula,
it is second only to
sugar maple (Acer saccharum
L.) in terms of standing volume, and it is an important
resource on more
than 1 million acres of commercial forest in the region,
Changing
patterns
of utilization
have resulted in
the need for mensurational
information
expressed
as weight or biomass (Young 1974). In addition, more
traditional
mensurational
units such as volume need
to be derived for various standards
of utilization.
Although regression equations are available for predicting biomass of many hardwood species including
red maple, most of these predictive
equations
are
based on limited sample numbers and sample sites.
Nothing in the theory of regression analysis suggests
that these equations can be applied elsewhere--they
are valid for regional
application
only if they are
based on regional sampling.
As part of a program
in growth and yield research
in northern
hardwoods,
volume and biomass information are presented
here for red maple. The study
objective was to predict weight and volume for red
maple stands and individual
trees across a range of
stand ages and site qualities.
The scope of the research included:
(1) developing
regression
estimators
for whole-tree
and component
weights
and volumes
for red maple and comparing
these
estimators
among
sites;
(2) preparing
weight
tables from regression
equations for the total tree and its components
by
d.b.h, and total height classes; and
(3) predicting
stand weights from measurements
as basal area and mean stand height,
such
METHODS
To provide a regional framework
for predicting
red
maple weight and volume, sample sites were selected
in Michigan
and Wisconsin
that represented
the population
of even-aged
hardwood
forests in the Lake
States.
Six sample stands,
each dominated
by red
maple, were selected as closely as possible to the
following age and site index (at age 50) specifications:
Stand age
Site index
(years)
(SI)
40
_<45
70
_<45
40
70
50-55
50-55
40
1>60
70
t>60
Sugar maple was a common associate
of red maple
on all sites. In the 70-year-old
stands, beech (Fagus
grandifolia
Ehrh.), yellow birch (Betula alleghaniensis Britton), basswood (Tilia americana L.), and hemlock (Tsuga canadensis (L.) Carr) were also common
components.
Other. species frequent
to the 40-yearold stands
include black cherry (Prunus
serotina
Ehrh.), pin cherry (Prunus pensylvanica
L.), paper
birch (Betula papyrifera Marsh.), and aspen (Populus
tremuloides
Michx).
Within a sample stand,
bered and d.b.h, measured
all red maple
and recorded.
were numThe num-
bered trees were partitioned
into five d.b.h, classes
(minimum
diameter
= 10 cm d.b.h.), with each class
having an equal number of stems. Within a class,
five trees were randomly
selected
for destructive
sampling,
thus providing
25 trees per site for a total
of 150 samples in the study (table 1.)
The procedures
used to sample biomass of individual trees have been presented elsewhere (Crow
1983). Total tree in our paper refers to aboveground
weight and is the sum of live canopy, dead branches,
bole, and stump. Total canopy includes live branches
and leaves but excludes dead branches,
tioned. The additional
sites, both located in Michigan, included a SI = 61, 50-year-old stand and a SI
= 63, 53-year-old stand. Volumes were predicted using the linear form of the allometric equation and a
simple linear model with D.B.H., D.B.H. 2, and D2H
as the independent variables.
Weight/tree dimension relations were expressed
in the linear form of the allometric equation:laY =
atotal
+ b(lnX)+
D.b.h.
D2H (D.b.h.variables;
squared green
times
height) lne.were
the and
independent
weight and dry weight were the dependent variables.
Both English and metric units are provided. Analysis of covariance
was used to determine
if significant differences
existed among sets of allometric
equations representing
the six sites (Snedecor and
Cochran 1967).
Standardized
curves were also developed for each
stand age (40 and 70 years) using dummy variables
in a multiple regression to control spacing (Jacobs
and Cunia 1980, Draper and Smith 1981).
By fitting
laY = lnBo + B1 laX + (_llnZ, + a21nZ2 + lne,
where (lnZl,lnZ2)= (1,0) for SI _<45
(lnZ,lnZ2) = (0,1) for SI 50-55
(lnZ,,lnZ2) = (0,0) for SI >I 60
and substituting
for the three sets of values for lnZ1
and lnZ2, three curves with the same slope but different intercepts are obtained. Uniform spacing among
intercepts
is obtained by regressing
the intercept
with site index and using the estimated
intercepts
in the standardized
curves.
A set of asymptotic
regressions
is also calculated
using the model, Y = _ + Bpz,
where: Y is the dependent variable that approaches
an asymptotic limit as Z approaches infinity;
represents the asymptotic values of Y;
B represents
the total change in Y as Z passes
from 0 to +;
P represents
the factor by which the rate of
change in Y reduces as Y approaches its
asymptote; and,.
Z is the independent
variable,
Schwandt's
(1979) procedures
vector parameters
for asymptotic
to simultaneously
for estimating
the
regression were used
fit the curves.
For volume predictors, two additional sampling
locations were added to the six sites previously men-
APPLICATION
OF
EQUATIONS
Diflerences in Stand age and site index did not
result in significant differences in biomass or volume
equations. Regardless of the independent
or dependent variable tested, no statistical
differences were
found at the P_<0.05 level in regression slopes or
intercepts
among the sample sites (Crow 1983).
These results indicate that a general biomass predictor is valid for red maple within the range of data
tested (table 1). Because the sample sites represent
the range of site and stand conditions for red maple
in the Lake States, the general predictors are recommended for regional inventories within the Lake
States (table 2). Application
of a general predictor
to a specific site or application
outside the sample
region, however, could result in substantial
bias.
The error associated with weight estimates
did
differ substantially
among components (table 2). Total tree weight or bole weight can be estimated with
greater
confidence
than canopy weight.
Although
differences
among the D2H predictors
were statistically
nonsignificant
using the test criterion P_<0.05, plots of individual
curves often indicated consistent trends among equations that were
correlated to site index and stand age (fig. 1). This
consistency suggests that for specific sites, greater
accuracy can be obtained by including site quality
and stand age in the predictive model. Under the
assumption that a larger sample size would result
in uniform spacing among curves in figure 1, the
original equations for total weight/D2H have been
"standardized"
using dummy variables
to control
spacing. When applying these predictors, simply select a table based on the weight units (English or
metric, green weight or dry weight) and select the
predictor that most closely represents
your sample
population in terms of stand age and site quality.
Total tree weights are given in the following tables:
Table 3ugreen weight-metric, stand age-40 years,
Table 4--green weight-metric, stand age-70 years,
Table 5--dry weight-metric,
stand age-40 years,
600
,
_
_
,
_
,
(A) 40-YEAR OLD STANDS
_'
_
_
,
750
.....
_
480
_
_
;
,
_
,
I
I
27,000
_
I
I
I
36,000
t
(D) 70-YEAROLDSTANDS
J
600
m
12o
15o
i
3,600
00
1
7,200
I
10,800
t
14,400
0
I
18,000
I
9,000
I
i
10,000
D=H (CM2M)
1,300
_
,
,
,
,
_
_
_
,
250
I...
,
,
,
_
,
:_
,
,
780
,
.....
Sl _<45
¢,
_
45,000
D2H (CM2M)
= .
150
¢
Q
,,,,I
260
520 _
00
9,000
18,000
27,000
SII_---60 J
36,000
J
_
50
_
100
0
45,000
4,000
D'H (CM2M)
350
J
_
_
,
J
Sl >'60
[
,,i
16,000
J
12,000
8,000
20,000
D2H (CM2M)
t
(C) 40-YEAR OLD STANDS
i
i
I
500
/J
_
l
_
_
_
v
_
,
,
,
(F) 70-YEAROLD STANDS
Sl _ 45
:3::
210
300
,,j
_
70
00
3,600
7,200
10,800
14,400
18,000
D_H (CM_M)
Figure 1.--Comparison
of allometric relation between D2H and (A) total tree dry weight for
40-year-old stands; (B) total tree dry weight for
70-year-old stands; (C) bole dry weight for 40-year-
100
0 _
9,000
'
'
18,000
_
_
27,000
'
'
36,000
_
45,000
D2H (CM_M)
old stands; (D) bole dry weight for 70-year-old
stands; (E) canopy dry weight for 40-year-old
stands; and (F) canopy dry weight for 70-year-old
stands.
Table 6--dry weight-metric, stand age-70 years,
Table 7--green
weightmEnglish,
stand age-40
years,
Table 8--green
weight--English,
stand age-70
years,
Table 9--dry weight--English, stand age-40 years,
Table 10--dry
weightnEnglish,
stand age-70
years,
600
,
_
i
;
i
,
With d.b.h.-dry weight as the variables, differences among sites were so small (fig. 2) that the
individual curves provided little additional resolution and the common regression in table 2 was used
to generate the valuesin table 11.
The term forest residuals applies to recoverable
and usable materials left in the forest followingharvest. Equations
presented in table 12 can be used to
,
750
(A) 4D-YEAR OLD STANDS
"-
J
i
f
,
,
i
(D) 70-YEAR OLD STANDS
480-
00
5
10
15
20
D.B.H
1,300
,
;
i
,
25
30
450
00
35
,
_
/
15
i
20
,
s,: _- ss
I
25
D.B.H.
250
,
i
10
5
40
(CM)
_
i
S
//
i
_
//
600
_
i
I
30
I
35
1
40
145
50
(CM)
....
,
i
_"
_- 200
(B) 70-YEAR OLD STANDS
_
(E) 40-YEAR OLD STANDS
150
Q
Q
_
s2o
00
lO0
_
S
10
lS
2O
25
30
3S
....
40
i
4S
s,_>6o
00
5i
_
10
15
I
50
20
i
25
i
30
I
35
.J.B.H. (CM)
D.B.H (CM)
i
(C) 40-YEAR OLD STANDS
_.
!
i
i
i
i
i
i
25
30
35
40
(F) 70-YEAR OLD STANDS
210
Q
7o
0
_ Ioo
5
10
15
D.B.H.
20
25
50
35
(CM)
Figure 2.nAllometric
relations between d.b.h, and
(A) total tree dry weight ['or 40-year-old stands;
(B) total tree dry weight ['or 70-year-old stands; (C)
bole dry weight [.or 40-year-old stands; (D) bole
0
5
10
15
20
D.B.H.
45
(CM)
dry weight for 70-year-old stands; (E) total canopy
['or40-year-old stands; and (F) total canopy ['or70year-old stands.
predict residual green weight
including canopy weight.
above a 4-inch top,
__
_
Y--,._,.
o_,x
Sy.x = 1¢25
/
C.V. OF Y : 7.S
Rz= .964
N=34
.
"
BASAL
AREA(M'VHA)
xMEANSTANDHEIGHT(M)
Figure 4.--Stand
dry weight expressed as a linear
function of mean stand height and stand basal
area for forests dominated by red maple.
merchantable
weight (above 1-foot stump to a 4-inch
top) in a full-tree harvest,
weight of stump, bole, and canopy), estimates ofmerchantable stem weight to various top diameters (in-
In addition to estimates of individual tree weight,
weight yields can be estimated
from stand measurements. Stand weights were estimated as a function
of stand basal area (B) and average total stand height
(H), and were expressed as a composite index (BH)
in a linear regression (fig. 4). Stand estimates were
derived by summing individual
tree estimates on 321,000 m 2 plots located on the six sample sites. In-
side bark) can be obtained by applying the ratios of
merchantable
weight:total
weight presented
in figure 5. These asymptotic
equations estimate the pro-
dividual
developed
in our study
applied totree
red regressions
maple. Published
regressions
were were
utilized for the other species (Zavitkovski 1971, Crow
1977). From
_"_
50
,o
u.
°"
_. 30
i
""
estimates
of total
stand
weight
(dry
_(29)
|
(18)
(5)
(14)
(10)
(7)
t
(9)
_10
oCQ250
?_
/
The percentage of total weight represented by residual material differs greatly with tree size (fig. 3).
The percentage
of residual weight declines rapidly
as tree size increases and it becomes constant at 2224 percent in the 18 to 26 cm d.b.h, range. The increase observed for the largest size classes reflects
the two-aged nature of most second-growth hardwood stands. The second-growth
stands originated
in most part from commercial clearcuts in which a
number of smaller stems or culls were not cut. As
dominants in the new stand, these residual trees
often developed large crowns and thus have large
residual weights. On the average, approximately a
30 percent increase in harvest yield would result for
red maple if residual weight is harvested along with
,
,
/
•
_ _o
_ ,,
_Q ,00
..
~_Y,,sT,,os
._ "
Q
o
'
loo
'
2oo
_
4oo'
s_)
00o'
7oo'
aoo'
00o'
1,00o
•portions of merchantable
weight as a function of average stand diameter and merchantable
top diameter.
For example, a stand with 35 m2/ha (152 ft2/a) of
basal area and a mean height (based on dominants
and codominants)
of 21 m (69 ft) has an estimated
aboveground stand weight'equal to 238 mt/ha (aboveground stand dry weight = 44.339 + 0.263 (735)
om figure 4). Given an average stand diameter of
8.5 inches and a 4-inch utilization limit, the ratio of
merchantable weightto total dry weight obtained in
figure 5 is 0.66. Thus, 0.66 x 238 = 157 mt/ha (70
short tons/a) represents the merchantable dry weight
of the stand.
sl
_.8
2 ,NCHE
_"
_
o.,.,.(c,)
Figure 3.--Residual biomass as a percentage of total
aboveground biomass presented as mean with +_
14
16
18
20
22
214 26
34
36
1SD 110by 12diameter
class
(e.g.
>t 10 <28 123_)cm312d.b.h
....
).
Values in parentheses represent number of samples
in diameter class. Residual biomass is defined as
tops above 4-inch diameter inside bark, branches,
and foliage,
|_
_.if
--
_
4
8
10
,
AVERAGE
STAND
DIAMETER
(INCHES)
Figure 5.--The ratio of merchantable weight to total
aboveground dry weight expressed as a function of
average stand d.b.h, and top diameter inside bark.
Regression
equations
for estimating
volume did
not differ significantly
among the sample sites, and
thus a single predictor was developed for all sites,
Stem volume inside bark and outside bark as well
as volume inside bark to 8-inch and 4-inch tops can
be estimated using the equations in table 13. The
equation for volume to an 8-inch top is based on a
variable length stem. Volume estimates to a 4-inch
top are based on full 100-inch sticks, with a minimum of 4-inches inside bark for the top 100-inch
stick,
Crow, T. R. Comparing
biomass regressions
by site
and stand age for red maple. Can. J. For. Res. (in
press.)
Draper, N.; Smith, H. Applied regression
analysis.
2nd ed. New York: John Wiley and Sons; 1981.
709 p.
Jacobs, M. W.; Cunia, T. Use of dummy variables to
harmonize tree biomass tables. Can. J. For. Res.
10: 483-490; 1980.
Schwandt, D. L. Asymptotic
regression with vector
parameters. Res. Note 28. L'Anse,MI: Michigan
Technological University, Ford Forestry Center;
1979.
lop.
LITERATURE
CITED
Beauchamp,
J. J.; Olson, J. S. Corrections for bias
in regression estimates
after logarithmic transformation. Ecology 54: 1403-1407; 1973.
Crow, T. R. Biomass and production regressions for
trees and woody shrubs common to the Enterprise
Forest. In: The Enterprise,
Wisconsin, Radiation
Forest, Radioecological
Studies. Washington, D.C:
ERDA; 1977: 63-67.
Table 1.--Characteristics
Snedecor, G. W.; Cochran, W. G. Statistical
Methods.
6th ed. Ames, IA: Iowa State University Press;
1967.
593p.
Young, H. E. Growth, yield, and inventory in terms
of biomass.
In: Proceedings,
IUFRO Biomass
Studies, IUFRO Working PartyS4.01-4.
Vancouver, B.C: Aug. 20-24, 1973; Orone, ME: University
of Maine; 1974: 1-9.
Zavitkovski,
J. Dry weight and leaf area of aspen
trees in northern
Wisconsin.
In: Forest Biomass
Studies. Orono, ME: University of Maine; 1971:
193-205.
of sample stands and sample trees
Sample trees--red
Standlocation
D.b.h.
Stand Site
Red
Other
age index
1 maple species Mean
Range
Wetmore, MI
SugarBush, MI
EagleRiver,Wl
RockRiver, MI
Argonne, Wl
Silver Falls, MI
Years
40
40
40
70
70
70
'Site Index-feet
at age 50.
<45
50-55
>160
_<45
50-55
i>60
---Stemsha............
685
537
13.7
564
412
13.7
483
407
17.1
607
41
24.0
643
167
20.5
478
305
28.5
maple
Totalheight
Mean
cm....................
10.0-26.6
13.85
10.0-24.6
13.83
10.0-33.2
17.70
10.4-46.1
19.42
10.5-36.2
19.74
14.0-52.2
24.92
Range
m...........
12.63-16.60
12.23-15.90
13.65-20.74
12.14-22.65
15.10-23.10
18.08-26.84
Table2.--General biomasspredictorsfor red maple in the Lake States (regressionmodel:lnY =a + blnX; In = natural
logarithms; N= 150; where Y= weight, X= d.b.h, or D2H)
Dependent
variable
'
Independent Intercept
variable
(a)
Dry Weight-kilograms
Slope
(b)
r2
SvxI
Correction
factor
2
Totaltree
Bolewood
Bolebark
Totalbole
Leaves
Branches
Totalcanopy
D.b.h.(cm)
D.b.h.
D.b.h.
D.b.h.
D.b.h.
D.b.h.
D.b.h.
-1.721
-1.833
-3.207
-1.637
-3.288
-4.899
-4.385
2.334
2.234
1.985
2.207
1.540
2.831
2.701
0.98
.97
.95
.97
.54
.85
.84
0.116
.152
.186
.150
.569
.479
.471
1.007
1.012
1.017
1.011
1.173
1.120
1.116
Totaltree
Bolewood
Bolebark
Totalbole
Leaves
Branches
Totalcanopy
D2H(cm2m)
D2H
D2H
D2H
D2H
D2H
D2H
-3.008
-3.158
-4.404
-2.943
-3.648
-6.128
-5.539
.928
.898
.801
.888
.556
1.087
1.035
.98
.99
.97
.99
.44
.79
.77
.139
.104
.142
.099
.627
.568
.559
1.009
1.005
1.010
1.005
1.213
1.173
1.166
DryWeight-pounds
Totaltree
Bolewood
Bolebark
Totalbole
Leaves
Branches
Totalcanopy
D.b.h.(inches)
D.b.h.
D.b.h.
D.b.h.
D.b.h.
D.b.h.
D.b.h.
1.245
1.040
-0.566
1.211
-1.062
-1.469
-1.077
2.334
2.234
1.985
2.206
1.540
2.831
2.701
.98
.97
.95
.97
.54
.85
.84
.116
.152
.186
.150
.569
.479
.471
1.007
1.012
1.017
1.011
1.173
1.120
1.116
Totaltree
Bolewood
Bolebark
Total
bole
Leaves
Branches
Totalcanopy
D2H(infft)
D2H
D2H
D2H
D2H
D2H
D2H
-1.545
-1.715
-3.038
-1.513
-2.434
-4.524
-3.976
.923
.894
.797
.883
.550
1.078
1.027
.97
.98
.96
.98
.43
.77
.76
.169
.135
.161
.131
.631
.585
.574
1.014
1 009
1 129
1 008
1 217
1 184
1 176
Green
Weight-kilograms
Totaltree
Totalbole
Branches
Leaves
Totalcanopy
D.b.h.(cm)
D.b.h.
D.b.h.
D.b.h.
D.b.h.
-1.249
-1.123
-4.712
-2.617
-3.942
2.320
2.177
2.885
1.592
2.688
.99
.93
.86
.58
.85
.112
.239
.464
.537
.459
1.006
1.029
1.112
1.153
1.109
Totaltree
Totalbole
Branches
Leaves
Totalcanopy
D2H(cm2m)
D2H
D2H
D2H
D2H
-2.539
-2.427
-6.005
-3.026
-5.096
.924
.878
1.113
.579
1.031
.98
.95
.80
.48
.78
.127
.204
.550
.597
.546
1.008
1.021
1.161
1.192
1.158
.............
........
(Table2 continuedon nextpage)
(Table 2 continued)
Dependent
variable
Totaltree
Totalbole
Branches
Leaves
Totalcanopy
Independent
Intercept
variable
(a)
Green Weight-pounds
D.b.h.(inches)
D.b.h.
D.b.h.
D.b.h.
D.b.h.
1.705
1.697
-1.232
-0.343
-0.645
Slope
(b)
r_
S,.,1
2.320
2.177
2.885
1.592
2.688
.99
.93
.86
.58
.85
.112
.239
.464
.537
.459
Totaltree
D2H(infft)
-1.086
.920
.97
.154
Totalbole
D2H
-1.014
.875
.94
.216
Branches
D2H
-4.385
1.104
.79
.567
Leaves
D2H
-1.792
.573
.47
.603
Totalcanopy
D2H
-3.537
1.023
.77
.561
'Standard error estimate in log, form.
^
2Correction
forbiasinherent
inapplying
logarithmic
transformations;
Y,,j= (exp(a
+b.lnx)).K
(Beauchamp
andOlson
1973).
Correction
factor
_
1.006
1.029
1.112
1.153
1.109
1.018
1.023
1.172
1.196
1.168
Table 3.--Total tree green weight of red maple trees
(stand age _ 40 years)
Table 4.--Total tree green weight of red maple trees
(stand age -_ 70)
(Inkilograms)
Totaltree height(meters)
D.b.h.
(cm)
12
14
16
18
20
22
<_45EQUATION:
Logo
(totaltreewt)= -2.888+0.975
Logo
(D2H)
(Inkilograms)
Totaltree height(meters)
D.b.h.
(cm)
16
18
20
22
24
26
SI_<45EQUATION:
Log,(totaltreewt)= -3.211+ 1.002
Logo
(D2H)
10
12
14
16
18
20
22
24
26
28
30
56
80
108
140
176
216
260
309
361
417
477
65
93
125
163
205
251
303
359
419
484
554
74
106
143
185
233
286
345
408
477
552
631
83
119
160
208
261
321
387
458
536
619
708
92
131
178
230
290
356
429
508
594
686
785
101
144
195
253
318
391
470
557
651
753
861
S150-55
EQUATION:
Logo(total
treewt)= -2.933+0.975
Logo
(D2H)
10
12
14
16
18
20
22
24
26
28
30
54
76
103
134
168
207
249
295
345
398
456
62
89
103
155
196
240
289
343
401
463
530
71
101
137
177
223
274
330
391
456
527
603
79
113
153
199
250
307
370
438
512
592
677
88
126
170
220
277
340
410
485
567
656
750
97
138
186
242
304
373
450
533
623
720
823
_>60EQUATION:
Logo
(totaltreewt)= -2.978+ 0.975
Logo(D2H)
10
12
14
16
18
20
22
24
26
28
30
51
73
99
128
161
198
238
282
330
381
436
59
85
115
149
187
230
277
328
383
443
506
68
97
131
169
213
262
315
373
436
504
577
76
108
146
190
239
293
353
419
490
566
647
84
120
162
210
265
325
392
464
542
627
717
92
132
178
231
291
357
430
509
595
688
787
14
16
18
20
22
24
26
28
30
32
34
128
168
213
263
318
378
444
515
592
673
760
145
189
239
295
358
426
500
580
666
758
856
161
177 193 209
210 231 252 273
266
293 319 346
328 361 394 427
397 437 477 517
473 521 568 615
556 611 667 723
644 709 774 838
740 814 888 963
842 927 1011 1095
951 1046 1142 1237
S150-55
EQUATION:
Log,(total
treewt)= -3.286+1.002
Logo
(D2H)
14
16
18
20
22
24
26
28
30
32
34
119
156
197
244
295
351
412
478
549
.625
706
134
175
222
274
332
395
464
538
618
703
794
149
195
247
305
369
439
515
598
687
781
882
164 179 194
214 234 253
271 296 321
335 366 396
406 443 480
483 527 571
567 619 670
658 718 778
755 824 893
860 938 1016
971 1059 1148
SII>60EQUATION:
Log,(totaltreewt)= -3.361+ 1.002
Log,(D2H)
14
16
18
20
22
24
26
28
30
32
34
111
145
183
226
274
326
382
444
509
580
655
124
163
206
254
308
366
430
499
573
652
737
138
181
229
283
342
407
478
555
637
725
819
152
199
252
311
376
448
526
610
701
798
901
166 180
217 235
275 298
339 368
411 445
489 530
574 622
666 722
765 828
870 943
983 1065
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r.nIx_.I_.
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0
Table 11.--Total tree weight--d.b.h. (N= 150)
Green
weight
1
Equations:
Log.(totaltreewt-kg)= -1.249+ 2.320log.
D.b.h.-cm)
og.(totaltreewt-lbs)= 1.705+ 2.320log°
(D.b.h.-in.)
D.b.h.
Weight
D.b.h.
Weight
cm
kg
in.
Ibs
10
60
4
138
12
92
5
231
14
132
6
353
16
179
7
505
18
236
8
689
20
301
9
905
22
24
26
28
30
32
34
36
38
40
42
375
10
1
459
11
1 156
442
553
12
1 765
657
13
2 125
771
14
2 524
896
15
2,962
1,031
16
3 440
1,177
17
3 960
1,334
18
4 522
1,503
19
5,126
1,683
20
5,774
Dryweight
1
Equations:
Log.(totaltreewt-kg)= -1.721+ 2.334Log.
(D.b.h.-cm)
Log,(totaltreewt-lbs)= 1.245+ 2.334Log°
(D.b.h.-in.)
D.b.h.
Weight
D.b.h.
Weight
Table 12.--Residual weight (green) assuming 4 inch
topdiameter inside bark; residue = canopy weight
+ bole weight above4-inch top
Stand
age/SI
Equations
1
Y = green weight (kg); X = d.b.h. (cm) 2
40_<45
4050-55
40>i 60
70_<45
7050-55
70I>60
InY =
InY =
InY=
InY=
InY=
InY=
-0.903+ 1.811In D.b.h.
O.111+ 1.395InD.b.h.
-1.264+ 1.909InD.b.h.
-2.512+ 2.338InD.b.h.
-1.746+2.044 InD.b.h.
-4.385+ 2.801InD.b.h.
Y = greenweight(kg);X = D2H(cm2m)
2
40 _<45
4050-55
40 i> 60
70_<45
7050-55
70 1>60
InY=
InY=
InY=
InY=
InY=
InY=
-2.533+0.811 In02H
-0.895+0.5951nD2H
-2.555+0.786 InD2H
-4.179+ 0.975InD2H
-3.492+ 0.876InD2H
-6.769+ 1.190InD2H
'In = naturallogarithms,basee.
2Forconversionto Englishunits:
kg x 2.2046 = pounds
cmx0.3937= inches
mx3.2808= feet
cm
kg
in.
Ibs
10
39
4
89
12
59
5
150
14
85
6
229
16
116
7
328
18
153
8
448
20
196
9
590
22
245
10
754
24
300
11
943
26
361
12
1,155
28
430
13
1,392
30
505
14
1,655
32
587
15
1,944
34
676
16
2,260
36
773
17
2,604
38
877
18
2,975
40
988
19
3,375
42
1,107
20
3,805
'Correction
factors
have
b_enapplied
toweight
estimates;
1.007.
13
Table 13.--Regression equations for estimating stem
volume of red maples; Y = cubic volume in m3
Correction
Equation
1
r2
S_-x factor(K)2
Y = volume(m3)outsidebark-total stem
X -- d.b.h. (cm)
sample number (N) = 331
Y - -0.012+0.00075(X
2) 0.92 0.085
InY= -7.900+2.207(Inx)
.95 .207
1.022
Y = volume (m 3) outside bark-total stem
X -- D2H (cm2m)
N = 331
Y = 0.042+0.000031(X)
.89 .097
InY = -9.403+0.910(INX)
.95
.194
1.019
Y = volume (m 3) inside bark-total stem
X = d.b.h. (cm)
N = 331
Y - -0.011+ 0.00067(X2) .91 .075
InY= -8.210+2.271(INX) .93 .248
1.031
Y = volume (m 3) inside bark-total stem
X = D2H(cm2m)
N = 331
Y = 0.037+0.000028(X)
.90 .084
InY= -9.759+0.937(INX) .94 .236
1.028
Y = volume (m 3) inside bark-above
1-ft stump to 8-inch
top
X = d.b.h. (cm)
N = 84
Y = -0.181+0.000577(X 2) .86 .096
InY= -12.544+3.338(INX) .83 .277
1.038
Y = volume (m 3) inside bark-above
1-ft stump to 8-inch
top
X = D2H (cm2m 2)
N = 84
Y = -0.108+0.000023(X) .86 .096
InY=-15.391+1.437(INX) .82 .289
1.042
Y = volume(m3)insidebark-above1-ftstumpto4-inch
top
X = d.b.h. (cm)
N = 262
Y =-0.037+0.000057(X 2) .92 .064
InY= -9.967+2.732(INX) .89 .319
1.052
Y = volume (m 3) inside bark-above
1-ft stump to 4-inch
top
X = D2H(cm2m)
N = 262
Y = 0.0052+0.000024(X) .93 .060
InY=-11.970+1.142(InX) .90 .308
1.048
1In = Loge
2Yadj
= (exp(a
+ b.lnX))-K"
14
u.s.
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