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Northeastern Forest
Experiment Station —.z

ESEARCH NOTE

1979

NE-275

FOREST SERVICE, U.S. DEPARTMENT OF AGRICULTURE, 370 REED ROAD, BROOMALL, PA. 19008

TREE GRADE DISTRIBUTION IN ALLEGHENY HARDWOODS

—RICHARD L. ERNST

Research Forester

—DAVID A. MARQUIS
Principal Research Silviculturist
Northeastern Forest Experiment Station
Warren, Pennsylvania

Abstract. Estimates of the distribution of tree grades by diameter
class were developed for six hardwood species on the Allegheny
Plateau. These estimates can be used to calculate present and pro-
jected stand values when actual tree grade measurements are not

available.

INTRODUCTION

From information developed as part of a
series of financial maturity studies in north-
eastern hardwoods it is possible to calculate
the value of a stand if one has data on the
numbers of trees by species, diameter at
breast height (dbh), merchantable height, and
tree grade. (DeBald and Mendel 1976a; Men-
del et al.; DeBald and Mendel 1976b; Grisez
and Mendel 1972). Unfortunately, informa-
tion on tree grade often is not included in data
collected during stand inventories, or in data
developed from yield tables or stand growth
simulators.

However, if tree grade, which is an indica-
tor of suitability for various wood products,
can be correlated with size class for each spe-
cies, estimates of stand quality and value can
be made for typical stands where specific tree

grade data is unavailable. We collected data
to develop empirical tree grade distributions
by dbh and species for typical cherry-maple
stands on the Allegheny Plateau.

METHODS

Empirical grade distributions were derived
from summaries of data on species, diameter,
and tree grade. Two sources were used: tim-
ber sale cruise data from the four districts on
the Allegheny National Forest, and data from
complete inventories of seven sample stands.

The timber sale data consisted of informa-
tion on species, dbh, and tree grade for about
12,500 trees, all of which were grade 3 or bet-
ter; trees that were not at least grade 3 were
not recorded. These data were from syste-
matic samples of trees to be included in clear-
cutting sales over a 3-year period. We used
grading rules described by Hanks (1971).

Because the first data set included only
trees that were grade 3 or better, we used a
second set so that we could calculate the
probability of a tree of a given species and
diameter being at least grade 3. This second
data set was collected from complete inven-
tories of seven additional cherry-maple stands.
A total of 3,650 trees greater than 10 inches
in dbh were recorded by species and dbh, and
each tree was classified as grade 3 and better
or less than grade 3. Thus, the two data sets
provided a means of calculating—for each
diameter class and species—the probability of
a tree being grade 1 or 2 or 38.

Each of these probabilities were plotted
separately as a function of diameter for each
species. Species with similar distributions were
grouped. These groups were: (1) black cherry
and yellow-poplar; (2) sugar maple and red
maple, (3) beech and birch.

Three regression equations were developed
for each species group. Each equation related
diameter to: (1) The proportion of trees
grade 3 and better: (2) The proportion of
grade 3 and better trees that were grade 1:
and (3) The proportion of grade 3 and better
trees that were grade 3. The proportion of
grade 3 and better trees that were grade 2
was obtained by subtracting the values for
equations 2 and 3 from equation 1.

Predicted values derived from these equa-
tions were tabulated and plotted for each
species group.

RESULTS

The regression statistics for tree grade dis-
tribution and the diameter range over which
these equations are valid are shown in Tables
1-3. The lower limit is the minimum dbh re-
quirement for a particular grade. The upper

Table 1.—Regression statistics for dependent variable
of percent of trees grade 3 or better.

2 Regression u Range in
Species Equation Re Diameter
Black cherry and inches
yellow-poplar 135.5— 806.5D-} 73 10-22
Sugar maple and
red maple 140.9 — 1083.5D4 84 10.22
Beech and birch 111.9— 980.2D4 87 10-22

Table 2.—Regression statistics for dependent variable
of percent of grade 3 or better trees in grade 1.

: Regression ' Range in
SSUES Equation Xe Diameter
Black cherry and inches
yellow-poplar 127.8— 839.7D2 65 16-26
Sugar maple and
red maple 157.8—1777D4 717 16-26
Beech and birch 178.4 — 2408.3D 84 16-26

Table 3.—Regression statistics for the dependent variable
of percent of grade 3 or better trees in grade 3.

3 Regression Range in
SI0SELES Equation Be Diameter
Black cherry and inches
yellow-poplar —17.44+431.6D2 62 13-23
Sugar maple and
red maple — 31.8+ 755.9D-1 64 13-22
Beech and birch — 425+ 896.6D-1 32 13-20

limit represents the upper limits of the data.
Extrapolating beyond this upper limit gives
unreasonable results; predictions beyond the
upper limit are made by assuming the same
value as that at the upper diameter limit.
Tree grade is dependent on two major fac-
tors: tree size (diameter), and the presence
of grade stoppers such as limbs, knots, decay,
sweep, and crook. Tree size alone is a major
determinant of grade—a large percentage of
the trees qualify for the next higher grade as
soon as they reach the minimum diameter.
For example, more than 60 percent of the
black cherry and yellow-poplar trees that we
examined qualified for grades 1, 2, or 3 when
they reached the minimum diameter for those
grades. This effect of diameter thresholds used
in defining grade is evident in Figures 1 to 3.
However, species differed considerably in
the extent to which diameter alone deter-
mines grade. Only 15 to 25 percent of the
beech and birch qualified for the next higher
grade when they reached the minimum diam-
eter. Thus, grade stoppers are more common

Figure 1—Grade distribution for

|| GRADE 1

RES] GRADE 2

100 GRADE 3

90
Q 80 SS
= m fo
Z 70
z BS .

60 =
= 50 Bd =
—! oe
= bad
u 40 =
S -
= 30 ES
= Ee
nw 20

10 a

re)

15

16 1

i

in the latter species and more often limit
grade after minimum diameter has been at-
tained.

The importance of grade stoppers in beech
and birch also is evident in data for trees of
large size—well beyond minimum diameter
for grade 1 and at or near economic maturity.
For example, less than half of the 23-inch
beech and birch qualified for grade 1; but
more than 90 percent of the black cherry and
yellow-poplar qualified at that size.

The numbers of grade stoppers in individ-
ual stands may vary widely due to factors
such as density, snow bending, ice breakage,
insect or disease attack, and site conditions.
So the grade distributions reported here repre-
sent average values that one might expect in
typical stands—and the values may be in
considerable error for an individual stand.
Thus, these estimates of grade distribution
are not intended to replace tree grading but
are to be used as a management planning tool.

These data were collected, and will apply
most accurately, in second-growth cherry-

black cherry/yellow-poplar group.

18 19

DIAMETER (INCHES)

3

PERCENT OF ALL TREES IN A STAND

PERCENT OF ALL TREES IN A STAND

Figure 2—Grade distribution for red maple/sugar maple group.

106 P| GRADE 1

90 GRADE 3

80
70
60
50
40
30
20

10

Opes tit 2eee 3 14 is 1G. - Ue. Ve 1S 2OR 2 222 324 2 26
DIAMETER (INCHES)

Figure 3—Grade distribution for beech/birch group.
100

90 = GRADE 1
pee GRADE 2

80 GRADE 3

70
60
50
40
30

20

10

oe ah MSR SS 3B or TS) ID
DIAMETER (INCHES)

maple stands on the Allegheny Plateau of
northwestern Pennsylvania—stands that were
uncut or had been thinned one time. Grade
distribution is likely to be substantially dif-
ferent in stands that have been under inten-
sive management over a long period, or that
have been high-graded.

Despite these limitations, the data are use-
ful for estimating stand value for typical
stands where specific grade information is
lacking. They can be used to estimate the
financial maturity of typical stands or to
evaluate short-term value changes that might
be expected from several cutting strategies in
typical stands.

Stand values may be calculated from stand
table data by proportioning the trees in each
species-dbh class into grades. Tree value con-
version standards (Mendel et al. 1976) can
then be applied to derive a value for the en-
tire stand.

vr U.S. GOVERNMENT PRINTING OFFICE: 1979—603-011/20

LITERATURE CITED

DeBald, Paul S., Joseph J. Mendel.
1976a. An individual-tree approach to making
stand evaluations. USDA For. Serv. Res. Pap.
NE-336. 13 p.

DeBald, Paul S., Joseph J. Mendel.
1976b. Composite volume and value tables for
hardwood pulpwood. USDA For. Serv. Res.
Pap. NE-338. 43 p.

Grisez, Ted J., Joseph J. Mendel.
1972. The rate of value increase for black
cherry, red maple and white ash. USDA For.
Serv. Res. Pap. NE-321. 26 p.

Hanks, Leland F.
1971. Interim hardwood tree grades for factory
lumber. USDA For. Serv. Res. Pap. NE-199.
29 p.

Hanks, Leland F.
1976. Hardwood tree grades for factory lumber.
USDA For. Serv. Res. Pap. NE-33. 81 p.

Mendel, Joseph J., Paul S. DeBald, and Martin

E. Dale.
1976. Tree value conversion standards for
hardwood sawtimber. USDA For. Serv. Res.
Pap. NE-337. 74 p.

MANUSCRIPT RECEIVED FOR PUBLICATION 22 JANUARY 1979

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