United States 

Department of 

Agriculture Estimating Northern Red Oak 

Forest Service Site-Index Class from Total 

,ore, Height and Diameter of Experiment Station 

NE-RP-605 Dominant and Codominant 

Trees in Central Appalachian 

Hardwood Stands 

Neil I. Lamson 
Abstract 

Northern red oak site-index (SI) class is estimated using height and diameter of 

dominant and codominant trees for five Appalachian hardwood species. Methods 

for predicting total height as a function of diameter are presented. Because the 

total height of 4- and 6-inch trees varies less than 5 feet for the three northern 

red oak SI classes, use trees that are at least 8 inches in d.b.h. when estimating 

site class. 

The Author 

NEIL I. LAMSON, research forester, received B.S. and M.S. degrees in silviculture and forest soils, respectively, from the State University of New York, College 

of Environmental Science and Forestry, Syracuse. He joined the USDA Forest 

Service, State and Private Forestry, in 1972. Currently he is engaged in timber 

management research at the Northeastern Forest Experiment Station's Timber 

and Watershed Laboratory at Parsons, West Virginia. 

Manuscript received for publication January 13, 1987 

Northeastern Forest Experiment Station 

370 Reed Road, Broomall, PA 19008 

August 1987 
Introduction 

Determining site quality is one of the first steps in managing forest land. Once site quality is known, growth of wood 

products can be estimated and various forest management 

practices evaluated. For eastern hardwoods, the generally 

accepted method for estimating site quality is site index 

(SI) based on the 50-year height growth of dominant and 

codominant trees (Carmean 1975; Schnur 1937). Yield 

tables for managed and unmanaged stands have been 

developed for most of the hardwood forest types (Gingrich 

1971 ; Leak and Filip 1970). Northern red oak (Quercus 

rubra L.) is one of the most widely used eastern hardwood 

SI species because it occurs over much of the eastern 

hardwood region and is found over a relatively wide range 

of site quality within most forest types (Fowells 1965). 

Site index based on height over age has been 'determined 

for several upland hardwood species. But difficulties arise 

in determining the age of trees. Hardwoods are difficult to 

bore and the pith often is missed because of 

unsymmetrical radial growth. Also, slow-growing trees are 

difficult to age without magnification. 

To avoid the problem of determining age, Stout and 

Shumway (1982) and Reinhardt (1983) described methods 

of estimating SI using height and diameter of dominant and 

codominant trees. This paper reports heightldiameter relationships for five central Appalachian species and explains 

how to use height and diameter of dominant and codominant trees to estimate northern red oak Sl class. 

Methods 

Fifty-six even-aged stands 20 to 80 years old were selected 

for study. All stands were located in north-central West 

Virginia within 25 miles of Parsons. Stand size ranged from 

5 to 15 acres. Site index was estimated using heightlage 

relationships of northern red oaks present in each stand 

(Schnur 1937). Within each stand, 10 to 60 dominant or 

codominant northern red oak, red maple (Acer rubrum L.), 

sugar maple (Acer saccharum Marsh.), yellow-poplar 

(Liriodendron tulipifera L.), or black cherry (Prunus serotina 

Ehrh.) trees that showed no outward signs of suppression 

or damage from fire, insects, or disease were selected for 

study. 

Total height and diameter at 4.5 feet (d.b.h.) were measured on 2,550 study trees. Height was measured using a 

telescopic measuring pole or Relaskop. Diameter ranged 

from 3.0 to 38.1 inches and total height ranged from 15 to 

115 feet. 

Data on tree height and diameter were grouped by 10-footstand northern red oak SI class: 60 for 56 to 65 feet, 70 for 

66 to 75 feet, and 80 for 76 to 85 feet. 

Following Stout and Shumway (1982), data for each 

specieslsite index group were fitted to the equation: 

Ln (H) = Ln (4.5 + a(l - EXP(- bD))) 

where H = total height 

D = diameter at breast height (4.5 feet) 

a = coefficient for the asymptote 

b = slope coefficient 

Ln = napierian logarithm 

Results and Discussion 

Asymptote and slope coefficients are shown in Table 1. 

Standard errors for the asymptote coefficients ranged from 

1.61 3 to 13.460; for slope coefficients, standard errors 

ranged from 0.003 to 0.018. 

These equations were used to estimate total height of 

dominant and codominant trees by 2-inch diameter class 

for each 10-foot SI class and species (Table 2). 

Using the measured height and diameter, Table 2 was then 

used to assign each of the original 2,550 trees an SI class. 

The proportion of trees classified correctly is shown in 

Table 3. For simplification, the diameter classes are combined into three groups. About two-thirds of the trees were 

classified correctly as the classification improved with 

increasing diameter. 

It is common to determine height and age of trees to estimate site index. When standing trees are used, workers 

commonly use an increment borer to extract a core and 

then count annual rings to obtain the age. Difficulties arise 

when the core does not include the pith because the tree is 

too large or unsymetrical. Also, it is difficult to detect 

annual rings of species such as sugar maple, or to count 

annual rings of slow-growing trees. Such difficulties are 

eliminated when total height and diameter are used to 

estimate SI class. 

The use of heightldiameter curves to estimate SI probably 

is accurate only when only dominant or codominant trees 

are used and -SI is estimated to the nearest 10-foot class. 

This method should not be used with trees of lower crown 

classes or used to estimate SI in smaller than 10-foot 

classes. 

When using Table 2, SI should be estimated to the nearest 

10-foot class because the data used to compute the regression were grouped by 10-foot SI class. For example, if a 

codominant red oak tree is 14 inches d.b.h. and 80 feet 

tall, the estimated northern red oak SI class would be 70 

feet. 
Table 1.-Number of trees measured, values of asymptote (a) and 

slope (b) coefficients, and associated standard errors 

Site-index No. of trees 

Species class measured a S E b SE 

Red oak 60 

70 

80 

Yellow-poplar 70 

80 

Black cherry 60 

70 

80 

Sugar maple 70 

80 

Red maple 60 

70 

80 

Table 2.-Estimated total height of dominant and codominant trees 

by diameter class, species, and northern red oak SI class 

(coefficients are from Table 1) 

Yellow- Black Sugar 

D.b.h. Red oak poplar cherry maple Red maple 

class SI S1 SI SI SI SI SI SI SI SI SI SI SI 

(inches) 60 70 80 70 80 60 70 80 70 80 60 70 80 
Table 3.-Proportion of correctly classified trees 

of five Appalachian hardwood species 

(values are from Table 2) 

010 of trees 

D.b.h. No. of classified 

Species groupa observations correctly 

Red oak 1 

2 

3 

Yellow-poplar 1 

2 

3 

Black cherry 1 

2 

3 

Sugar maple 1 

2 

3 

Red maple 1 

2 

3 

a 1 = 4 to 8 inches; 2 = 10 to 16 inches; 3 = 18 + inches. 

The height1d.b.h. formulae shown in Table 1 will be useful 

in estimating volume as a function of diameter and total 

height (Martin 1981). This should aid in the development of 

growth and yield models for mixed Appalachian hardwood 

stands where tree species and d.b.h. are observed and 

total height is estimated. 

There is little variation in the estimated height of small 

trees. For example, the total height of trees 4 inches d.b.h. 

ranges from 36 to 41 feet for the five species across the 

three site classes (Table 2). Similarly, total height for 6-inch 

trees ranges from 47 to 53 feet. Therefore, to estimate site 

class using these data, use trees at least 8 inches d.b.h. 

The larger the trees, the more accurate will be the estimated site class. 

Literature Cited 

Carmean, W. H. 1975. Forest site quality evaluation in 

the United States. Advances in Agronomy. 

27: 209-269. 

Fowells, H. A., compiler. 1965. Silvics of forest trees of 

the United States. Agric. Handb. 271. Washington, 

DC: U.S. Department of Agriculture. p. 588-592. 

Gingrich, Samuel F. 1971. Management of young and 

intermediate stands of upland hardwoods. Res. Pap. 

NE-195. Upper Darby, PA: U.S. Department of Agriculture, Forest Service, Northeastern Forest Experiment 

Station. 26 p. 

Leak, William B.; Filip, Stanley M. 1970. Cutting strategies 

and timber yields. Res. Pap. NE-153. Upper Darby, 

PA: U.S. Department of Agriculture, Forest Service, 

Northeastern Forest Experiment Station. 19 p. 

Martin, A. Jeff. 1981. Taper and volume equations for 

selected Appalachian hardwood species. Res. Pap. 

NE-490. Broomall, PA: U.S. Department of Agriculture, 

Forest Service, Northeastern Forest Experiment Station. 

22 p. 

Reinhardt, Elizabeth. 1983. Using heightldiameter curves 

to estimate SI in old-growth western larch stands. 

Res. Note 20. Missoula, MT: Montana Forest and Conservation Experiment Station, School of Forestry, University of Montana. 4 p. 

Stout, Benjamin B.; Shumway, Durland L. 1982. Site quality estimation using height and diameter. Forest Science. 28(3): 639-645. 

Schnur, G. Luther. 1937. Yield, stand, and volume tables 

for even-aged upland oak forests. Tech. Bull. 560. 

Washington, DC: US. Department of Agriculture. 87 p. 

Dominant and codominant red oak, black cherry, and red 

maple trees will be about 9 inches d.b.h. at stand age 50 

on SI class 60 areas (Table 2). Dominants and codominants at stand age 50 average about 10 inches d.b.h. on SI 

class 70 areas and about 11 inches d.b.h. on SI class 80 

areas. These are reasonable values for stands in the central Appalachian hardwood region. _., 
Lamson, Neil 1. 1987. Estimating northern red oak site-index class from 

total height and diameter of dominant and codominant trees in central 

Appalachian hardwood stands. NE-RP-605. Broomall, PA: US. Department of Agriculture, Forest Service, Northeastern Forest Experiment 

Station. 3 p. 

Northern red oak site-index (SI) class is estimated using height and diameter of dominant and codominant trees for five Appalachian hardwood species. Methods for predicting total height as a function of diameter are presented. Because total height of 4- and 6-inch trees varies less than 5 feet 

for the three northern red oak SI classes, use trees that are at least 8 

inches in d.b.h. when estimating site class. 

ODC 541 :522.31 (Appalachian hardwoods):176.1 

Keywords: Site quality; height curves 

*U.S.COVERNNENT PRINTING OFFICE:1987-748-076:40033 

i 

I 
Headquarters of the Northeastern Forest Experiment Station are in Broomall, Pa. 

Field laboratories are maintained at: 

Amherst, Massachusetts, in cooperation with the University of Massachusetts. 

Berea, Kentucky, in cooperation with Berea College. 

Burlington, Vermont, in cooperation with the University of Vermont. 

Delaware, Ohio. 

Durham, New Hampshire, in cooperation with the University of New Hampshire. 

Hamden, Connecticut, in cooperation with Yale University. 

Morgantown, West Virginia, in cooperation with West Virginia University, 

Morgantown. 

Orono, Maine, in cooperation with the University of Maine, Orono. 

Parsons, West Virginia. 

Princeton, West Virginia. 

Syracuse, New York, in cooperation with the State University of New York 

College of Environmental Sciences and Forestry at Syracuse University, 

Syracuse. 

U~iversity Park, Pennsylvania, in cooperation with the Pennsylvania State 

University. 

Warren, Pennsylvania. 

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should be reported to the Secretary of Agriculture, Washington, DC 20250.