United States 

Department of 

Agricuiture 

Forest Service 

Southeastern Forest 

Experiment Station 

Research Paper 

SE-282 

Stem Profile Equations 

for Southern Tree Species 

Alexander Clark Ill 

Ray A. Souter 

Bryce E. Schlaegel 
STEM PROFILE EQUATIONS FOR SOmImN WEE SPECIm 

U. S, Department of' Agriculture, Forest Service 

Sou theas tern Pores t hperimen t Station Research Paper SE-282 

The present page 76 should have been printed as pege 78, and 

the present page 70 should have been printed as pege 76, 

Therefore: 

(1) The present pege 76 begins (Yellw-poplar through All hardwoods 

combined) wi tll coefficients for the Appalachian Mountains, 

(2) The present pege 77 begins (All, sol! t llarrlwoods crmtined tltrougl~ 

All l~ardwoods combined) with coef ficienta for the Piedmont, 

(3) n~e present page 78 begins (Longleaf pine through All llardwoods 

combined) wit11 coefficients for the Gulf and Atlantic Coastal 

Plain. 

(4) The present pege 79 begins (Maite oak through A11 hardwoods 

combined) wi ttl coefficients Tor the Upper Coastal Plain. 
The Authors: 

Alexander Clark I11 is Wood Scientist, Utilization of 

Southern Timber, USDA Forest Service, Forestry Sciences 

Laboratory, Athens, GA. Ray A. Souter is Statistician, 

Statistics Group, USDA Forest Service, Forestry Sciences 

Laboratory, Athens, GA. Bryce E. Schlaegel is 

Mensurationist, Region 8, USDA Forest Service, Atlanta, GA. 

Southeastern Forest Experiment Station 

P.O. Box 2680 

Asheviile, North Carolina 28802 
Stem Profile Equations 

for Southern Tree Species 

Alexander Clark Ill 

Ray A. Souter 

Bryce E. Schlaegel 
Contents 

Page 

Introduction. ................................. 1 

Model Development ............................... 2 

Evaluation of Existing Models ....................... 2 

Form-Class Segmented-Profile Model for Total Height ............ 3 

Form-Class Segmented-Profile Model for Height to 

4-,7-,or9-1nchD.O.B.Top ...................... 7 

Data ....................................... 12 

Procedure. .................................. 14 

Results .................................... 15 

Summary .................................... 20 

Literaturecited ................................ 21 

Appendixes 

1 How to use form-class segmented-profile 

equations (I), (2), and(3). ..................... 23 

2 How to use form-class segmented-profile 

equations (4), (5), and(6). ..................... 27 

Tables 

1 Trees measured for development of stem-profile 

equations by species and tree size class ............... 31 

2 Accuracy of stemwood volume estimates obtained by 

using Southwide and subregional coefficients and 

segmented-profile equations. ..................... 34 

3 Inside-bark form-class segmented-profile coefficients 

for use when total height is known, for southern tree 

species and species groups ...................... 36 

4 Outside-bark form-class segmented-profile 

coefficients for use when total height is known, 

for southern tree species and species groups ............. 39 

5 Inside-bark form-class segmented-profile 

coefficients for use when height to 4-inch d.0.b. top 

is known, for southern tree species and species groups ........ 42 

6 Outside-bark form-class segmented-profile 

coefficients for use when height to 4-inch d.0.b. top 

is known, for southern tree species and species groups ..... 

7 Inside-bark form-class segmented-profile 

coefficients for use when height to 7-inch d.0.b. top 

(southern softwood species) or 9-inch d.0.b. top 

(southern hardwood species) is known ................. 48 

iii 
Outside-bark form-class segmented-profile 

coefficients for use when height to 7-inch d.0.b. top 

(southern softwood species) or ?-inch d.0.b. top 

(southern hardwood species) is known ................. 51 

Regression coefficients for estimating d.i.b. at 4.5 feet 

from d.b.h., for southern tree species and species groups. ...... 54 

Regression coefficients for estimating d.i.b. at 17.3 feet from 

d.0.b. at 17.3 feet, for southern tree species and species groups. .. 56 

Regression coefficients for estimating d.i.b. at 

17.3 feet from d.b.h. and total height, for species and 

species groups across the South and in seven subregions. ....... 58 

Regression coefficients for estimating d.0.b. at 

17.3 feet from d.b.h. and total height, for species and 

species groups across the South and in seven subregions. ....... 66 

Regression coefficients for estimating d.i.b. at 17.3 feet 

from d.b.h. and height to 4-inch d.0.b. top, for species and 

species groups across the South and in seven subregions. ....... 74 

Regression coefficients for estimating d.0.b. at 17.3 feet 

from d.b.h. and height to 4-inch d.0.b. top, for species and 

species groups across the South and in seven subregions. ....... 82 

Regression coefficients for estimating d.i.b. at 17.3 feet 

from d.b.h. and height to 7-inch d.0.b. top (softwoods) and 

height to 9-inch d.0.b. top (hardwoods), for species and 

species groups across the South and in seven subregions. ....... 90 

Regression coefficients for estimating d.0.b. at 17.3 feet 

from d.b.h. and height to 7-inch d.0.b. top (softwoods) and 

height to 9-inch d.0.b. top (hardwoods), for species and 

species groups across the South and in seven subregions. ....... 98 

Average d.i.b. at 4.0 and 7.0 inches d.0.b. (softwoods) 

andat4.0 and 9.0 inches d.0.b. (hardwoods) ............. 106 

Regression coefficients for estimating topwood ratios used 

to expand volume to a 7-inch d.0.b. top (softwoods) or to 

a 9-inch d.0.b. top (hardwoods) to volume to a 4-inch d.0.b. 

top, by species and species groups .................. 108 

Accuracy of volume estimates obtained by using form-class 

segmented-profile equations and of volume estimates obtained 

by using Max and Burkhart's segmented-profile equation. 

Accuracy based on actual and simulated field measurements 

of loblolly pine, yellow-poplar, and white oak ............ 111 

Accuracy of volume estimates obtained by using form-class 

segmented-profile equations and known d.b.h. and total 

height, known d.b.h. and height to 4-inch d.0.b. top, and 

known d.b.h. and height to 7-inch or 9-inch d.0.b. top ........ 113 
ABSTRACT 

Form-class segmented-profile equations for 58 southern tree 

species and species groups are presented. The profile equations are 

based on taper data for 13,469 trees sampled in natural stands in 

many locations across the South. The profile equations predict 

diameter at any given height, height to given diameter, and volume 

between two heights. Equation coefficients for use in estimating 

diameters and volumes inside and outside bark are presented. D.b.h. 

and total height, d.b.h. and height to 4-inch top, d.b.h. and height 

to 9-inch top (hardwoods), and d.b.h. and height to T-inch top 

(softwoods) are used as predictors. A measure of diameter at 17.3 

feet is required also, and equations are presented for estimating 

d.0.b. and d.i.b. at 17.3 feet from d.b.h. and height. Equations 

for estimating d.i.b. at 4.5 and 17.3 feet from d.o.b, are given. 

Keywords: Taper functions, volume equations, d.0.b. and 

d.i.b. equations 

The USDA Forest Service, Southern Region of the National Forest System, needs 

estimates of stemwood volume for timber sale preparation, forest inventory, and 

planning. For decades, local, hand-derived, board-foot volume tables for various 

tree species have been used to estimate merchantable stem volume. However, the 

Forest Service's new policy of expressing timber volume in cubic feet, the need to 

work with data that can be analyzed by computer, and changing utilization limits 

dictate that the Southern Region develop accurate but more flexible estimators of 

stemwood volume. Direct volume estimators can be developed for each utilization 

limit, but the variety of utilization limits in use and the frequency with which 

these limits change make direct estimation impractical, 

Stem-profile models--taper models--are flexible, accurate, easy to use in the 

age of computers, and ideally suited to meet the Forest Service's changing needs. 

Profile models predict stem diameter at any height but can be integrated to solve 

for volume to a given height or dicrmeter, This paper discusses a form-class 

segmented-profile model developed to predict the volume of southern tree species. 

Equations and coefficients for estimating stem volume inside and outside I/ bark, diameter at a given height, and height to a given diameter are presented- . The predictors used are d.b.h. and total height, d. b.h. and height to 4-inch 

diameter outside bark (d.0.b.) top, d.b.h, and height to 7-inch d.0.b. top 

(softwoods), and d.b.h. and height to 9-inch d.0.b. top (hardwoods). Coeficients 

for estimating diamter inside bark (d.i.b. ) from d.0.b. at 4.5 and 17.3 feet above 

ground are included, as are equations for estimating both d.i.b. and d.0.b. at 17.3 

feet from d.b.h. and height. Equation coefficients are presented for 58 species and 

species groups. 

L/~~~~~ data files containing coefficients presented are available on floppy disk 

from the Utilization of Southern Timber RWU, Southeastern Forest Ekperiment 

Station, Forestry Sciences Laboratory, Green Street, Athens, GA 30602. 
MODEL DEVELOPMm 

Evaluation of Existing Models 

Many forms and types of stem profile models have been published 

(Sterba 1980) and evaluated for accuracy and precision (Czaplewski and others 1~882~

Alberta Forest Service 1987; Martin 1981; Cao and others 1980). Martin (1981) 

evaluated five profile models for predicting diameter, height, and volume and found 

no single model best for all applications. He reported that the Max and Burkhart 

(1976) model was best overall. Cao and others (1980) evaluated six profile models 

for predicting diameter and ranked Max and Burkhart's segmented-profile polynomial 

model first and Cao's segmented-profile model second. Cao's segmented-profile model 

was ranked first for estimating volumes to various top diameters. A polynomial 

ratio model was ranked second, Burkhart's (1977) ratio model was third, and Max and 

Burkhart's segmented-profile model fourth. The Alberta Forest Service (1987) 

evaluated 15 stem-profile models and judged Max and Burkhart's model best because of 

its accuracy and ease of computation. 

Based on these evaluations, no one stem-profile model appears to be best for 

estimating volume, diameter, and height on the basis of measurements of standing 

trees. Therefore, three flexible stem-profile models that are reported to be 

accurate were selected for additional testing in the Southern Region. These were 

the segmented-profile polynomial models developed by Max and Burkhart and by Cao and 

others, and Schlaegel's (1983) form-class profile model. 

Max and Burkhartis model consists of three submodels that describe the neiloid 

frustum of the lower tree stem, the paraboloid frustum of the middle stem, and the 

conical shape of the upper bole. The three submodels are spliced together at two 

join points to form an overall segmented polynomial tree model. The join points are 

simply proportions of total height. The lower join point is usually close to 

one-tenth of total tree height, and the upper point is usually close to seven-tenths 

of total tree height. The Max-Burkhart equation is conditioned so that estimated 

diameter equals zero when height equals total height and so that the taper line 

proceeds smoothly and continuously from one parabolic equation to the next. Since' 

the Max-Burkhart model consists of three joined second-degree polynomials, it can be 

inverted to predict height given a diameter and integrated to estimate stem volume. 

The Cao and others model consists of three submodels that join at two points, 

Each submodel has the form of a modified Goulding and Murray (1976) model. Cao's 

model can be inverted to predict height and integrated for volume. 

Schlaegel's form-class model incorporates Girard's form class into a flexible 

profile model, Form class is included so that a single species equation can 

accurately describe trees in a range of geographic or physiographic areas, This 

model divides the stem into two segments: (1) the lower bole from stump to 17.3 

feet, and (2) the upper bole from 17.3 feet to the tip of the tree. The two segment 

models are conditioned to join and be equal at a bole height of 17.3 feet, the 

Girard form class measurement point. Schlaegel's model is also conditioned to 

assure that estimated d.i.b. equals actual d.i,b. when height is 4.5 feet, that 

estimated d.i.b. equals actual d.i.b, at 17.3 feet, and that estimated diameter is 

zero when height equals total height. 

Z/~zaplewski , R. L. ; Bechtold, W. A. ; McClure , J . P. 1988. Quantification of bias 

in stem-profile models. USDA Forest Service, SEFES unpublished report. 8 pp. 
Schlaegel's form-class profile model can be solved to estimate d.i.b. at any 

height or volume between any two heights. However, it cannot be solved directly to 

estimate height at a given diameter above 17.3 feet because the top equation does 

not have a unique solution. The measurements required to solve the form-class model 

for stem volume inside bark are d.i.b. at 4.5 feet, d.i.b. at 17.3 feet, and total 

height. Species bark-thickness equations are required for estimating d.i.b. at 4.5 

and 17.3 feet from d.0.b. 

Stem taper data collected at 4-foot intervals up the stems of approximately 100 

sawtimber-size loblolly pine, yellow-poplar, and white oak trees were used to 

conduct benchmark tests. Each of the profile models tested was developed for each 

species. The profile models were evaluated to determine how well they: 

1. estimated diameter at a given height, 

2. estimated height to a given diameter, and 

3. estimated volume between two given heights. 

The form-class profile model predicted total stem volume and volume to given 

heights more accurately than the Max-Burkhart and Cao models because it accounted 

for differences in taper as measured by form class. The form-class model also 

performed better than the other models in its ability to estimate height to a given 

diameter up to 17.3 feet. However, it cannot be used to estimate height to a given 

diameter above 17.3 feet without interactive procedures. The Max-Burkhart model 

produced negative squared diameters above the 2-inch d.0.b. top for yellow-poplar 

and white oak, and Schlaegel's model exhibited some consistent biases in the stem 

below 4.5 feet. 

Form-Class Segmented-Profile Model for Total Height 

A segmented-profile model combining the better attributes of Schlaegel's 

form-class model and Max and Burkhart's segmented-profile model was developed using 

d.b.h., diameter at 17.3 feet, and total height as the independent variables. The 

form-class segmented-profile model divides the stem into four segments: (1) butt 

(groundline to 4.5 feet), (2) lower stem (4.5 to 17.3 feet), (3) middle stem (17.3 

feet to 40 to 70 percent of total height), and (4) upper stem (40 to 70 percent of 

total height to tip of stem) (fig. 1). A Schlaegel-type equation is used to 

estimate diameter in the butt, and Schlaegel's form-class equation is used to 

estimate diameter in the lower stem. An equation of the Max-Burkhart type is used 

to estimate diameters in the middle and upper stem segments. The equation is 

quadratic for the lower segment and linear for the top segment, The segment 

equations are conditioned so that the joins between segments are continuous. The 

total height equation can be applied to trees having both d.b.h. L 5.0 inches and 

total height > 17.3 feet. 

Listed below are definitions of basic symbols, indicator variables, and 

parameters used in the profile model for predicting diameter at a given height from 

d.b.h., diameter at 17.3 feet, and total height. 

Basic S-mbols 

D = diameter at breast height (4.5 feet above ground) in inches 

F = diameter at 17.3 feet above ground (Girard's form class height) 

in inches 

H = total tree height in feet 

d = diameter at a particular height, h, in inches 

h = height above ground (associated with a particular diameter, d), in feet 
UPPER 

STEM 

MID-STEM 

LOWER 

STEM 

BUTT 

Figure I.--Schematic showing stem segments of the form-cZass 

segmented-profile model. * 
Indicator Variables 

Is = 1 if h < 4.5 

= 0 otherwise 

= 0 otherwise 

I, = 1 if h > 17.3 

= 0 otherwise 

= 0 otherwise 

Parameters 

r, c, e: regression coefficients for stem section below 4.5 feet 

p: regression coefficients for stem section between 4.5 and 17.3 feet 

a, b: regression coefficients for stem section above 17.3 feet 

The equation for predicting stem diameter (d) at a given height (h) from d.b.h. 

and total height is: 

(1-b)/a2) (a-(h-17.3)/(~-17.3) )2)110*5 (1 

2 Under the assumption that h is a decreasing function of d , the definitions for 

the indicator variables for estimating height to a given diameter are as follows: 

Indicator Variables 

2 2 

Is =lifd - >D 

= 0 otherwise 

= 0 otherwise 

= 0 otherwise 

= 0 otherwise 
Combined Variables 

G = (1-4.5/~)~ 

Height (h) at a given diameter (d) is estimated by: 

The form-class segmented-profile model based on d.b.h. and total height has 

been integrated to solve for the volume of the stem between any two heights. 

Listed below are additional basic symbols, combined variables, and indicator 

variables used in the volume equation: 

Basic Symbols 

V = stem volume between two heights, L and U, in cubic feet 

L = lower height of interest in feet 

U = upper height of interest in feet 

Combined Variables 

L1 = maximum of L and 0 

U1 = minimum of U and 4.5 

L2 = maximum of L and 4.5 

U2 = minimum of U and 17.3 

L = maximum of L and 17.3 3 

U3 = minimum of U and H 
Indicator Variables 

= 0 otherwise 

= 0 otherwise 

= 0 otherwise 

= 0 otherwise 

= 0 otherwise 

= 0 otherwise 

Stem volume (V) between any two heights is predicted by: 

Form-Class Segmented-Profile Model for Height to 49, 79, or 

9-Inch D.O.B. Top 

A profile model based on d.b.h. and height to 4-inch d.0.b. top was developed for 

each species. Also, a form-class segmented-profile model based on d.b.h. and height 

to ?-inch d.0.b. top was developed for each softwood species, and a model based on 

d.b.h. and height to g-inch d.0.b. top was developed for each hardwood species. 

The form-class segmented-profile models based on d.b.h. and height to a fixed 

d.o.b, top divide the stem into three segments: butt (groundline to 4.5 feet, lower 

stem (4.5 to 17.3 feet), and upper stem (17.3 feet to a fixed d.0.b. top). 

Schlaegel-type form-class equations are used to estimate diameter in the butt, 

lower stem, and upper stem. The segment equations are conditioned for smooth 

joins between segments. 
The form-class segmented-profile model based on d.b.h. and height to a 4-inch top 

can be applied to all trees having both d.b.h. > 5.0 inches and height to 4-inch top 

> 17.3 feet. The softwood form-class model based on d.b.h. and height to 7-inch top 

is to be applied to trees with d.b.h. > 9.0 inches and height to 7-inch top > 17.3 

feet. The hardwood form-class model based on d.b.h. and height to 9-inch top is to 

be applied to trees with d.b.h. - > 11.0 inches and height to 9-inch top > 17.3 feet. 

Listed below are definitions of basic symbols, indicator variables, and 

parameters used in the profile model for predicting diameter (d) at a given height 

(h) from d.b.h., diameter at 17.3 feet, and height to a fixed diameter top. 

Basic Symbols 

D = diameter at breast height (4.5 feet above ground) in inches 

Dx = 4 inches if outside-bark prediction is based on height to 4-inch d.0.b. 

top or = d.i.b. at 4-inch d.0.b. top for inside-bark prediction 

= 7 inches if outside-bark prediction is based on height to 7-inch d.0.b. 

top or = d.i.b. at 7-inch d.o.b. top for inside-bark prediction for 

softwood species 

= 9 inches if outside-bark prediction is based on height to 9-inch d.0.b. 

top or = d.i.b. at 9 inches d.0.b. for inside-bark prediction for 

hardwoods 

F = diameter at 17.3 feet above ground, in inches 

Hx = tree height to a 4-inch or 7-inch d.0.b. top for softwoods, or height to 

a 9-inch d.0.b. top for hardwoods, in feet 

d = diameter at a particular height, h, in inches 

h = height above ground (associated with a particular diameter, d) in feet 

Indicator Variables 

= 0 otherwise 

= 0 otherwise 

= 0 otherwise 

Parameters 

r, c, e: regression coefficients for stem section below 4.5 feet 

p: regression coefficients for stem section between 4.5 and 17.3 feet 

q: regression coefficients for stem section above 17.3 feet 
The equation for predicting stem diameter (d) at a given height (h) from d.b.h., 

diameter at 17.3 feet, and height to a fixed d.0.b. is: 

Below are listed the indicator variables and combined variables used in the 

equation for estimating height (h) to a given diameter (d). 

Indicator Variables 

2 2 Is=lifd LD 

= 0 otherwise 

= 0 otherwise 

= 0 otherwise 

Combined Variables 

The equation for estimating height (h) at a given diameter (d) from d.b.h., 

diameter at 17.3 feet, and height to a fixed-d.0.b. top is: 
The form-class segmented-profile model has been integrated to solve for 

volume of the stem between any two heights. Listed below are additional basic 

symbols, combined variables, and indicator variables used in the volume equation 

based on d.b.h., diameter at 17.3 feet, and height to a fixed-d.0.b. top: 

Basic Symbols 

V = stem volume between two heights, L and U, in cubic feet 

L = lower height of interest in feet 

U = upper height of interest in feet 

Combined Variables 

L1 = maximum of L and 0 

U1 = minimum of U and 4.5 

L2 = maximum of L and 4.5 

U2 = minimum of U and 17.3 

L3 = maximum of L and 17.3 

U3 = minimum of U and Hx 

Indicator Variables 

I, = 1 if L < 4.5 

= 0 otherwise 

= 0 otherwise 

I = 1 if U > 4.5 3 

= 0 otherwise 

= 0 otherwise 

The equation for predicting stem volume (V) between any two heights from d.b.h., 

diameter at 17.3 feet, and height to a fixed-d.0.b. top is: 
When solving for a diameter inside bark (d), a height (h) to an inside-bark 

diameter (d), or a stem volume inside bark (V), use inside-bark values for D and F 

and inside-bark parameters in equations (1-6). 

Linear equations for estimating d.i.b. at 4.5 feet from d.0.b. at 4.5 feet were 

developed for each species and species group. The equations have the form: 

DIBD = a + b(D) (7) 

where 

DIBD - d. i . b . at breast height (4.5 feet above ground) , in inches 

D = d.0.b. at breast height, in inches (d.b.h.) 

a and b - regression coefficients , 

D.0.b. at 17.3 feet above ground can be estimated visually or measured using 

devices such as a pentaprism caliper. For each species and species group, linear 

equations were developed for estimating d.i.b. from d.0.b. at 17.3 feet. These 

equations have the form: 

DIBl7 = a + b(F) 

where 

DIBl7 = d.i.b. at 17.3 feet above ground, in inches 

F = d.0.b. at 17.3 feet above ground, in inches 

a and b = regression coefficients 

Equations for estimating d.i.b. or d.0.b. at 17.3 feet from d.b.h. and total 

height were developed for each species or species group for use when diameter at 17.3 

feet is not measured. These equations have the forms: 

DIB17 = D(a + b(17. 3/~)~) 

where 

DIBl7 = d.i.b. at 17.3 feet in inches 

H = tree total height in feet 

D- = d.b.h. in inches 

a and b = regression coefficients 

and 

DOBl7 = D(a + b(17.3/~)~) 

where 

DOBl7 = d.0.b. at 17.3 feet. in inches 

Equations for estimating d.i.b. or d.0.b. at 17.3 feet from d.b.h. and height to 

9-, 7-, or 4-inch d.0.b. top were also developed. These equations have the forms: 

2 DIBl7 = D(a + b(17.3/Hx) ) 

and 

2 DOB17 = D(a + b(17.3/Hx) ) (12) where 

Hx = tree height to a 9-. 7-, or 4-inch d.0.b. top, in feet 

a and b = regression coefficients 

When inside-bark volume is to be calculated, d.i.b. at the fixed-d.0.b. top must be 

determined. Various models for estimating d.i.b. at the fixed d.0.b. were tested and 

accounted for only 5 to 17 percent of the variation in d.i.b. D.i.b. was therefore 

estimated as species average d. i .b. at 4- and 7-inch d.0.b. tops (softwoods) and 4- 

and 9-inch d.0.b. tops (hardwoods). 
The model based on height to a 7- or 9-inch d.o.b. top cannot provide topwood 

volume estimates to a 4-inch top. Thus, the exponential ratio model shown below was 

developed to estimate a ratio for expanding stem volume to a 7- or 9-inch top to a 

4-inch top. 

where: YR = stem volume to 4-inch top/stem volume to 7- or 9-inch top 

D = d.b.h. in inches 

FC = Girard Form Class--when form class is not measured, d.i.b. at 17.3 

feet (F) estimated using equation 9 or 11 can be substituted for 

DFC in equation 13 

H = tree height to a 7- or 9-inch d.o.b. top in feet 

a,b,c = regression coefficients 

e = base of natural logs = 2.71828 

DATA 

Stem taper measurements were collected on 13,469 trees of 48 species. Most of 

the trees measured were on National Forest lads. Contractors working for the' 

Southern Region measured 11,472 trees, and the Utilization of Southern Timber 

Research Work Unit of the Southeastern Forest Ekperiment Station measured 1,997, All 

measured trees were growing in natural fully stocked stands. 

Trees measured by contractors were felled, and their d.b.h. and total height were 

recorded. D.0.b. and bark thickness were measured at stump height and at 1-inch 

taper intervals from the stump to the tip of the tree. Diameters were measured with 

a diameter tape and recorded to the nearest 0.1 inch. At each measurement height, 

bark thickness was measured with a bark gauge at two points separated by 1/3 of the 

stem's circumference, The two readings were added and recorded as double bark 

thickness. Trees measured by research were felled also. Their diameters were 

measured at groundline, 1 and 2 feet, breast height, and at intervals of 

approximately 4 feet above breast height. Bark thickness was determined by examining 

cross-sectional disks cut from boles. 

The tree data collected by contractors and research were merged and edited for 

bark thickness, butt flare, taper, and excessive reverse taper, Max-Burkhart d.o.b, 

and d.i.b. profile functions developed for each species and national forest were used 

in editing the data. When the distance between l-inch taper points was >8 feet, 

d.i.b. and d.0.b. at 4-foot intervals between measurement points was estimated by 

interpolation based on the observed d.i.b. and d.0.b. and the appropriate MaxBurkhart profile coefficients. Inside- and outside-bark stem volumes of each tree 

were calculated for each measurement point by Smalian's formula. Table 1 summarizes 

measurement characteristics of trees sampled by species and species groups. 

The Southern Region was divided into seven geographic areas based on physiographic region, species form and distribution, and Forest Service administrative 

units (fig. 2). The national forests on which trees were sampled are listed below: 
Appalachian Mts 

Arkansas Area 

Coastal Plain 

Figure 2.--Location of seven geographic areas 

and national forests on which trees were sampled 

for equation development and verification. 

National forests in which trees were measured for development of subregional species equations 

Gulf and Atlantic Appalachian Upper Arkansas 

Coastal Plain Piedmont Mountain Coastal Plain Deep South Area Delta Area 

Croatan Uwharrie George Washington Talladega Desoto Ozark Delta 

Francis Marion Sumter* Jefferson Bankhead Bienville Ouachita St. Francis 

Osceola Oconee Cherokee Holly Springs Kisatchie 

Savannah River Pisgah Tombigbee Sabine 

Plant 

Ocala Nantahala Tuskegee Angelina 

Appalachicola Chattahoochee Davy Crockett 

Conecuh Sumter** Sam Houston 

Homochitto 

*All districts except Andrew Pickens 

**Andrew Pickens District 
PROCEDURE 

Form-class segmented-profile equations were developed for the 48 species and 

also for major species groups--all pines, major southern pines, other pines, all 

cypress, soft hardwoods, hard hardwoods, white oaks, red oaks, all oaks, and all 

hardwoods combined. 

Taper data for each geographic area and species were divided into two data 

sets--a profile data set and a validation data set (Picard and Berk 1990). For 

species equation development, two of every three trees were selected at random from 

each 2-inch d.b.h. class for profile equation development and the third tree used 

for equation validation when 90 or more trees of the same species were measured 

within an equation area. For development of species-group equations, one-third of 

the trees were used for equation development and two-thirds used for validation. 

Coefficients for polynomial form-class segmented-profile equations were developed 

for each species and species group sampled in each of the seven subregions. The 

data from the geographic areas were pooled and Southwide equations were developed. 

For the Southwide equations, one-third of the trees were randomly selected for use 

in equation development and two-thirds for use in validation. Southwide 

coefficients and coefficients based on data from each area were used to calculate 

volumes of the same trees in each area, and the volume estimates obtained by the two 

methods were compared. 

The accuracy of estimates obtained by applying the form-class segmented profile 

equations was compared to the accuracy of estimates obtained by the Max-Burkhart 

method of estimating stem volume inside bark to various heights. The form-class 

segmented-profile model and the Max-Burkhart model were evaluated using observed stem 

measurements. The Southwide form-class model was also evaluated using several 

procedures to simulate possible tree measurement practices. The Southwide form-class 

segmented-profile equations for loblolly pine and yellow-poplar (excurrent species) 

and white oak (deliquescent species) were used in the comparison. The Max-Burkhart 

equations were developed from the same profile data used to develop the form-class 

segmented-profile equations, and both models were applied to the same validation data. 
RFSULTS 

Statistical analysis of the P coefficients for the major species showed that 

differences among subregional coefficients were significant at the 0.05 level. 

However, Southwide equations and equations developed for use in specific areas 

yielded very similar estimates of stemwood volume. The two types of equations were 

used to estimate volumes of loblolly pine, yellow-poplar, white oak, slash pine, 

shortleaf pine, sweetgum, hickory, southern red oak, and other species. The 

loblolly pine, yellow-poplar, and white oak estimates generated by the two methods 

are compared in table 2. I 

These comparisons indicate that a single form-class segmented-profile species 

equation based on data collected across the South can be used to estimate stem 

volume accurately anywhere in the region. The Southwide species equations yield 

accurate estimates because they account for location-to-location differences in stem 

form. Form-class segmented-profile equation coefficients based on d.b.h., diameter 

at 17.3 feet. and total height are listed in table 3 (db) and in table 4 

(d.0.b.). Tables 3 and 4 also show that the model used to estimate diameters in the 

butt of the stem below 4.5 feet accounted for over 90 percent of variation in stem 

diameter in all species except lowland blackgum, water tupelo, and pond cypress. 

Schlaegel's (1983) form-class taper model accounted for 97 to 99 percent of the 

variation in diameter of the lower stem (4.5 to 17.3 feet). The Max-Burkhart-type 

model accounted for 93 to 99 percent of the variation in stem diameter at heights 

above 17.3 feet. 

Form-class segmented-profile equation coefficients based on d.b.h. and height to 

4-inch d.0.b. top are listed in table 5 (inside bark estimates) and in table 6 

(outside bark estimates). Form-class segmented-profile equation coefficients based 

on d.b.h. and height to 7-inch d.0.b. top (softwoods) and d.b.h. and height to 

9-inch d.0.b. top (hardwoods) are listed in table 7 (inside bark estimates) and in 

table 8 (outside bark estimates). 

To illustrate the flexibility of the form-class segmented-profile model, the 

estimated d.i.b. profiles of northern red oak, water tupelo, yellow-poplar, loblolly 

pine, and bald cypress trees of the same d.b.h., diameter at 17.3 feet, and total 

height are plotted in figure 3. The three-coefficient segmented-profile model used 

to estimate stem profile from groundline to 4.5 feet is flexible and allows each 

species equation to estimate butt profile characteristics of the species. 

To use the form-class segmented-profile models (1-6) to estimate inside-bark 

diameter, volume, or height, d.i.b. at breast height and 17.3 feet are required. 

Regression coefficients for estimating d.i.b. at 4.5 feet using equation (7) and 

d.b.h. as the independent variable are presented in table 9. Table 10 gives 

regression coefficients for estimating d.i.b. at 17.3 feet using equation (8) and 

d.0.b. at 17.3 feet as the independent variable. Tables 9 and 10 also give the 

standard error of estimate, coefficient of determination, and coefficient of variation for each equation. The equations in tables 9 and 10 do a good job of predicting 

d.i.b. from d.o.b., accounting for 97 to 99 percent of the variation in d.i.b. 

Southwide species regression coefficients for estimating d.i.b. at 17.3 feet 

using equation (9) and d.b.h. and total height as the independent variables are 

listed in table 11. Also included in table 11 are species regression coefficients 

based on trees sampled in each geographic area. For general volume estimates the 

Southwide coefficients will provide good estimates. However, for accurate local 

estimates the regional coefficients should be used to account for geographic 

variation in stem form when diameter at 17.3 feet or form class is not measured. 
Northern Water Yellow- Loblolly Baldred oak tupelo poplar pine cypress 

Figure 3.--Comparison of species stem profiles estimated with the 

form-class segmented-profile equation for trees of identical d.b.h., 

diameter at 17.3 feet, and total height. 
Table 12 gives species coefficients for estimating d.0.b. at 17.3 feet using d.b.h. 

and total height as independent variables for all trees sampled and trees sampled 

within each geographic area, 

Tables 13 and 14 list species coefficients for estimating d.i.b. and d.0.b. at 

17.3 feet from d.b.h. and height to 4-inch d.0.b. top. Tables 15 and 16 give 

species coefficients for estimating d.i.b. and d.0.b. at 17.3 feet from d.b.h. and 

height to 7-inch d.0.b. top (softwoods) and d.b.h. and height to g-inch d.0.b. top 

(hardwoods). Tables 13-16 list species coefficients for all trees sampled across 

the South and for species sampled within each subregion. 

To use the form-class segmented-profile model based on height to a 40, 7-, or 

g-inch d.0.b. top to estimate inside-bark volume, one must know d.i.b. at a 4-, 7-, 

or 9-inch top. Average d.i.b. at 4.0- and 7.0-inch d.0.b. tops (softwoods) and at 

4.0- and 9.0-inch d.0.b. tops (hardwoods) is shown in table 17. 

Table 18 gives regression coefficients for estimating topwood ratios using 

equation (13). These topwood ratios are used to expand estimated stem volume to a 

7- or 9-inch top to stem volume to a 4-inch top. Regression coefficients are 

presented for expanding stem volume inside and outside bark. 

The Southwide species coefficients for estimating stem volume inside bark based 

on d.b.h. and total height were applied to the loblolly pine, yellow-poplar, and 

white oak validation data. For comparison purposes, Max-Burkhart equations were 

developed from the same profile data and applied to the same validation data. The 

Max-Burkhart model fit the loblolly pine data well but did not accurately predict 

upper-stem diameter of white oak or yellow-poplar. The Max-Burkhart equation 

predicted negative diameters above 88 percent of total height for white oak and 

above 92 percent of total height for yellow-poplar. 

When observed tree measurements are used to predict stem volume to a 4-inch top, 

both profile models do a good job (table 19). However, the form-class segmentedprofile model is more accurate. For example, the form-class segmented-profile model 

predicted volume to 4-inch tops to within 3.7 to 4.1 percent of observed values, 

while the Max-Burkhart model predicted these volumes to within 6.9 to 7.7 percent of 

observed values, The form-class segmented-profile model is more accurate because it 

can account for differences in stem form when diameter at 17.3 feet is measured. 

The two models estimate volumes at heights above 17.3 feet equally well, but the 

form-class segmented-profile model gives better estimates of volume in the first 

log, the most valuable portion of the tree. 

It is difficult to measure diameter at 17.3 feet, the additional measurement 

required to solve the form-class segmented-profile model, on standing trees. The 

effects of estimating inside-bark diameters on the accuracy of the form-class 

segmented-profile model are summarized in table 19 for five simulated field 

measurement procedures and the loblolly pine, yellow-poplar, and white oak 

validation data. The procedures simulated were: I 

1. D.0.b. at 4.5 feet and 17.3 feet is observed, and d.i.b. at 4.5 feet and 

17.3 feet is estimated using equations (7) and (8). 

2. D.b.h. is observed, and d.i.b. at 4.5 feet is estimated using equation (7). 

D.0.b. at 17.3 feet is measured to within a constant bias of 2 0.2 inches, 

and d.i.b. at 17.3 feet is estimated using equation (8). 

3. D.i.b. at 4.5 feet is estimated from observed d,b.h. using equation (7). and 

Cirard's form class is estimated to within a constant bias of - + 2 units. The 

estimated form class is used to calculate d.i.b. at 17.3 feet. 
4. D.i.b. at 4.5 feet is estimated from observed d.b.h. using equation (7) and 

d.i.b. at 17.3 feet is estimated using equation (g), d.b.h., and total 

height. 

5. D. i .b. at 4.5 feet is estimated from observed d.b..h. using equation (7) , and 

an average form class is used for pole timber and an average used for 

sawtimber. 

The results, which are given in table 19, show that the form-class 

segmented-profile model yields accurate volume estimates under each of these 

data-collection regimes. The most accurate estimates are obtained when d.b.h. and 

d.0.b. at 17.3 feet are observed and d.i.b. is estimated using the appropriate 

equations. If d.0.b. at 17.3 feet is measured to within ~fi 0.2 inches or form class 

estimated within + 2 units, estimates of stem volume are more accurate than those 

obtained by using-the Max-Burkhart model. When d.i.b. at 17.3 feet is estimated 

based on d.b.h. and total height, the form-class segmented-profile model is 

slightly more accurate than the Max-Burkhart model. 

The bias of the form-class segmented-profile equation was also examined for the 

loblolly pine, yellow-poplar, and white oak validation data. Biases in predicted 

stem volume to a 4-inch top when diameter at 17.3 feet is measured, when diameter at 

17.3 feet is estimated from d.b.h. and total height, and when volume is estimated 

using the Max-Burkhart model are shown in figure 4. The form-class segmentedprofile model has less bias associated with it than the Max-Burkhart model for 

loblolly pine or yellow-poplar and about as much bias as the Max-Burkhart model for 

white oak. Because the bias of the form-class segmented-profile model was less than 

3 percent for any diameter class when diameter at 17.3 feet was measured and because 

bias was not consistent from species to species, no correction for bias was made. 

When diameter at 17.3 feet is not measured, equations (9-12) do a good job 

estimating diameter at 17.3 feet for sawtimber-size trees. Caution should be used 

when applying equations (9-12) to short poletimber trees because some bias may occur 

in estimating diameter at 17.3 feet. Equations (9-12) should not be used 

indiscriminately across tree sizes without testing. 

When using the form-class segmented-profile model to estimate volume, timber 

cruisers can measure total height, height to a &inch d.0.b. top, or height to a 

9-inch d.0.b. top for hardwoods or height to a 7-inch d.0.b. top for softwoods. The 

accuracy of stemwood volume estimates to merchantable sawlog tops and 4-inch d.0.b. 

tops is shown in table 20. Table 20 compares the accuracy of volume predictions 

based on observed and predicted d.i.b. at 4.5 and 17.3 feet for the loblolly pine, 

yellow-poplar, and white oak validation data. The independent variables measured 

for the d.b.h. and total height model include d.b.h., height to a sawlog 

merchantable top, and total height. Height to a 4-inch d.0.b. top was estimated 

using equation (2). The independent variables measured for the d.b.h. and height to 

4-inch top equation include d.b.h., sawlog merchantable height, and height to a 

4-inch d.0.b. top. The independent variables measured for the d.b.h. and height to 

a 9- or 7-inch d.0.b. top equation include d.b.h., sawlog merchantable height, and 

height to a 9- or 7-inch d.0.b. top. Topwood ratio equation (13) was used to expand 

volume to a 9- or 7-inch top to volume to a '+-inch top. 

Estimating stem d.i.b. by means of equations (9) and (11) rather than measuring 

it reduces the accuracy of volume estimates by 2 to 4 percent. Differences in 

accuracy obtained by measuring total height, height to a 4-inch top, and height to a 

9- or 7-inch top were less than 1 percent when stemwood volume to a sawlog 

merchantable top was estimated. For loblolly pine and yellow-poplar, estimates of 

volume to a 4-inch d.0.b. top obtained by using height to a 9- or 7-inch d.0.b. top 

and the topwood ratio equation (13) were the most accurate ones. These estimates 

were only slightly less accurate than estimates of white oak volume to a 4-inch 

d.0.b. top where height to the &inch top was measured. 
FC YG EQ. Wn17 YEAS. FC SEG ~~.o~.VI/D17 ES.' 

W-BURKW SEG EQ. I 

'PC SEG EQ. WB17 MEAS. FC SEG E$-W_/p17 EST. 

MAX-BURK-fl SEG EQ. 

-4 

-5 

-6 

-7 

-8 

-9 

I. -8 - ..a 

-9 - : I t I I I I I I 

-1o-I I' 

6 8 10 12 14 16 18 20 22 24 

DBH CLASS (IN.) 

- 

- 

- 

- 

- 

- 

-10 ' I I I 1 I I I I I 

6 8 10 12 14 16 18 20 22 24 

DBH CLASS (IN.) 

4 WHITE OAK 

5 

94 

4 -2 * -3 

10 

-9 

- 10 t1 I I I I I I I I 

6 8 10 12 14 16 18 20 22 

DBH CLASS (IN.) 

9 

8 

7 

6 

Figure 4.--Bias in estimated stem volume to a 4-inch top 

for pine, yellow-poplar, and white oak. Volume is estimated 

by means of (1) the form-class segmented-profile model when 

diameter at 17.3 feet is measured, (21 the form-class segmentedprofile model when diameter at 17.3 feet is estimated from d.b.h. 

and total height, and (3) the !!fax-Burkhart equations. 

- 

- FC fEG EP. W/D17 YEAS. FC SEG $_W1'17 EST.~ 

- 

- W-BF.f SEG EQ. 

A 
SUMMARY 

The USDA Forest Service collected felled-tree taper measurements on over 13,000 

trees from natural fully stocked stands across the South. Stem-profile equations 

that are flexible, accurate, and easy to use with computers were developed from the 

data collected. The better attributes of Schlaegel's (1983) form-class model and 

the Max-Burkhart segmented-profile model (1976) were combined in form-class 

segmented-profile models in which d.b.h., diameter at 17.3 feet, and total height 

were independent variables. 

Form-class segmented-profile equations in which d.b.h. and height to a 9-, 7-, 

or 4-inch d.0.b. top were predictors were developed. The profile equations based on 

d,b.h. and height to &-inch top can be applied to any tree that is > 5 inches d.b.h. 

and has a height to 4-inch d.0. b. top > 17.3 feet. The profile equations based on 

d.b.h. and height to a 7-inch d.0.b. top were developed for softwoods that are > 9.0 

inches deb. h. and have a height to 7-inch d.0.b. top > 17.3 feet. The profile equations based on d.b.h. and height to a g-inch d.0.b. top were developed for hardwoods 

that have d.b.h. - > 11.0 inches and have a height to 9-inch d.0.b. top > 17.3 feet. 

The form-class segmented-profile equations predict diameter at any given height, 

height to a given diameter, or volume between any two heights. A single Southwide 

equation for each species was acceptable since the profile equation accounts not 

only for differences in d.b.h. and height but also for differences in stem form as 

measured by diameter at 17'. 3 feet. 

Ssuthwide inside- and outside-bark form-class segmented-profile coefficients are 

presented for 58 southern tree species and species groups. Southwide equations for 

estimating d.i.b. from d.0.b. at 4.5 and 17.3 feet are also listed for each species 

and species group. Southwide and local regression coefficients for estimating 

d.i.b. and d.0.b. at 17.3 feet using d.b.h. and total height or height to 40, 7-, or 

9-inch d.0.b. top as independent variables are also presented for each species. 

Topwood-ratio equations for expanding volume estimates to a 9- or 7-inch top to a 

4-inch d.0.b. top are also presented for each species and species group. 
LITERATURE CITED 

Alberta Forest Service. 1987. Evaluation and fitting of tree taper functions 

for Alberta. Pub. No. Dept. 106. Edmonton, AB: Silvacom, Ltd. 148 pp. 

Burkhart, H.E. 1977. Cubic-foot volume of loblolly pine to any merchantable top 

limit. Southern Journal of Applied Forestry 1:7-9. 

Cao, Q.V.; Burkhart, H.E.; Max, T.A. 1980. Evaluation of two methods for 

cubic-volume prediction of loblolly pine to any merchantable limit. Forest 

Science 26(1):71-80. 

Goulding, C.J.; Murray, J.C. 1976. Polynomial taper equations that are compatible 

with tree volume equations. New Zealand Journal of Forest Science 5(3):313-322. 

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 Ekperiment Station. 22 pp. 

Max, T.A.; Burkhart, H.E. 1976. Segmented polynomial regression applied to 

taper equations. Forest Science 22(3):283-289. 

Picard, Richard R.; Berk, Kenneth N. 1990. Data splitting. The American 

Statistician 44(2):140-147. 

Schlaegel, Bryce E. 1983. Development of a form class taper model for willow oak. 

Athens: University of Georgia. 69 pp. + viii. Dissertation. 

Sterba, H. 1980. Stem curves--a review of the literature. Forestry Abstracts. 

41 (4) : 141-145. 
APPENDIX 1--How to use form-class segmented-profile equations (I), (2), and (3) 

The following examples show how to use equations (I), (Z), and (3) to estimate 

diameter at a given height, height to a given diameter, and inside-bark volume 

between two given heights when d.b.h. and total height are known. 

Assume that the following measurements are recorded for a loblolly pine sawtimber 

tree growing in the Deep South subregion: 

D = 16.0 inches (d.b.h.) 

H = 90 feet (total tree height) 

Estimating diameter (d) at a given height (h) using equation (1) 

If we want to estimate d inside bark at a height of 50 feet, we first estimate 

d.i.b. at breast height using equation (7) and coefficients for loblolly pine from 

table 9. 

DIBD = a + b(D) 

= -0.48140 + 0.91413(16) 

= 14.1 inches 

Next, we estimate diameter, F, inside bark at 17.3 feet using equation (9) and 

coefficients for loblolly pine in the Deep South subregion from table 11. 

F = DIB17 2 = D(a + b(17.3/H) ) 2 = 16.0(0.87759 + (-1.50283)(17.3/90) ) 

= 13.2 inches 

To estimate d inside bark at 50 feet for our sample tree we use equation (1). 

Since we are solving for diameter inside bark all diameters in equation (1) are 

inside bark. Thus, the basic symbols are defined as follows: 

D = DIBD = 14.1 inches 

F = DIBl7 = 13.2 inches 

H = 90 feet 

h = 50 feet 

d = estimated d.i.b. at 50 feet 

To solve equation (I), first calculate the values of indicator variables based on 

h = 50 as follows: 

I, = 1 if h < 4.5 = 0 otherwise, thus IS = 0 

I, = 1 if 4.5 - < h - < 1'7.3 = 0 otherwise, thus IB = 0 

IT = 1if h > 17.3 

= 0 otherwise, thus IT = 1 

I, = 1 if h < (17.3 + a(H-17.3)) 

= 0 otherwise, thus IM = 1 

where a = 0.68464, from table 3 (loblolly pine). 
Calculate diameter, d, at 50 feet using equation (1) and the following loblolly pine 

coefficients from table 3: 

The estimated diameter, d, inside bark at 50 feet is 9.83 inches. 

Estimating height h to a given diameter d using equation (2) 

If we want to estimate the height to an inside-bark diameter of 9.83 inches for 

the above loblolly pine tree, we use the inside-bark values calculated for D and F in 

the previous example. To solve equation (2), we first determine the values of the 

indicator variables based on d = 9.83, D = 14.1, and F = 13.2: 

= 1 if ti2 > D 2 

= 0 otherwise, thus IS = 0 

2 2 1~=1if~ >d - >F~ 

= 0 otherwise, thus I* = 0 

2 2 IT=lifF >d 

= 0 otherwise, thus IT = 1 

2 2 2 IM = 1 if d > b(a-1) F 

= 0 otherwise, thus IM = 1 

where b ='2.36232 and a = 0.68464 (table 3). 

Next, we calculate the values of the combined variables G, W, X, Y, 2, T, Q , and Q as defined in the text using the following coefficients from table 38 

C 

Qb ' 

Thus, G = 0.19709, W = 0.76423, X = 0.64421, Y = 0.16040, Z = 50.78513, 

T = 166.09391, Qa = -0.54414, Qb = -0.74582 and Qc = 0.44543. 

We substitute the appropriate values into equation (2) and calculate h at 9.83 inches 

d.i.b. The height at which d.i.b. is 9.83 inches is estimated to be 50.0 feet. 

Estimating volume between two heights using equation (3) when 

d.b.h. and total height are known 

Assume that we want to estimate stem volume inside bark from a 1-foot stump to a 

height of 50.0 feet for the loblolly pine described above. The basic symbols for 

equation (3) are thus defined as follows: 

L = 1.0, lower height of interest in feet 

U = 50.0, upper height of interest in feet 

V = stem volume between L and U in cubic feet 
Because we want volume inside bark, we use the inside-bark diameters for D and F 

already estimated using equations (7) and (11). To solve equation (3) we first 

calculate the L and U combined variables: 

L1 = maximum of L and 0, thus L1 = 1.0 

U1 = minimum of U and- 4.5, thus U1 = 4.5 

L2 = maximum of L and 4.5, thus L2 = 4.5 

U2 = minimum of U and 17.3, thus U2 = 17.3 

L = maximum of L and 17.3, thus L = 17.3 3 3 

U3 = minimum of U and H, thus U = 50.0 3 

Next, we find the values of the indicator variables: 

I1 = 1 if L < 4.5 = 0 otherwise, thus I1 = 1 

I, = 1if L < 17.3 = 0 otherwise, thus I2 = 1 

I = 1 if U > 4.5 = 0 otherwise, thus I = 1 3 

I4 = 1if U > 17.3 = 0 otherwise, thus I,, = 1 

I, = 1 if (L-17.3) < a(H-17.3) 

= 0 otherwise, thus I = 1 5 

I, - 1 if (U-17.3) < a(H-17.3) 

= 0 otherwise, thus I6 = 1 

We must also calculate G, W, 2, and T, which we defined when we discussed equation 

(2) . From table 3, r = 31.66250, c = 0.57402, e = 110.96000, b = 2.36238, and 

a = 0.68464. Thus, G = 0.19709, W = 0.76423, Z = 50.78513, and T = 166.09391. 

Finally, the appropriate values are substituted into equation (3) and the estimated 

volume V of stemwood is calculated. In this instance, V is 41.96 cubic feet. 
APPENDIX 2--How to use form-class segmented-profile equations (4), (5). and (6) 

Three of the examples that follow show how to use equations (4), (5), and (6) to 

estimate diameter at a given height, height to a given diameter, and inside-bark 

volume between two given heights when d.b.h. and height to a given d.0.b. are known. 

A fourth example shows how to expand estimated volume to volume to a 4-inch top using 

equation (13). 

Assume that the following measurements are recorded for a loblolly pine sawtimber 

tree growing in the Coastal Plain subregion: 

D = 18.0 inches (d.b.h.) 

Hx= 60 feet (height to a 7.0-inch d.0.b. top) 

MHT = 49.9 feet (merchantable height, three 16.3 -foot sawlogs plus 1.0- foot 

stump ) 

Estimating diameter (d) at a given height (h) using equation (4) 

Assume that we are to estimate d inside bark at a height of 49.9 feet. We first 

estimate d.i.b. at breast height using equation (7) and coefficients for loblolly 

pine from table 9. 

DIBD = a + b(D) 

= -0.48140 + 0.91413(18,0) = 15.97 inches 

Next, we must estimate diameter, F, inside bark at 17.3 feet using equation 

(11) and coefficients for loblolly pine in the Coastal Plain subregion from table 15. 

F = ~1~17 2 = D(a + b(17*3/Hx) 1 

= 18.0(0.81309 + (-0.20403) (17.3/60)~) = 14.3 inches 

I To estimate d inside bark at 49.9 feet we use equation (4). Since we are solving for 

diameter inside bark all diameters in equation (4) are inside bark. Thus, the basic 

symbols are defined as follows: 

D = DIBD = 15.97 inches 

F = DIBl7 = 14.3 inches 

Hx = 60.0 feet (height to a 7.0-inch d.0.b. top) 

Dx = 6.4 inches (d.i.b. at a d.0.b. of 7.0 inches for loblolly pine, 

from table 17) 

I h = 49.9 feet 

d = estimated d.i.b at 49.9 feet 
To solve equation (4), we first calculate the values of the indicator variables 

based on h = 49.9 feet as follows: 

I, = 1 if h < 4.5 = 0 otherwise, thus IS = 0 

I, = 1 if 4.5 5 h < 17.3 = 0 otherwise, thus I, = 0 

I, = 1 if h > 17.3 = 0 otherwise, thus IT = 1 

Next, calculate the diameter, d, at 49.9 feet using equation (4) and the 

following loblolly pine coefficients from table 7: 

The estimated inside-bark diameter at 49.9 feet is 9.67 inches. 

Estimating height (h) to a given diameter (d) using equation (5) 

Suppose that we are to estimate the height to the point where the above loblolly 

pine's d.i.b. is 9.67 inches. Since we want height to an inside-bark diameter we use 

the values of D and F calculated in the previous example. To solve equation (5), we 

first determine the values of the indicator variables when d = 9.67, D = 15.97 and 

F = 14.3: 

Is = 1 if dL > D' 

= 0 otherwise, thus IS = 0 

IB = 1 if D~ > d2 - > F~ 

= 0 otherwise, thus IB = 0 

2 2 IT=lifF >d 

= 0 otherwise, thus IT = 1 

Next, we calculate the values of the combined variables G, W, X, Y, Z, T, J, R, and 

N as defined in the text using the following coefficients from table 7: 

Thus, G = 0.28987, W = 079623, X = 0.64798, Y = 0,15061, Z = 101.63661, 

T = 189.18241, J = 0.76517, R = 213.71582, and N = 40.96. 

Finally, substitute the appropriate values into equation (5) and calculate h. In 

this instance, h is 49.9 feet. 
Estimating volume between two heights using equation (6) when 

d.b.h. and height to a 4.0-, 7.0- or 9.0-inch d.0.b. top are known 

Assume that we want to calculate stem volume d.i.b, from a l-foot stump to a 

height of 49.9 feet for the loblolly pine tree described above. The basic 

symbols for equation (6) are defined as follows: 

L= 1.0, lower height of interest in feet 

U= 49.9, upper height of interest 

V= estimated stem volume between L and U in cubic feet 

Because we want volume inside bark, we use the inside-bark values of D and F already 

estimated using equations (7) and (11) and the inside-bark value for Dx from table 

17. Values of these variables are: 

D = 15.97, d.i.b. at breast height in inches 

Hx = 60.0, height to a 7.0-inch d.0.b. top in feet 

Dx = 6.4, d.i.b. at the 7.0-inch d.0.b. top in feet 

F = 14.3, d.i.b. at 17.3 feet in inches 

To solve equation (6) we first calculate the combined L and U variables: 

L1 = maximum of L and 0, thus L1 = 1 

U1 = minimum of U and 4.5, thus U1 = 4.5 

L2 = maximum of L and 4.5, thus L2 = 4.5 

U2 = minimum of U and 17.3, thus U2 = 17.3 

L = maximum of L and 17.3, thus L = 17.3 3 3 

u3 = minimum of U and H, thus U3 = 49.9 

Next, we find the values of the indicator variables: 

I, = 1 if L < 4.5 = 0 otherwise, thus I1 = 1 

I, = 1 if L < 17.3 = 0 otherwise, thus I2 = 1 

= 1 if U > 4.5 

I3 = 0 otherwise, thus I = 1 3 

I4 = 1 if U > 17.3 = 0 otherwise, thus I4 = 1 

We must also calculate G, W, 2, T, R, and N, which we defined when we discussed 

equation (5). From table 7, r = 15.88358, C = 0.51074, e = 222.760, p = 5.56549, 

and q = 0.78687. Thus, G = 0.28987, W = 0.79623, Z = 101.63661, T = 189.18241, 

R = 213.71582, and N = 40.96000. Finally, the appropriate values are substituted 

into equation (6) and V, the volume of stemwood, is calculated. In this instance, 

V is 48.33 cubic feet. 
Expanding volume to 7.0-inch d.0.b. top to volume to 4.0-inch top 

The form-class segmented-profile equation (6) for height to a 7- or 9-inch 

d.0.b. top cannot provide topwood volume estimates above the 7- or 9-inch top. Thus, 

ratio equation (13) was developed for expanding estimated volumes to a 4-inch d.0.b. 

top. 

Suppose that we want to estimate the volume of wood between 1.0 foot and a 

4.0-inch d.0.b. top for a loblolly pine with d.b.h. = 18.0 inches, Hx = 60, and F = 

14.3. First we calculate the volume to a 7-inch d.0.b. top using equation (6) as in 

the preceding example. We find that the inside-bark volume, V7, of the stem from 

1.0 to 60.0 feet is 52.207 cubic feet. Next, we calculate Y the ratio for R' expanding volume to a 4-inch top, using equation (13) and the coefficients for 

loblolly pine (inside bark) from table 18: 

where F is substituted for DFC since form class was not measured. 

Volume to a 4-inch d.0.b. top, V4, is then estimated as: 

I = 53.00 cubic feet to 4-inch d.0.b. top 
&I111011 11Il1111I Ill1 

NmOmNNOd r)*PIInma3In4340 urlmm :Inme moos In cr?mmcr?cr?eInum muam a. 

C 

-4 

91 U U 

C C U-43 

EaO 

-4 

a u Z 

v 0 

oar( 

C L. *P Q a'a V) U> k 

0 

U E C .r( 

-4 a u a E & 

-c 5 w a-cc C .r 040 

u (rO 

-4k-4 

s-44 

3 ;. a 

Table 1.--Trees measured for development or stem-profile equations by species and tree size class--Continued 

Pole timber Sawt imber 

Total Form St emwood Total Form St emwood 

Species or Sample ~.b.h. height class volume Sample D.b.h. height class volume 

species group trees Avg. Range Avg. Range Avg. Range Avg. Range trees Avg. Range Avg. Range Avg. Range Avg. Range 

- Number Inches, - Feet Cubic feet , Number Inches - Feet Cubic feet 

All white oaks combined 302 8.5 5.1-10.9 62 29- 93 74 35-86 9.2 1.6-20.1 1,178 16.1 11.0-35.1 80 52-117 79 58-93 43-4 12.5-232 

Scarlet oak 54 8.2 5.1-10.9 61 36- 76 74 61-82 8.7 2.3-19.3 238 15.7 11.0-30.9 79 53-110 81 68-90 41.5 12.7-179 

Southern red oak 57 8.2 5.1-10.9 59 41- 81 69 51-83 8.0 1.9-15.8 281 15.3 11.0-26.0 77 56-102 76 64-88 35.0 13.0-114 

Cherrybark oak 9 8.9 7.5-10.6 67 57-83 73 60-87 9.9 4.6-15.3 37 16.1 11.2-21.4 87 66-107 79 71-85 44.2 19.5-92 

Laurel oak 20 8.0 5.1-10.5 58 37-78 75 67-82 8.3 2.1-17.6 12 13.8 11.2-17.3 61 49-90 76 67-80 23.2 11.1-34 

Water oak 46 8.3 5.0-10.9 68 43- 90 78 61-89 10.5 2.4-20.3 185 15.2 11.0-23.6 85 65-106 80 70-91 40.3 14.4-107 

Nuttall oak 11 9.2 7.7-10.8 62 37- 80 75 65-80 10.5 5.3-17.8 96 21.5 11.3-36.0 99 72-120 81 71-89 96.4 18.4-304 

Willow oak 24 8.8 6.2-10.5 69 52- 83 74 65-80 10.4 4.0-17.7 107 15.3 11.1-23.1 83 63-105 77 68-86 37.5 13.1- 99 

Northern red oak 75 8.1 5.1-10.9 65 41-101 76 60-87 9.4 2.0-22.1 275 17.2 11.3-28.2 85 58-118 80 68-90 52.5 18.2-152 

Bla'ck oak 73 8.4 5.3-10.9 62 40- 77 73 58-86 8.7 1.8-18.1 32% 16.3 11.0-28.7 80 54-116 78 66-87 44.3 13.0-151 

All red oaks combined 370 8.3 5.0-10-9 63 36-101 74 51-89 9.1 1.8-22.1 1,552 16.3 11.0-36.0 82 49-120 79 64-91 45.8 11.1-304 

All oaks combined 672 8.4 5.0-10.9 63 29-101 74 35-89 9.1 1.6-22.1 2,730 16.2 11.0-36.0 82 49-120 79 58-93 44.8 11.1-,304 

Black locust 25 8.9 6.0-10.7 73 53- 91 74 67-79 10.7 3.7-18.8 50 15.2 11.0-20.5 90 71-110 76 67-84 36.3 16.9- 73 

All hardwoods combined 1,727 8.3 5.0-10.9 64 29-103 73 35-92 9.2 1.6-26.3 5,372 16.1 11.0-36.0 84 39-135 79 50-93 45.4 8.3-304 
0 0 C C mV,OO EE 

aaaa 

Q)aJvu 

aJaJ.d-4 

n n a E4 

C 

-4 

as 

4 C nQ)u a 3 4-40 

03zn 

u C mC,a 

03Q) OOU 

omn 
Table 2.--Accuracy of stemwood volume estimates obtained by using Southwide and subregional coefficients and segmented-profile equations-- 

Continued 

Average absolute difference (observed-predicted) and standard deviation 

Total Stemwood volume from stump to-- 

Source of Coefficients applied to st emwood Hgt to 9-in Hgt to 7-in ~gt to 4-in 

coefficients trees sampled in-- volume 4.5 feet 17.3 feet d.0.b. top d.0.b. top d.0.b. top 

WHITE OAK 

Appalachian Mountains Appalachian Mountains 4.0 + 3.2 5.6 2 4.1 2.9 + 2.7 3.6 2 3.3 4.6 + 6.6 - - 3.7 + 3.0 

Southwide Appalachian Mountains 4.0 + 3.2 5.9 + 4.2 2.4 + 2.3 - - 3.9 2 3.2 4.6 - + 6.1 3.8 + 3.0 

Arkansas Area Arkansas Area 4.0 + 4.2 5.2 2 3.8 2.0 2 1.9 2.9 2 2.5 3.4 + 2.9 3.4 + 2.7 

Sou t hwide Arkansas Area 4.0 2 4.1 5.4 + 4.6 1.8 2 1.5 3.2 + 2.7 3.8 + 4.5 3.5 + 2.7 

Coastal Plain 

Southwide 

Deep South 

Southwide 

Delta 

Southwide 

Piedmont 

Southwide 

Upper Coastal Plain 

Southwide 

Coastal Plain 

Coastal Plain 

Deep South 

Deep South 

Delta 

Delta 

Piedmont 

Piedmont 

Upper Coastal Plain 

Upper Coastal Plain 
1 / 

Table 3.--Inside-bark form-class segmented-profile coefficients for use khen total height is known, for southern tree specie8 and ipeciee groupsStem profile sections 

Butt (stuap to 4.5 ft) Lower stem (4.5 to 17.3 ft) Upper stem (above 17.3 ft) 

Species or species group Coefficients Statistics - Coefficient Statistics Coefficients Statistics 

2/ R2 2/ r c e MSE - P USE- a MSE- 2/ R2 2/ 2/ R2 a/ 

All pines combined 24.20656 0.46472 72.22792 21.674 0.97 7.15667 5.438 0.99 2.27267 0.66773 10.462 0.98 

Shortleaf pine 25.43531 0.45525 28.38927 18.358 0.98 8.21438 4.761 0.99 2.86552 0.72623 9.519 0.98 

Slash pine 

Longleaf pine 

Loblolly pine 31.66250 0.57402 110.96000 24.911 0.97 8.573 6.220 0.99 2.36238 0.68464 10.995 0.98 

A1.l major pines combined 29.69748 0.55416 44.79679 21.944 0.97 7.03196 5.240 0.99 2.54412 0.70799 10.678 0.97 

Sand pine 22.11866 0.24225 30.35804 4.287 0.99 2.39719 2.674 0.99 2.20596 0.67682 4.242 0.97 

Spruce pine 30.60204 0.53021 -41.90943 14.106 0.99 4.62512 5.325 0.99 1.89883 0.62823 12.477 0.96 

Table Mountain pine 15.05927 0.26895 -4.14299 11.413 0.95 1.85472 6.925 0.97 1.57211 0.55552 10.219 0.95 

Pitch pine 

Pond pine 

White pine 

Virginia pine 8.77959 0.30226 27.58681 11.750 0.97 7.18305 3.882 0.99 2.07630 0.61061 6.784 0.97 

All other pines combined 2.97297 0.29746 35.05930 16.905 0.98 7.36602 6.020 0.99 1.81562 0.58400 10.300 0.98 

All cypress combined 29.85766 2.01552 2467.74000 107.160 0.72 12.19350 7.527 0.99 2.80837 0.76859 6.418 0.98 

Baldcypress 

Pondcypress 

Hemlock 22.76763 0.58987 9.28454 39.350 0.97 8.48372 10.543 0.99 1.55322 0.59329 15.848 0.97 

All soft hardwoods combined 0.76387 0.66804 62.00767 57.590 0.93 14.04531 10,287 0.99 1.38226 0.43214 15.360 0.96 

Cherry 32.34510 0.50231 -11.55418 26.448 0.92 6.51400 2.638 0.99 1.55640 0.52157 7.912 0.96 

Red maple 20.22964 0.48000 117.15000 26.937 0.96 7.63003 7.967 0.99 1.12677 0.21122 13.584 0.94 

Buckeye -0.31952 0.56300 -86.84458 53.657 0.92 5.74912 14.024 0.98 1.36316 0.45678 12.673 0.96 

Continued 
Table 3. --lnalde-bark +form-class segmented-profile coefficients for use when total height is known, for southern tree epecies and species groupsL/-- 

Continued 

Stem profile sections 

Butt (stump to 4.5 ft) Lower stem (4.5 to 17.3 ft) Upper stem (above 17.3 it) 

Species or species group Coefficients Statistics Coefficient Statistics Coefficients Statistics 

2/ R2 i/ r c e MSE - P a MSE- 2/ R2 2/ MSE- 2/ R2 

Hackberry 9.85600 0.83775 39.78865 45.209 0.97 15.24815 17.691 0.98 1.10274 0.18436 21.455 0.93 

Sweet gum 39.27999 0.99797 -12.28068 25.450 0.99 18 .01587 9.188 0 .99 1.50811 0.48173 13.614 0.96 

Sweet bay 26.40590 1.43248 -3.16336 41.697 0.91 11.54432 8.765 0.98 1. 56727 0.54963 5.962 0.97 

Water tupelo -24.38581 1,27165 28.48718 37.265 0.88 11.73778 4.288 0.98 1.48108 0.73666 3.294 0.94 

Blackgum (Upland) 12.27907 0.47988 234.31000 23.309 0.95 14.15661 6.291 0.99 1.58441 0.47041 10.271 0.96 

Blackgum (Lowland) 3.85938 1.51531 168.05000 71.666 0.86 16.30110 8.876 0.99 2.12815 0.68482 11.695 0.95 

Sycamore 28.54231 0.73200 63.49480 28.377 0.95 13.80676 6.727 0.99 1.59877 0.58084 9.112 0.97 

Magnolia 32.65160 0.87127 -117.56000 21.660 0.93 4 .14724 3.939 0.99 1.42352 0.40489 8.361 0.96 

Basswood 34 -92280 0.63078 -II~.~OOOO 31.468 0.96 7.65548 6.528 0.99 1. 54223 0.51305 14.344 0.96 

Elm 0.32727 0.83154 -72.51669 55.778 0.95 19.16713 9.171 o .99 1.20639 0.26369 17.753 0.95 

All hard hardwoods combined 16.59025 0.82445 -50.66507 46.213 0.96 12.94614 10.253 0.99 1.25121 0.30693 18.030 0.95 

Beech 44.69823 1.23348 53.34998 33.709 0.95 6.76763 7.46 0.99 1. 10386 0.13563 14.793 0.94 

Birch 51.28318 1.07553 -109.52000 20.017 0.97 9.97617 4.54803 0.99 1.17446 0.22942 8.22 0.96 

Hickory 29.12050 0.74397 25.20574 27.693 0.96 16.91338 7.716 0.99 1.30183 0.31675 12.863 0.95 

Pecan 

White ash 

Green ash 

White oak 

Overcup oak 

Chestnut oak 

15.54633 0.84611 75- 40930 44.751 0.97 18.87904 19.445 0.98 1.37417 0.38353 22.432 0.95 

1.21 583 0.52363 85.64375 28.912 0.91 9.06721 7.825 0.99 1.38969 0.42542 9.261 0.96 

6.55702 0.68587 190.64000 45.597 0.98 12.89430 17.427 0.99 1.30346 0.39763 16.615 0.95 

27.18247 0.88257 174.73000 31.61974 0.95 12.99263 8.409 0.99 1 .288ii 0.29565 13.767 0.95 

13.23593 0.72601 436.83000 52.863 0.98 16.35515 15.549 0.99 1.31793 0.35603 27 .o71 0.95 

25.38194 0.52813 126.23000 27.446 0.97 10.28050 9.865 0.99 1.31163 0.35547 14.062 0.96 

Continued 
W 

Co 1 / Table 3.--Inside-bark form-class segmented-profile coefficients for use when total height is known, for southern tree species and species groups- -- 

Cont i nued 

Stem profile sections 

Butt (stump to 4.5 it) Lower stem (4.5 to 17.3 ft) Upper stem (above 17.3 It) 

Species or species group Coefficients Statistics - Coefficient Statistics Coefficients Statistics 

2 R2 2/ 2/ R2 3/ r c e MSE - P MSE- b a MSE- 2,' R2 i/ 

Post oak 34.64245 0.92900 158.65000 19.271 0.95 9.53959 5.741 0.99 1.24843 0.27255 11.524 0.93 

All white oaks combined 26.04458 0.74703 209.32000 36.323 0.97 13.249 10,272 0.99 1.24871 0.31537 18.393 0.95 

Scarlet oak 47.31765 0.89697 108.22000 27.957 0.96 14.17655 7.698 0.99 1.25713 0.30215 14.773 0.94 

Southern red oak 

Cherrybark oak 

* 

Laurel oak 

Water oak 34.89075 1.05711 19.83006 31.010 0.95 11.33225 7.199 0.99 1.32858 0.36417 10.964 0.96 

Nuttall oak -7.08703 0.91 570 -441.90000 80.402 0.97 20.83134 15.647 0.99 1.23544 0.27706 35.209 0.94 

Willow oak 36.75301 1.28866 -6.10171 27.537 0.96 11.56397 6.531 0.99 1.20946 0.26427 12.538 0.95 

Northern red oak 32.44798 0.84396 12.01150 32.719 0.97 11.66991 6.162 0.99 1.39963 0.38637 17.217 0.96 

Black oak 33.04640 0.86211 90.25670 28.895 0.98 12.69298 7.485 0.99 1.34191 0.33751 13.289 0.96 

All red oaks combined 16 03176 0.92868 -160.34000 54.036 0.96 14.18646 9.121 0.99 1. 24080 0.28549 18.562 0.95 

All oaks combined 18.46026 0.85487 -31.64460 49.607 0.96 13.79400 9.619 0.99 1.24408 0.29817 18.488 0.95 

Black locust 34.01475 0.47442 -19.13306 17.327 0.97 7.50541 6.037 0.99 1. 19776 0.32282 9.915 0.95 

All hardwoods combined 5.79579 0.75160 -29.11988 57.897 0.96 13.58742 11 .860 0.99 1.25073 0.32213 19.472 0.95 

 or use in equations 1. 2, and 3. 

2/MSE = mean squared error. 

- 3'R2 = coefficient of determination. 
1 / 

Table 4.--outside-bark form-class segmented-profile coefficients for use when total height is known, for southern tree species and apeciee groups- 

- - 

Stem profile sections 

Butt (stump to 4.5 ft) Lower stem (4.5 to 17.3 ft) Upper stem (above 17.3 ft) 

Species or species group Coefficients Statistics Coefficient Statistics Coefficients Statistics 

All pines combined 

Short leaf pine 

Slash pine 

Longleaf pine 

Loblolly pine 

All major pines combined 

Sand pine 

Spruce pine 

Table Mountain pine 

Pitch pine 

Pond pine 

White pine 

Virginia pine 

All other pines combined 

A11 cypress combined 

Baldcypress 

Pondcypress 

Hemlock 

All soft hardwoods combined 

Cherry 

Red maple 

Buckeye 

157.11000 

107.65000 

65.52791 

22.15904 

221.45000 

119.76000 

60.41609 

-43.19648 

257 35000 

96.50804 

126.7800 

59.64184 

48.07668 

85 37754 

2639.19000 

1183.93000 

2782.32000 

47 97097 

97.98536 

1.50579 

166. ioooo 

-154.72000 

Continued 
c. 

0 

1 / 

Table 4.--outside-bark form-class segmented-profile coefficients for use when total height is known, for southern tree species and species groups- -- Continued 

Stem profile sections 

Butt (stump to 4.5 ft) Lower stem (4.5 to 17.3 ft) Upper stem (above 17.3 It) 

Species or species group Coefficients Statistics Coefficient Statistics Coefficients Statistics 

r c 

Hackberry 7.58001 0.77904 

Swee tgum 39.02874 0.92761 

Yellow-poplar 26.40588 0.51359 

Sweetbay 23.01219 1.33139 

Water tupelo -17.29187 1.39778 

Blackgum (~~lanh) 13.27517 0.43775 

Blackgum (Lowland) 3.85564 1.45568 

Sycamore 25.41167 0.72445 

Magnolia 29.53040 0.84545 

Basswood 35.87830 0.61921 

Elm 0.81866 0.77141 

All hard hardwoods combined 17.37375 0.76817 

Beech 44.36826 1.22158 

Birch 49.41385 1.01241 

Hickory 26.74384 0.71015 

Pecan 19.65583 0.76605 

White ash 0.64600 0.49680 

Green ash 

White oak 

Overcup oak 

Chestnut oak 

2 1 

MSEContinued 
1 / Table 4.--outside-bark form-class segmented-profile coefficients for use when total height is known, for southern tree species and species groups- -- 

Continued 

Stem profile sections 

Butt (stump to 4.5 ft) Lower stem (4.5 to 17.3 it) Upper stem (above 17.3 It) 

Species or species group Coefficients Statistics Coefficient Statistics Coefficf ents Statistics 

2/ R2 s/ r c e MSE- P MSE- b a HSE- 2/ R2 2/ R2 z/ 

Post oak 30.82091 0.83441 335.71000 21.435 0.95 10.33370 6.020 0.99 1.29478 0.30931 13.627 0.94 

All white oaks Combined 23.711 10 0.66796 349.50000 41.173 0.97 11.92633 10.702 0.99 1.28727 0.34249 21.440 0.95 

Scarlet oak 42.73753 0.86145 214.31000 32.763 0.96 13.53863 8.095 0.99 1.29882 0.33330 17,582 0.94 

Southern red oak 31.98221 0.92734 119.69000 29.508 0.96 12.75583 6.898 0.99 1.37269 0.36674 14.270 0.96 

Cherrybark 50.51179 1.36917 -215.92000 24.040 0.98 9.30537 8.794 0.99 1.28815 0.31282 13.379 0.97 

Laurel oak 34.80988 1.36792 39.52792 25.157 0.95 10.25955 3.677 0.99 1.31060 0.31023 8.061 0.95 

Water oak 34.76470 1.08768 -6.46961 34,842 0.95 10.78112 8.175 0.99 1.36987 0.38666 12.605 0.96 

Nuttall oak -5.45119 0.88020 -457.82000 81.811 0.97 21 .ox569 16.227 0.99 1.28504 0.31629 38.728 0.94 

Willow oak 35.40807 1.26850 38.61354 30.555 0.96 11.59408 7.578 0.99 1.23843 0.28533 14.855 0.95 

Northern red oak 31.32975 0.81328 78.94096 37.204 0.97 11.45671 6.678 0.99 1.43496 0.39984 19.615 0.96 

Black oak 31.60343 0.81484 124.19000 31.542 0.98 12.19245 8.574 0.99 1.39091 0.35814 15.981 0.97 

All red oaks combined 18.48034 0,90302 -118.39000 55.972 0.97 14.01655 10.290 0.99 1.28801 0.31908 21.295 0.95 

All oaks combined 19.20350 0.80440 55.79724 53.215 0.96 13.13272 10.506 0.99 1.28810 0.32973 21.353 0.95 

Black locust 25.57939 0.35922 -8.66136 16.244 0.98 7.02926 5.234 0.99 1.24010 0.35218 12.585 0.96 

All hardwoods combined 7.62604 0.70780 19.34425 61.236 O. 96 12.85326 12.978 0.99 1.30536 0.35815 22.678 0.95 

"For use in equations 1. 2, and 3. 

"MSE = mean squared error. 

'/R2 = coefficient of determination. 
C C .r( 4 

waa 

C 

d*.(h aarl 
Table 5.--Inside-bark form-class segmented-profile coefficients for use when height to 4-inch d.0.b. top is known, for southern tree species 

and species groupsL/--Continued 

Stem profile sections 

Butt (stump to 4.5 ft) Lower stem (4.5 to 17.3 ft) Upper stem (above 17.3 ft) 

Species or species group Coefficients Statistics Coefficient Statistics Coefficient Statistics 

r c e MSE- P MSE- MSE- 2/ R2 2/ 2/ R22/ 

Nackberry 9.36889 0.86292 176.99000 44.457 0.97 12.35128 17.134 0.98 1.30637 21.410 0.93 

Sweet gum 30.26910 0.97162 27.97553 25.953 0.99 14.25132 9.880 0.99 1.00000 14.861 0.96 

Swee tbay 15.34203 1.28997 24.48406 42.259 0.91 8.72476 9.155 0.98 0.98665 6.975 0.96 

Water tupelo -13.37220 1.28913 26.96067 40.679 0.87 7.58979 5.555 0.96 1.07271 4.816 0.90 

Blackgum (Upland) 16.69555 0.59628 211.22000 26.097 0.95 8.80290 7.773 0.99 0.86816 9.890 0.96 

Blackgum (Lowland) 1.65312 1.48029 174.46000 71.943 0.86 13.20124 9.507 0.98 0.91073 11.555 0.95 

Sycamore 19.16546 0.69450 88.01033 28.737 0.95 10.40165 7.116 0.99 0.98498 9.699 0.96 

Magnolia 23.16078 0.82787 -87.83604 21.759 0.93 3.11163 3.989 0.99 0.90353 9.099 0.94 

Basswood 31.06399 0.64665 -ll0.9l000 31.421 0.96 6.20686 6.711 0.99 1.01855 15.047 0.95 

Elm 7.62297 0,91368 -240.91000 42.184 0.97 14.84517 9.554 0.99 1.14963 19.144 0.94 

All hard hardwoods combined 15.32087 0,84179 -24.78451 46.842 0.96 10.85296 10.762 0.99 *1.11952 20.609 0.94 

Beech 

Birch 

Hickory 25.05401 0.77669 70.92241 29.268 0.95 12.72475 7.305 0.99 0.98817 14.483 0.94 

Pecan 

White ash 

Green ash 5.16768 0.68273 199.85000 45.606 0.98 10.39890 16.952 0.99 1.12269 19.185 0.94 

White oak 19.96023 0.84871 199.76000 30.394 0.96 9.78031 6.966 0.99 1.01687 16.630 0.93 

Overcup oak 11.98363 0.72520 519.63000 52.729 0.98 13.59938 15.613 0.99 1.13856 31.939 0.94 

Chestnut oak 12.36718 0.49047 76.86862 27.422 0.97 6.13653 10.231 0.99 1.10297 15.657 0.95 

Post oak 19.27158 0.95880 31.31768 24.283 0.92 5.93130 5.904 0.99 0.99587 12.148 0.92 

Continued 
.F' 

C. Table 5.--Inside-bark form-class segmented-profile coefficients for use when height to 4-inch d.0.b. top is known, for southern tree species 

and species groupsL/--Continued 

Stem profile sections 

Butt (stump to 4.5 ft) Lower stem (4.5 to 17.3 ft) Upper stem (above 17.3 ft) 

Species or species group Coefficients Statistics Coefficient Statistics Coefficient Statistics 

r c e MSE- MSE- 4 MSEAll white oaks combined 19.78864 0.72426 269.52000 36.418 0.97 10.42000 10.605 0.99 1.13753 21.031 0.94 

Scarlet oak 27.54356 0.74944 263.92000 30.058 0.95 9.04254 7.152 0.99 1.02048 15.341 0.94 

Southern red oak 22.97463 0.93866 131.18000 25.705 0.96 9.35568 6.160 0.99 0.97967 11.629 0.95 

Cherrybark oak 39.22492 1.42308 -165.61000 22.408 0.98 7.12822 8.366 0.99 1.02097 14.102 0.95 

Laurel oak 22.87976 1.23888 75.16753 22.374 0.94 7.07049 3.508 0.99 0.96518 8.639 0.92 

Water oak 24.68063 1.00719 38.43151 30.150 0.95 8.86923 5.720 0.99 0.99800 12.627 0.94 

Nuttall oak -5.68827 0.91707 -443.84 79.986 0.97 17.23428 15.888 0.99 1.23161 39.764 0.93 

Willow oak 24.43783 1.20379 47.53710 28.315 0.96 8.45645 6.604 0.99 1.07274 13.339 0.94 

Northern red oak 22.87602 0.74119 114.37000 30.924 0.97 8.61102 7.292 0.99 1.03013 17.456 0.95 

Black oak 26.20262 0.82750 76.51710 23.948 0.98 9.77858 7.646 0.99 1.02112 15.941 0.95 

All red oaks combined 14.17341 0.94250 -163.27000 54.012 0.96 10.97372 9.522 0.99 1. 13660 21.861 0.94 

All oaks combined 14.94166 0.85216 -14.39119 49.688 0.96 10.75215 9.982 0.99 1. 13698 21.515 0.94 

Black locust 27.28041 0.47147 -3.85360 17.289 0.97 5.94068 5.985 0.99 1.20251 11.739 0.93 

All hardwoods combined 6.29407 0.76029 -3.87970 56.991 0.95 10.91724 11.725 0.99 1.13731 21.480 0.94 

"For use in equations 4. 5. and 6. 

"MSE = mean squared error. 

3/R2 

- = coefficient of determination. 
Table 6.--outside-bark form-class segmented-profile coefficients for use when height to 4-inch d.0.b. top is known, for southern tree species 

1 / and species groupsStem profile sections 

Butt (stump to 4.5 ft) Lower stem (4.5 to 17.3 ft) Upper stem (above 17.3 ft) 

Species or species group Coefficients Statistics Coefficient Statistics Coefficient Statistics 

r C e MSE- MSE- Q 2,' R2 3,' MSEAll pines combined 17.03335 0.49585 187.04000 27.973 0.97 6.27498 7.090 0.99 0.88020 12.787 0.98 

Shortleaf pine 

Slash pine 

Longleaf pine 

Loblolly pine 

All major pines combined 19.99295 0.57042 161.45000 27.275 0.97 6.37299 6.848 0.99 0.84760 12.970 0.97 

Sand pine 6.63555 0.26378 56.40624 5.843 0.99 3.32246 2.999 0.99 0.80428 3.816 0.98 

Spruce pine 23.54403 0.50010 -29.21153 14.188 0.99 2.80640 5.834 0.99 0.95645 13.525 0.96 

Table Mountain pine 14.76190 0.23248 284.17000 15.288 0.94 1.79905 8.561 0.96 0.92816 13.089 0.93 

Pitch pine 5.93734 0.26492 111.31000 17.553 0.99 5.08038 6.623 0.99 0.81543 15.758 0.96 

Pond pine 

White pine 

Virginia pine 8.34415 0.41147 37.23535 11.763 0.98 6.82874 5.210 0.99 0.81026 6.866 0.97 

All other pines combined 4.05998 0.31481 92.38752 19.212 0.99 6.73109 7.583 0.99 0.98242 13.878 0.97 

All cypress combined 18.91994 1.71949 2757.29000 116.080 0.70 10. 07695 8.635 0.99 0.83509 6.924 0.98 

Baldcypress 43.97643 2.68374 1419.45000 47.816 0.95 12.65276 6.539 0.99 0.82606 7.428 0.99 

Pondcypress 19.68886 2.08883 3079.83000 130.300 0.59 8.88798 9.355 0.98 0.85698 6.291 0.98 

Hemlock 17.26344 0.53402 80.87129 41.391 0.98 7.549 13.097 0.99 1.06779 19.075 0.98 

All soft hardwoods combined 2.57141 0.64085 101.92000 63.452 0.93 10.06803 11.169 0.99 1.01619 19.948 0.95 

Cherry 40.31196 0.55528 53.74985 27.629 0.92 4.68815 3.033 0.99 0.90774 8.899 0.96 

Red maple 19.70452 0.42526 251.53000 29.172 0.96 8.13298 7.184 0.99 1.20080 16.421 0.94 

Buckeye 10.69027 0.64442 -154.67000 59.784 0.92 3.60211 14.086 0.99 0.96773 14.884 0.96 

Continued 
* 

0\ Table 6.--0utside-bark form-class segmented-profile coefficients for use when height to 4-inch d.0.b. top is known, for southern tree species 

and species groupsi/--Continued 

Stem profile sections 

Butt (stump to 4.5 ft) Lower stem (4.5 to 17.3 ft) Upper stem (above 17.3 ft) 

Species or species group Coefficients Statistics Coefficient Statistics Coefficient Statistics 

]P c e MSE- 2/ R2 A/ P MSE- 2/ R2 A/ Q MSE- 2/ R2 3/ 

Hackberry 8.59560 0.80638 228.08000 48.354 0.97 11.97301 16.891 0.99 1. 26616 24.481 0.93 

Swee tgum 29.53672 0.89545 68.16672 27.311 0.99 14.04794 10.243 0.99 0.94866 18.127 0.96 

Sweetbay 13.13011 1.19408 76.12475 49.332 0.90 8.46177 9.795 0.98 0.93539 8.166 0.97 

Water tupelo -9.75790 1.42474 -45.91624 37.941 0. 91 6.97370 5.660 0.97 0.98789 5.679 0.91 

Blackgum (Upland) 16.10484 0.52007 350.56000 28.068 0.96 8.78543 8.055 0.99 0.81991 12.405 0.97 

Blackgum (Lowland) 1,55029 1.41937 240.71000 80.370 0.86 12.86649 10.069 0.99 0.84081 13.759 0.95 

Sycamore 16.72042 0.68982 79.52287 30.418 0.95 10.19695 7.571 0.99 0.98453 10.422 0.96 

Magnolia 20.80044 0.80718 -147.79000 22.450 0.94 3.57440 4.922 0.99 0.88822 10.450 0.94 

Basswood 31 71748 0.63109 -112.07000 33.914 0.96 7.08946 7.497 0.99 0.98108 16.730 0 95 

Elm 7.40033 0.84312 -233.82000 42.954 0.97 14.58889 9.731 0.99 1.10244 21.757 0 94 

All hard hardwoods combined 14.82198 0.77600 59.81238 50.502 0.96 10.21737 11.951 0.99 1.07939 23.754 0.94 

Beech 

Birch 

Hickory 

Pecan 

White ash 

Green ash 

White oak 

Overcup oak 

Chestnut oak 

239.81000 

-14.36625 

81.89285 

162.59000 

158.25000 

299.06000 

264.73000 

738.42000 

169. ooooo 

Post oak 17.13062 0.85820 188.43000 27.556 0.93 6.69397 7.045 0.99 0.96379 14.195 0.92 

Continued 
Table 6.--outside-bark form-class segmented-profile coefficients for use when height to 4-inch d.0.b. top is known, for southern tree species 

and species groupsi/--Continued 

Stem profile sections 

Butt (stump to 4.5 ft) Lower stem (4.5 to 17.3 ft) Upper stem (above 17.3 ft) 

Species or species group Coefficients Statistics Coefficient Statistics Coefficient Statistics 

2/ R2 z/ r c e MSE- MSE- Q MSE2/ R2 z/ 

All white oaks combined 18.04800 0.64723 429.72000 41.224 0.97 9.32459 11.102 0.99 1. 10492 24.373 0.94 

Scarlet oak 25.83014 0.74355 416.62000 33.518 0.95 9.00692 8.075 0.99 0.99455 .17 817 0.94 

Southern red oak 

Cherrybark oak 

Laurel oak 23.41607 1.23280 120.81000 26.058 0.94 7.50920 3.961 0.99 0.93122 10.398 0.92 

Water oak 

Nuttall oak 

Willow oak 

Northern red oak 

Black oak 24.70984 0.78767 116.49000 26.763 0.98 9.32619 -8.388 0.99 0.97788 19.586 0.95 

All red oaks combined 15.30089 0.90603 -106.35000 55.996 0 97 10.78307 10.738 0.99 l.O9OlO 25.015 0.94 

All oaks combined 

Black locust 

All hardwoods combined 6 ~3383 0.71024 55.86839 60.987 0.96 10.31848 12.720 0.99 1.09029 24.792 0.94 

'/For use in equations 4. 5, and 6. - 

2/MSE = mean squared error. 

'/I?* = coefficient of determination. 

Table 7.--Inside-bark form-class segmented-profile coefficients for use when height to 7-inch d.0.b. top (southern softwood species) or 

9-inch d.0. b. top (southern hardwood species) is knownL/--Continued 

Stem profile sections 

Butt (stump to 4.5 ft) - Lower stem (4.5 to 17.3 ft) Upper stem (above 17.3 ft) 

Species or species group Coefficients Statistics Coefficient Statistics Coefficient Statistics 

2/ R2 r c e MSE- P MSE- MSE- 2/ R2 3/ 

Hackberry 5.18978 0.81944 291.32000 49.379 0.96 8.92998 19.696 0.97 0.86631 23.159 0.92 

Swee tgum 19.20174 0.88488 227.60000 32.336 0.98 10.86478 12.950 0.99 0.77359 15.084 0.96 

Swee tbay 2.59433 1.18333 -306.80000 54.995 0.84 5.97795 11.969 0.96 0.85325 8.289 0.94 

Blackgum (Upland) 8.25373 0.52928 270.28000 29.553 0.92 6.43568 9.310 0.98 0.77604 9.869 0.95 

Blackgum (Lowland) -2.71851 1.38885 97.84611 88.253 0.78 8.39752 14.318 0.95 0.84134 11.426 0.93 

Sycamore 12.96010 0.66258 191.64000 32.670 0.91 7.11830 8.338 0.98 0.94439 9.043 0.94 

Magnol i a 13.14198 0.79169 -119.21000 24.537 0.87 1.87158 4.833 0.98 0.64756 6.984 0.96 

Basswood 21.68899 0.63425 -132.52000 35.689 0.93 4.60915 7.702 0.99 0.78797 12.467 0.96 

Elm -0.44140 0.94606 -513.62000 57.424 0.95 11.10968 14.224 0.99 0.80767 19.782 0.94 

All hard hardwoods combined 7.60744 0.80668 -135.64000 51.822 0-96 8.13717 12.666 0.99 0.82778 20.602 0.95 

Beech 

Birch 

Hickory 15.08240 0.74606 -10.47815 33.448 0.93 9.35044 8.838 0.98 0.71776 13.948 0.94 

Pecan 10.43971 0.81311 364.38000 46.592 0.96 13.40870 19.725 0.98 0.82007 24.951 0.93 

White ash 6.47354 0.38099 563.99000 33.488 0.85 2.59500 10.328 0.97 0.76787 9.817 0.95 

Green ash 4.99216 0.66430 414.55000 47.289 0.97 7.22585 19.562 0.98 0.83080 20.170 0.92 

White oak 14.81018 0.75907 561.93000 32.982 0.93 6.95857 8.076 0.99 0.67254 14.660 0.94 

Overcup oak 10.15596 0.69455 950.57000 56.115 0.97 10.74129 16.969 0.99 0.81700 34.139 0.93 

Chestnut oak 

Post oak 

All white oaks combined 14.52198 0.66306 607.65000 40.178 0.96 7.90665 12.152 0.99 0.83351 21.782 0.94 

Continued 
VI 

0 Table 7.--Inside-bark form-class segmented-profile coefficients for use when height to 7-inch d.0.b. top (southern softwood Species) or 

9-inch d. 0. b. top (southern hardwood species) is knownL/--Continued 

Stem profile sections 

Butt (stump to 4.5 ft) Lower stem (4.5 to 17.3 ft) Upper stem (above 17.3 ft) 

Species or species group Coefficients Statistics Coefficient Statistics Coefficient Statistics 

Scarlet oak 18.30355 0.60872 689.33000 33.485 0.92 6.33216 8.530 0.98 0.71691 13.008 0.95 

Southern red oak 15.60123 0.85057 330.49000 28.150 0.94 6.44760 7.442 0.99 0.74774 11.706 0.94 

Cherrybark oak 25.85612 1.30682 18.28815 25.574 0.97 5.44066 9.015 0.98 0.68075 12.522 0.94 

Water oak 

* Nuttall oak 

Willow oak 12.19866 1.06860 82,03535 32.315 0.94 5- 51792 7.571 0.99 0.72478 10.528 0.95 

Northern red oak 19.27614 0.71461 395.04000 33.326 0.96 6.19723 8.424 0.99 0.76292 14.575 0.96 

Black oak 16.94705 0.76609 154.47000 26.986 0.98 7.35601 8.735 0.99 0.73888 13.214 0.96 

All red oaks combined 4.78943 0.90327 -456.56000 57.856 0.96 8.15359 11.373 0.99 0.84437 20.426 0.95 

All oaks combined 6.82692 0.81097 -138.20000 54.439 0.95 8.05425 11.707 0.99 0.83987 20.988 0.95 

Black locust 21.74255 0.43665 191.42000 20.470 0.95 3.85237 7.397 0.98 0.90554 13.751 0.89 

All hardwoods combined 1.23461 0.73829 -103.39000 65.643 0.94 7.86939 14.699 0.99 0.85016 22.418 0.95 

"For use in equations 4. 5. and 6. 

"MSE = mean squared error. 

3/R2 

'" = coefficient of determination. 
Table 8.--outside-bark form-class segmented-profile coefficients for use when height to 7-inch d.0.b. top (southern softwood species) 

1 / or 9-inch d.0.b. top (southern hardwood species) is knownStem profile sections 

Butt (stump to 4.5 ft) - Lower stem (4.5 to 17.3 ft) Upper stem (above 17.3 ft) 

Species or species group Coefficients Statistics Coefficient Statistics Coefficient Statistics 

r C e P 9 MSE- 2/ R2 2/ MSE- 2/ R2 2/ MSE2/ R2 z/ 

All pines combined 15.47887 0.45692 399.42000 29.704 0.96 5.11517 7.918 0.99 0.80988 11.936 0.98 

Shortleaf pine 15.14298 0.49814 185.44000 25.094 0.97 6.23138 6.732 0.99 0.71935 10.598 0.98 

Slash pine 15.86071 0.79879 32.01650 26.918 0.94 3.10595 4.899 0.99 0.84105 6.895 0.98 

Longleaf pine 

Loblolly pine 

All major pines combined 16.87203 0.52890 334.25000 29.284 0.96 5.21364 7.709 0.99 0.78227 12.426 0.98 

Sand pine 5.82114 0.20544 150.96000 6.690 0.98 2.47016 3.499 0.99 0.88019 3.248 0.98 

Spruce pine 18.61713 0 . 48793 -24.79783 15.355 0.99 2.35354 6.207 0.99 0.85707 10.822 0.97 

Table Mountain pine 11.59543 0.21424 334.83000 15.213 0.94 1.18296 8.768 0.96 0.81719 11.888 0.92 

Pitch pine 6.19294 0.24259 236.19000 18.515 0.98 4.09038 7.583 0.99 0.74272 16.195 0.95 

Pond pine 5.62236 0.34069 271.80000 17.839 0.95 2.32202 4.777 0.99 0.80551 6.920 0.98 

White pine 

Virginia pine 

All other pines combined 

All cypress combined 

Baldcypress 

Pondcypress 

Hemlock 

All soft hardwoods combined 

Red maple 

Buckeye 

12.758 0.99 

6.162 0.97 

12.744 0.98 

6.732 0.98 

7.039 0-99 

6.226 0.98 

18.100 0.98 

19.198 0.96 

21.340 0.93 

13.506 0.97 

Continued 

Table 8.--Outside-bark form-class segmented-profile coefficients for use when height to 7-inch d.0.b. top (southern softwood Species) 

or 9-inch d.0. b. top (southern hardwood species) is knowni'--Continued 

Stem profile sections 

Butt (stump to 4.5 ft) Lower stem (4.5 to 17.3 ft) Upper stem (above 17.3 ft) 

Species or species group Coefficients Statistics Coefficient Statistics Coefficient Statistics 

2/ R2 r c e MSE- P MSE- MSEAll white oaks combined 13.91640 0.58215 963.71000 44.756 0.96 7.04293 12.692 0.99 0.82616 24.515 0.95 

Scarlet oak 16.44524 0.57534 1035.09000 36.510 0.93 6.28220 9.681 0.98 0.70493 14.638 0.95 

Southern red oak 13.60924 0.82728 420.35000 34.706 0.94 6.37541 8.512 0.99 0.74081 13.534 0.94 

Cherrybark oak 24.95933 1.22038 120.96000 27.740 0.97 5.21492 9.754 0.99 0.68417 13.901 0.95 

Water oak 18.24345 0.98079 345.89000 36.429 0.93 6.04975 7.729 0.99 0.69141 lo. 899 0.95 

Nuttall oak -4.97844 0.88006 -739.03000 83.756 0.97 13.79754 17.467 0.99 0.84317 42.863 0.93 

Willow oak 

Northern red oak 

Black oak 15.94679 0.73065 213.62000 29.948 0.98 7.04140 9.499 0.99 0.71335 15.566 0.96 

All red oaks combined 6.20263 0.86079 -356.31000 60,283 0.96 7.97778 12.758 0.99 0.82102 22.864 0.95 

All oaks combined 7.80341 0. 75012 72.13668 58.452 0.95 7.59305 12.757 0.99 0.82304 23.546 0.95 

Black locust 15.13623 0.31591 229.66000 19.169 0.97 3.55627 6.413 0.99 0.88818 17.125 0.91 

All hardwoods combined 2.24727 0.68306 20.11288 69.215 0.95 7.42340 15.997 0.99 0.82862 25.302 0.95 

"For use in equations 4, 5, and 6. 

"MSE = mean squared error. 

'/R2 = coefficient of determination. 
Table 9.--Regression coefficients for estimating d.i.b. at 4.5 feet from d.b.h, for southern tree 

1 / species and species groupsSpecies or species group 

- 

Standard 

Regression error of Coefficient of Coefficient 

coefficients estimate determination of variation 

2 a b S R C.V. 

A11 pines combined 

Shortleaf pine 

Slash pine 

Longleaf pine 

Loblolly pine 

All major pines combined 

Sand pine 

Spruce pine 

Table Mountain pine 

Pitch pine 

Pond pine 

White pine 

Virginia pine 

All other pines combined 

All cypress combined 

Baldcypress 

Pondcypress 

Hemlock 

All soft.hardwoods combined 

Cherry 

Red maple 

Buckeye 

Hackberry 

Sweet gum 

Yellow-poplar 

Swee tbay 

Water tupelo 

Blackgum (Upland) 

Blackgum (Lowland) 

Sycamore 

Magnolia 

0.98 4.40 

0.99 1.06 

0.97 4.44 

0.99 1.70 

0.99 2.73 

0.99 1.01 

0.99 1.42 

0.99 1.66 

0.99 1.76 

0.99 1.78 

0.99 2.01 

0.99 2.48 

0.99 3.02 

0.99 2.86 

0.99 2.27 

0.99 1.25 

0 99 1.40 

Continued 
Table 9.--Regression coefficients for estimating d.i.b. at 4.5 feet from d.b.h, for southern tree 

species and species groupsv--Continued 

Standard 

Regression error of Coefficient of Coefficient 

Species or species group coefficients estimate determination of variation 

2 a b S R C.V. 

y.x 

Basswood 

Elm 

All hard hardwoods combined 

Beech 

Birch 

Hickory 

Pecan 

White ash 

Green ash 

White oak 

Overcup oak 

Chestnut oak 

Post oak 

All white oaks combined 

Scarlet oak 

Southern red oak 

Cherrybark oak 

Laurel oak 

Water oak 

Nuttall oak 

Willow oak 

Northern red oak 

Black oak 

All red oaks combined 

All oaks combined 

Black locust 

All hardwoods combined 

YDIBD = a + b 

where: DIBD = diameter inside bark at 4.5 feet 

D = diameter outside bark at 4.5 feet 

a and b = regression coefficients. 
Table 10.--Regression coefficients for estimating d.i.b. at 17.3 feet from d.0.b. at 17.3 feet, 

1 / for southern tree species and species groupsStandard 

Regression error of Coefficient of Coefficient 

Species or species group coefficients estimate determination of variation 

2 a b S R C.V. 

All pines combined 

Shortleaf pine 

Slash pine 

Longleaf pine 

Loblolly pine 

All major pines combined 

Sand pine 

Spruce pine 

Table Mountain pine 

Pitch pine 

Pond pine 

White pine 

Virginia pine 

All other pines combined 

All cypress combined 

Baldcypress 

Pondcypress 

Hemlock 

All soft hardwoods combined 

Cherry 

Red maple 

Buckeye 

Hackberry 

Swee tgum 

Yellow-poplar 

Swee tbay 

Water tupelo 

Blackgum (Upland) 

Blackgum (Lowland) 

Sycamore 

Magnolia 

0 99 2.01 

0.99 1-33 

0.99 3.84 

0.99 3.76 

0 99 0.82 

0.98 4.45 

0.99 1.61 

0.99 3.04 

0 99 1.61 

0 99 1.54 

0.99 2.06 

0.99 1.63 

0.99 2.12 

0 99 1.94 

0.99 3.13 

0.99 1.25 

0.99 2.89 

0.99 2.51 

0.99 I. 26 

0.99 1.51 

Continued 
Table 10.--Regression coefficients for estimating d.i.b. at 17.3 feet from d.0.b. at 17.3 feet, 

for southern tree species and species groupsA/--Continued 

Standard 

Regression error of Coefficient of Coefficient 

Species or species group coefficients estimate determination of variation 

2 a b S R C.V. 

Y.X 

Basswood 

Elm 

All hard hardwoods combined 

Beech 

Birch 

Hickory 

Pecan 

White ash 

Green ash 

White oak 

Overcup oak 

Chestnut oak 

Post oak 

All white oaks combined 

Scarlet oak 

Southern red oak 

Cherrybark oak 

Laurel oak 

Water oak 

Nuttall oak 

Willow oak 

Northern red oak 

Black oak 

All red oaks combined 

All oaks combined 

Black locust 

All hardwoods combined 

"DIB17 = a + b (P) 

where: DIBl7 = diameter inside bark at 17.3 feet 

P = diameter outside bark at 17.3 feet 

a and b = regression coefficients. 
Table 11.--Regression coefficients for estimating d.i.b. at 17.3 feet from d.b.h and total 

1 i height, for species and species groups across the South and in seven subregionsSpecies or species group 

Standard 

Regression error of Coefficient of Coefficient 

coefficients estimate determination of variation 

2 a b S R C.V. 

All pines combined 

Shortleaf pine 

Slash pine 

Longleaf pine 

LoOlolly pine 

All major pines combined 

Sand pine 

Spruce pine 

Table Mountain pine 

Pitch pine 

Pond pine 

White pine 

Virginia pine 

All other pines combined 

All cypress combined 

Baldcypress 

Pondcypress 

Hemlock 

All soft hardwoods combined 

Cherry 

Red maple 

Buckeye 

Hackberry 

Swee tgum 

Yellow-poplar 

Sweetbay 

Water tupelo 

Blackgum (Upland) 

Blackgum (Lowland) 

Sycamore 

SOUTHWIDE 

-1.01846 

-1.20730 

-1.34827 

-1.05479 

-1.31295 

-1.13131 

-1.12377 

-1.16238 

-2.09975 

-1.09157 

-0.76690 

-0.57310 

-0.57823 

-0.77470 

-2.34185 

-1.51481 

-1.62356 

-0.53500 

-1.37220 

-0.90888 

-1.61935 

- 1.70436 

-1.04218 

-1.47259 

-1.60124 

-0.50453 

-0.71437 

-0.78551 

-1.16431 

-1.17967 

0.99 5.55 

0 99 5 07 

0.99 4.99 

0.99 4.94 

0.99 5.06 

0.99 5.49 

0.99 4.53 

0 99 3.45 

0 99 4.02 

0.99 4.41 

0.99 4.92 

0.99 4.46 

0 99 4.00 

0.99 5.67 

0.99 9.09 

0.99 6.41 

0.99 9.76 

0.99 4.82 

0 99 6.59 

0.99 3.58 

0.99 5.74 

0.99 6.15 

0.99 6.61 

0.99 5 65 

0.99 4.47 

0.99 8.42 

0.99 10.98 

0.99 5.28 

0.99 7.80 

0.99 4.87 

Continued 
Table 11.--Regression coefficients for estimating d.i.b. at 17.3 feet from d.b.h and total 

height, for species and species groups across the South and in seven subregionsg--Continued 

Species or species group 

Standard 

Regression error of Coefficient of Coefficient 

coefficients estimate determination of variation 

2 a b S R C.V. 

Magnolia 

Basswood 

Elm 

All hard hardwoods combined 

Beech 

Birch 

Hickory 

Pecan 

White ash 

Green Ash 

White oak 

Overcup oak 

Chestnut oak 

Post oak 

All white oaks combined 

Scarlet oak 

Southern red oak 

Cherrybark oak 

Laurel oak 

Water oak 

Nuttall oak 

Willow oak 

Northern red oak 

Black oak 

All red oaks combined 

All oaks combined 

Black locust 

All hardwoods combined 

All pines combined 

Slash pine 

0.83258 

0.86843 

0.80897 

0.82379 

0.83420 

0.82093 

0 83307 

0.82617 

0.83439 

0.82857 

0.80385 

0.82131 

GULP AND 

0.83618 

0.85504 

-1.41913 0.480 

-1.94723 0.511 

-0.59108 0.374 

-0.59447 0.443 

-0.88657 0.848 

-1.02266 0.517 

-0.81521 0.538 

-0.88969 0.486 

-0.94555 0.619 

-0.81753 0.637 

-1.12726 0.449 

-0.94452 0.851 

ATLANTIC COASTAL PLAIN 

-0.91452 0 + 536 

-1.52260 0.488 

0.99 5.64 

0.99 5.43 

Continued 
Table 11:--Regression coefficients for estimating d.i.b. at 17.3 feet from d.b.h and total 

height, for species and species groups across the South and in seven subregions?-j--Continued 

Species or species group 

Standard 

Regression error of Coefficient of Coefficient 

coefficients estimate determination of variation 

2 a b S R C.V. 

Longleaf pine 

Loblolly pine 

All major pines combined 

Sand pine 

Pond pine 

All cypress combined 

Baldcypress 

Pondcypress 

All soft hardwoods combined 

Swe e tgum 

Yellow-poplar 

Sweetbay 

Blackgum (Lowland) 

Red maple 

Water tupelo 

All hard hardwoods combined 

White oak 

Laurel oak 

Water oak 

Willow oak 

All red oaks combined 

All oaks combined 

All hardwoods combined 

All pines combined 

Shortleaf pine 

Longleaf pine 

Loblolly pine 

All major pines combined 

Virginia pine 

All soft hardwoods combined 

-0.04295 

-1.16431 

-1.64805 

-0.71437 

-0.95711 

-1.53124 

-0.59108 

-0.50661 

-1.96750 

-0.49418 

-0.90255 

-1.36470 

PIEDMONT 

-1.01837 

- 1.30480 

-1.17085 

-1.14334 

-1.10383 

-0.53918 

-1.50180 

0.99 5.66 

0 . 99 5.22 

0.99 3.77 

0.99 5.42 

0.99 5.46 

0.99 4.95 

0.99 5.78 

Continued 
Table 11.--Regression coefficients for estimating d.i.b. at 17.3 feet from d.b.h and total 

height, for species and species groups across the South and in seven subregionsg--Continued 

Standard 

Regression error of Coefficient of Coefficient 

Species or species group coefficients estimate determination of variation 

2 a b S R C.V. y.x 

Red maple 0.75662 0.01564 0.348 0.99 4.83 

Sweet gum 0.84185 -1.81811 0.544 0.99 6.18 

Sycamore 0.84403 -1.16307 0 587 0.99 5.16 

Elm 0.86488 -1 . 59558 0,767 0 99 7-38 

All hard hardwoods combined 0.86025 -1.32287 0.558 0 99 5-52 

Hickory 0 - 83736 -0.83608 0.631 0.99 6.07 

White oak 

Chestnut oak 

Post oak 0.79081 -0.34721 0.486 0.99 4.92 

All white oaks combined 0.87557 -1.52320 0.513 0- 99 4.91 

Scarlet oak 0.86356 -0.94497 0.569 0.99 5.18 

Southern red oak 

Water oak 

Black oak 0.83478 -1.15638 0.496 0 99 5.05 

All red oaks combined 

All oaks combined 

All hardwoods combined 

All pines 

Shortleaf pine 

Table Mountain pine 

Pitch pine 

Virginia pine 

All yellow pines combined 

White pine 

Hemlock 

All soft hardwoods combined 

Red maple 

Buckeye 

0.85797 -1.39149 0,547 

0.86172 -1.34644 0,549 

0.83911 -1.15690 0.592 

APPALACHIAN MOUNTAINS 

0.83153 -0.59760 0.560 

0.89145 -1.23279 0.407 

0 94135 -2 09975 0.427 

0.84422 -1.09157 0.456 

0.84378 -0.35007 0.393 

0.86999 -1.02577 0.502 

0.81014 -0.57310 0.535 

0.81151 -0.53500 0,563 

0.84509 -1.15525 0.641 

0.86689 -1.36809 0.476 

0.88025 -1.70436 0.678 

0.86519 -2.04685 0,523 0 99 3.88 

Continued 
Table 11.--Regression coefficients for estimating d.i.b. at 17.3 feet from d.b.h and total 

height, for species and species groups across the South and in seven subregions"--Continued 

Standard 

Regression error of Coefficient of Coefficient 

Species or species group coefficients estimate determination of variation 

2 a b S R C.V. y.x 

Blackgum (Upland) 0.78470 -0.65579 0.802 0.99 6.85 

Basswood 0.84116 -0.49826 0.510 0.99 4.38 

All hard hardwoods combined 0.82671 -0.84167 0 . 738 0.99 7.11 

Birch 0.80280 -0.06620 0 697 0.99 7 39 

Hickory 0.83626 -1.07179 0.673 0 99 5.82 

Beech 

White ash 

White oak 

Chestnut oak 

All white oaks combined 

Scarlet oak 

Southern red oak 

Northern red oak 

Black oak 

All red oaks combined 

All oaks combined 

Black locust 

All hardwoods combined 

All pines combined 

Shortleaf pine 

Loblolly pine 

All major pines combined 

Virginia pine 

All soft hardwoods combined 

Swee tgum 

Yellow-poplar 

All hard hardwoods combined 

Hickory 

White oak 

Chestnut oak 

0.85250 -0.62346 0.341 

0.83090 -1.18637 0.433 

0.8114; -0.56323 0.735 

0.79580 -0 45995 0.664 

0.81548 -0.67382 0.672 

0.87070 -1.22351 0.511 

0.82778 -1.31455 0.690 

0.84559 -1.13114 0.550 

0.82254 -0.78424 0.429 

0.83966 -0.97461 0.548 

0.82813 -0.84795 0.636 

0.80385 -1.12726 0.449 

0.83678 -1.03135 0.645 

UPPER COASTAL PLAIN 

0.85116 -0.91480 0.624 

0.99 3.37 

0.99 5.73 

0.99 5.4 

0.99 3.6 

0 . 99 4.90 

0-99 5.81 

0.99 2.65 

0.99 4.93 

0.99 4-52 

0.99 4.45 

0.99 2.95 

Continued 
Table 11.--Regression coefficients for estimating d.i.b, at 17.3 feet from d.b.h and total 

height, for species and species groups across the South and in seven subregionsii--Continued 

Standard 

Regression error of Coefficient of Coefficient 

Species or species group coefficients estimate determination of variation 

2 a b S R C.V. y.x 

Post oak 0.79353 -0. 29955 0.55 0.99 5.76 

All white oaks combined 0.86600 -1.32802 0.537 0.99 4.70 

Scarlet oak 0 79932 -0.04135 0.739 0.99 5 85 

Southern red oak 0.82383 -1.13440 0.305 0.99 2.63 

All red oaks combined 0.82231 -0.74373 0.630 0 99 5.19 

All oaks combined 0.85175 -1.18487 0 590 0.99 5.03 

All hardwoods combined 0.84184 -1.03862 0.612 0.99 5.20 

DEEP SOUTH 

All pines combjned 

Shortleaf pine 

Slash pine 0.84805 -1.20946 0.477 0 99 4.84 

Spruce pine 0.88631 -1.16238 0 378 0.99 3.45 

Longleaf pine 0.89579 -1.48645 0.409 0.99 4.16 

~oblolly pine 0.87759 -1.50283 0 535 0.99 4.44 

All major pines combined 0 87535 -1.32793 0.527 0.99 4.94 

All soft hardwoods combined 0.83316 -0.96759 0.567 0.99 5.71 

Red maple 0.86263 -1.48044 0.629 0 99 6.36 

Swee tgum 0.85619 -1.82974 0.476 . 0.99 4.53 

Magnolia 0.83468 -0.51887 0 503 0.99 5.16 

Swee tbay 0.83164 -0.95206 0.363 0.99 4.20 

Blackgum (Upland) 0.80203 -0.86517 0.472 0.99 5.03 

Sycamore 0.84479 -1.23611 0 477 0.99 4.78 

Elm 0.93595 -2.15166 0.566 0.99 5.30 

All hard hardwoods combined 0.85487 - 1.30362 0.660 0.99 6.25 

Hickory 0.g0gi8 -2.81354 0.547 0.99 5-30 

Beech 0.87673 -0.65131 0.501 0.99 4.50 

Green ash 0.84047 -1.71696 0.771 0.99 9.01 

White oak 0.88643 -1.90252 0.613 0.99 5.65 

Post oak 0.83044 -0.86119 0.597 0.99 6.00 

All white oaks combined 0.84877 -1.10681 0.623 0.99 6.00 

Continued 
Table 11.--Regression coefficients for estimating d.i.b. at 17.3 feet from d.b.h and total 

height, for species and species groups across the South and in seven subregions"--Continued 

Standard 

Regression error of Coefficient of Coefficient 

Species or species group coefficients estimate determination of variation 

2 a b S R C.V. 

Y-x 

Southern red oak 

Cherrybark oak 

Water oak 

Willow oak 

All red oaks combined 

All oaks combined 

All hardwoods combined 

All pines combined 

Shortleaf pine 

Loblolly pine 

aiackgum (UpPandj 

All hard hardwoods combined 

Hickory 

White oak 

Post oak 

All white oaks combined 

Southern red oak 

Northern red oak 

Black oak 

All red oaks combined 

All oaks combined 

All hardwoods combined 

All soft hardwoods combined 

Hackberry 

Swee tgum 

Yellow-poplar 

Elm 

All hard hardwoods combined 

Hickory 

ARKANSAS AREA 

0.85116 -0.59055 0.610 0 99 4.78 

0.87049 -0.84867 0.578 0.99 4.67 

-1.05156 

-1.67304 

-1.30848 

-0.69129 

-1.31605 

-1.81272 

-0.68467 

-0.90267 

-0.82252 

-0.93016 

-1.18410 

DELTA AREA 

-1.25757 

-0.88550 

-1.47259 

-1,68268 

-1.49121 

-0.49207 

-1.64459 

0.99 5.18 

0.99 6.02 

0.99 5.65 

0.99 3 45 

0.99 5.65 

0.99 8 97 

0 + 99 4.35 

Continued 
Table 11.--Regression coefficients for estimating d.i.b. at 17.3 feet from d.b.h and total 

height, for species and species groups across the South and in seven subregionsg--Continued 

Species or species group 

Standard 

Regression error of Coefficient of Coefficient 

coefficients estimate determination of variation 

2 a b S R C.V. 

Pecan 

Green ash 

White oak 

Post oak 

Overcup oak 

All white oaks combined 

Southern red oak 

Nuttall oak 

Black oak 

All red oaks combined 

All oaks comb.ined 

All hardwoods combined 

2 

L'DIB17 = D(a + b(l7.3,H) 1 

where: DIBl7 = d.i.b. at 17.3 feet in inches 

D = d.b.h. in inches 

H = tree total height in feet 

a and b = regression coefficients 
Table 12.--Regression coefficients for estimating d.0.b. at 17.3 feet from d.b.h and total li height, for species and species groups across the South and in seven subregionsStandard 

Regression error of Coefficient of Coefficient 

Species or species group coefficients estimate determination of variation 

2 a b S R C.V. 

y . x 

All pines combined 

Shortleaf pine 

Slash pine 

Longleaf pine 

Loblolly pine 

All major pines combined 

Sand pine 

Spruce pine 

Table Mountain pine 

Pitch pine 

Pond pine 

White pine 

Virginia pine 

All other pines combined 

All cypress combined 

Baldcypress 

Pondcypress 

Hemlock 

All soft hardwoods combined 

Cherry 

Red maple 

Buckeye 

Hackberry 

Swee tgum 

Yellow-poplar 

Swee tbay 

Water tupelo 

Blackgum (Upland) 

Blackgum (Lowland) 

Sycamore 

Continued 
Table 12.--Regression coefficients for estimating d.0.b. at 17.3 feet from d.b.h and total 

height, for species and species groups across the South and in seven subregions"--Continued 

Species or species group 

Standard 

Regression error of Coefficient of Coefficient 

coefficients estimate determination of variation 

2 a b S R C.V. 

Magnolia 

Basswood 

Elm 

All hard hardwoods combined 

Beech 

Birch 

Hickory 

Pecan 

White ash 

Green ash 

White oak 

Overcup oak 

Chestnut oak 

Post oak 

All white oaks combined 

Scarlet oak 

Southern red oak 

Cherrybark oak 

Laurel oak 

Water oak 

Nuttall oak 

Willow oak 

Northern red oak 

Black oak 

All red oaks combined 

All oaks combined 

Black locust 

All hardwoods combined 

All pines combined 

Slash pine 

0 89035 -0.36485 0 - 547 

0.87854 0.18247 0.510 

0.83337 0.41856 0.765 

0.87243 -0.23513 0.809 

0.91141 -0.66730 0.525 

0.85516 -0,00134 0.667 

0.89772 -0.39920 0.641 

0.87734 -0.53003 0.907 

0 91531 -0.96788 0.618 

0 94193 -1.49985 0.940 

0.93266 -1.23167 0.590 

0.85146 -0.33596 0.827 

0.89280 -0.08423 0.579 

0.87574 -0.24370 0.497 

0.87759 -0.15654 0.681 

0.92204 -0.83926 0.467 

0 89375 -0.94777 0.549 

0.91590 -1.31763 0.577 

0.84882 -0.29314 0.400 

0.86881 -0.29747 0.452 

0.86807 -0.36240 0.860 

0.87548 -0.57500 0.513 

0.88329 -0.32529 0 - 517 

0.88567 -0.21760 0.528 

0.88290 -0.40049 0.639 

0.88047 -0.29054 0.658 

0.92160 -1 07997 0 537 

0.88067 -0.62804 0.876 

GULF AND ATLANTIC COASTAL PLAIN 

0.90439 -0.64356 0 493 

0.92729 -1.05973 0.465 

0.99 4.67 

0.99 4.57 

Continued 
Table 12.--Regression coefficients for estimating d.0.b. at 17.3 feet from d.b.h and total 

height, for species and species groups across the South and in seven subregions"--Continued 

Species or species group 

- - 

Standard 

Regression error of Coefficient of Coefficient 

coefficients estimate determination of variation 

2 a b S R C.V. 

Longleaf pine 

Loblolly pine 

All major pines combined 

Sand pine 

Pond pine 

All cypress combined 

Baldcypress 

Pondcypress 

All soft hardwoods combined 

Swee tgum 

Yellow-poplar 

Sweetbay 

Blackgum (Lowland) 

Red maple 

Water tupelo 

All hard hardwoods combined 

White oak 

Laurel oak 

Water oak 

Willow oak 

All red oaks 

All oaks combined 

All hardwoods combined 

All pines combined 

Shortleaf pine 

Longleaf pine 

Loblolly pine 

All major pines combined 

Virginia pine 

All soft hardwoods combined 

-0.12807 

-0 99155 

-1.38937 

-0.55725 

-0.83316 

-1.23167 

-0.29314 

-0.17495 

-1.08120 

-0.31186 

-6.72850 

-1.17512 

PIEDMONT 

-0.96754 

-1.03904 

-1.11778 

-1.04471 

-0,96128 

-0.43848 

-1.33900 

0.540 0.99 4.86 

0.494 0.99 4.57 

0.361 0 99 2.91 

0.552 0.99 4.81 

0 538 0 . 99 4.76 

0.406 0.99 4.27 

0.602 0.99 5.63 

Continued 
Table 14.-ch egression coefficients for estimating d.0.b. at 17.3 feet from d.b.h. and height to 

1 / &-inch d.0.b. top, for species and species groups across the South and in seven subregions- -- Continued 

Standard 

Regression error of Coefficient of Coefficient 

Species or species group coefficients estimate determination of variation 

2 a b S R C.V. y.x 

Magnolia 0.89693 -0.25550 0.534 0.99 5-07 . 

Basswood 0.88197 0.05921 0.507 0.99 4.01 

Elm 0.84680 0.07349 0 769 0.99 5 83 

All hard hardwoods combined 0.87101 -0.10646 0.766 0.99 5-99 

Beech 

Birch 

Hickory 

Pecan 

White ash 

Green ash 

White oak 

Overcup oak 

Chestnut oak 

Post oak 

All white oaks combined 

Scarlet oak 

Southern red oak 

Cherrybark oak 

Laurel oak 

Water oak 

Huttall oak 

Willow oak 

Northern red oak 

Black oak 

All red oaks combined 

All oaks combined 

Black locust 

All hardwoods combined 

All pines combined 

Slash pine 

GULP AND ATLANTIC COASTAL PLAIN 

0.99 4.10 

0.99 3.75 

Continued 
Table 14.--Regression coefficients for estimating d,o.b. at 17.3 feet from d.b.h. and height to 

1 I 4-inch d.0.b. top, for species and species groups across the South and in seven subregions- -- Continued 

Standard 

Regression error of Coefficient of Coefficient 

Species or species group coefficients estimate determination of variation 

2 a b S R C.V. y.x 

Longleaf pine 0. 90652 -0,30980 0 371 0 99 3.42 

Loblolly pine 0.89380 -0.39562 0.538 0.99 4.43 

All major pines combined 0.89848 -0.30721 0 453 0.99 4.06 

Sand pine 0.89177 -0.23376 0.380 0 99 4.84 

Pond pine 0.90114 -0.22623 0.351 0.99 3.49 

All other pines 0.89918 -0.24201 0.369 0.99 4.13 

All cypress 0.85891 -0.68793 0.724 0 99 6.95 

Baldcypress 

Pondcypress 

All soft hardwoods 

Swee tgum 

Yellow-poplar 

Sweetbay 

Blackgum (Lowland) 

Red maple 

Water tupelo 

All hard hardwoods combined 

White oak 

Laurel oak 

Water oak 

Willow oak 

All red oaks combined 

All oaks combined 

All hardwoods combined 

All pines combined 

Shortleaf pine 

Longleaf pine 

Loblolly pine 

All major pines combined 

Virginia pine 

-0.50806 

-0.51290 

-0.25298 

-0,26051 

-0.20585 

-0.07172 

-0.27067 

-0.14734 

-0.06215 

-0.26303 

-0.35564 

-0.04946 

-0.01205 

-0.65710 

-0.11646 

-0.26361 

-0.28475 

PIEDMONT 

-0.37140 

-0.28596 

-0.68607 

-0.41558 

-0.35629 

-0.21645 

5.66 

7-32 

8.19 

4.70 

4.57 

8.16 

7.26 

4.66 

lo. 58 

5.21 

4.79 

4.88 

4.16 

3.90 

4.24 

5-27 

7-67 

0.99 3.95 

0.99 3.26 

0.99 2.86 

0.99 4.11 

0.99 3.85 

0 99 4.12 

Continued 
Table 12.--Regression coefficients for estimating d.0.b. at 17.3 feet from d.b.h and total 

height, for species and species groups across the South and in seven subregions"--Cont inued 

Standard 

Regression error of Coefficient of Coefficient 

Species or species group coefficients estimate determination of variation 

2 a b S R C.V. y.x 

Red maple 0.78534 0.32305 0.361 0.99 4.70 

Sweet gum 0.90716 -1.58897 0.597 0.99 6.17 

Sycamore 0.87537 -1.22361 0- 595 0.99 5.04 

~lm 0.93432 -1.51214 0 757 0.99 6.66 

All hard hardwoods combined 0.92492 -0.96243 0.612 0.99 5.46 

Hickory 0.91940 -0.69950 0.659 0.99 5.69 

White oak 0.93949 -1.33686 0.618 0.99 5.53 

Chestnut oak 

Post oak 

All white oaks combined 

Scarlet oak 

Southern red oak 

Water oak 

Black oak 

All red oaks combined 

All oaks combined 

All hardwoods combined 

All pines and hemlock combined 

Shortleaf pine 

Table Mountain pine 

Pitch pine 

Virginia pine 

All yellow pines combined 

White pine 

Hemlock 

All soft hardwoods combined 

Red maple 

Buckeye 

Yellow-poplar 

0.97530 -1.16493 0.430 

0.85762 -0.05520 0.491 

0.94716 -1.22230 0.597 

0.93148 -0.81537 0.580 

0.89310 -0.85748 0.617 

0.92112 -1.18873 0.380 

0.92716 -0.99562 0.554 

0.91384 -0.92692 0 565 

0 92305 -0.93937 0.605 

0.90281 -0.80783 0.645 

APPALACIIIAN MOUNTAINS 

0.89200 -0.43162 

0.94609 -0.86655 

I. 00657 -1 95639 

0.91948 -0.70394 

0,87457 -0.22573 

0.92528 -0.77946 

0 87525 -0.49510 

0.88233 -0.47214 

0.92008 -1.10972 

0,92495 -1.23198 

0 95219 -1.83725 

0.92431 -1.19955 

0.99 4.516 

0.99 3.39 

0.99 3.65 

0.99 3.84 

0.99 4.06 

0 99 4.25 

0.99 3.95 

0 99 4.43 

0.99 4.59 

0 99 3.84 

0.99 5.93 

0.99 3 50 

Continued 
Table 12.--Regression coefficients for estimating d.0.b. at 17.3 feet from d.b.h and total 

height, for species and species groups across the South and in seven subregions"--Continued 

Standard 

Regression error of Coefficient of Coefficient 

Species or species group coefficients estimate determination of variation 

2 a b S R C.V. y.x 

Blackgum (Upland) 

Basswood 

All hard hardwoods combined 

Birch, 

Hickory 

Beech 

White ash 

White oak 

Chestnut oak 

All white oaks combined 

Scarlet oak 

Southern red oak 

Northern red oak 

Black oak 

All red oaks combined 

All oaks combined 

Black locust 

All hardwoods combined 

All pines combined 

Shortleaf pine 

Loblolly pine 

All major pines combined 

Virginia pine 

All soft hardwoods combined 

Swee tgum 

Yellow-poplar 

All hard hardwoods combined 

Hickory 

White oak 

Chestnut oak 

0.90024 

0.87854 

0.88636 

0.85516 

0. go046 

0.88404 

0.89948 

0.86488 

0.86544 

0.88037 

0.g1ogo 

0.89986 

0.88453 

0.88139 

0.88785 

0.87967 

0.92160 

0. goo85 

UPPER 

0.92503 

0.93193 

0.89604 

0.91629 

0.84114 

0.91264 

0.88671 

0.90533 

0.92820 

0.92886 

0.95156 

0.89084 

-0.74702 

-0.18247 

-0.34851 

-0.00134 

-0.48444 

-0.50032 

-0.53103 

-0.12071 

0.16634 

-0,18030 

-0.61067 

-0.83810 

-0.44088 

-0.09673 

-0.36663 

-0.19478 

-1.07997 

-0.67373 

COASTAL PLAIN 

-0.76642 

-0.55548 

-0.45007 

-0.53803 

0.10523 

-0.88947 

-0.54030 

-0.02909 

-0.90130 

-0.60142 

- 1.38428 

0.25894 

Continued 
Table 12.--Regression coefficients for estimating d.0.b. at 17.3 feet from d.b.h and total 

height, for species and species groups across the South and in seven subregions'--Continued 

----- 

Standard 

Regression error of Coefficient of Coefficient 

Species or species group coefficients estimate determination of variation 

2 a b S R C.V. y.x 

Post oak 

All white oaks combined 

Scarlet oak 

Southern red oak 

All red oaks combined 

All oaks combined 

All hardwoods combined 

All pines combined 

Shortleaf pine 

Slash pine 

Spruce pine 

Longleaf pine 

Loblolly pine 

All major pines combined 

All soft hardwoods combined 

Red maple 

Sweet gum 

Yellow-poplar 

Magno 1 i a 

Swee tbay 

Blackgum (Upland) 

Sycamore 

Elm 

All hard hardwoods combined 

Hickory 

Beech 

Green ash 

White oak 

Post oak 

All white oaks combined 

0.86909 -0.03502 0.487 0.99 4.56 

0 93382 -0.95965 0 527 0.99 4.17 

0.86030 0.55111 0.683 0.99 4.88 

0.92595 -1.37014 0.410 0 99 3-17 

0.90158 -0.57238 0.616 0.99 4.56 

0 - 92319 -0.87283 0.575 0.99 4.41 

0.92231 -0.83441 0.581 0.99 4.43 

DEEP SOUTH 

Continued 
Table 12.--Regression coefficients for estimating d.0.b. at 17.3 feet from d.b.h and total 

height, for species and species groups across the South and in seven subregionsi'--Continued 

Species or species group 

Standard 

Regression error of Coefficient of Coefficient 

coefficients estimate determination of variation 

2 a b S R C.V. 

Southern red oak 

Cherrybark oak 

Water oak 

~ill&w oak 

All red oaks combined 

All oaks combined 

All hardwoods combined 

All pines combined 

Shortleaf pine 

Loblolly pine 

Blackgum (Upland) 

All hard hardwo~ds combined 

Hickory 

White oak 

Post oak 

All white oaks combined 

Southern red oak 

Northern red oak 

Black oak 

All red oaks combined 

All oaks combined 

All hardwoods combined 

All soft hardwoods combined 

Hackberry 

Swe e t gum 

Yellow-poplar 

Elm 

All hard hardwoods combined 

Hickory 

-1.28107 

-1.31763 

-0.361 59 

-0.82396 

-0.60736 

-0.74529 

-0.83634 

ARKANSAS AREA 

-0.36350 

-0.58351 

-0.70493 

-1.07520 

-0.65860 

-0.51377 

-0.84192 

-0.35511 

-0.91297 

-1.30454 

-0.39776 

-0.66191 

-0.44289 

-0.601 57 

-0.83578 

DELTA AREA 

-1.20721 

-0.66456 

-1.14145 

-2.04733 

-1.02602 

-0.14761 

-1.07190 

0 99 4 95 

0.99 5.72 

0.99 5.61 

0-99 3.16 

0.99 5.48 

0.99 7.92 

0.99 4.13 

Continued 
Table 12.--Regression coefficients for estimating d.0.b. at 17.3 feet from d.b.h and total 

height, for species and species groups across the South and in seven subregions"--Continued 

-- - 

Standard 

Regression error of Coefficient of Coefficient 

Species or species group coefficients estimate determination of variation 

2 a b S R C.V. y.x 

Pecan 

Green ash 

White oak 

Post oak 

Overcup oak 

All white oaks combined 

Southern red oak 

Nuttall oak 

Black oak 

All red oaks combined 

All oaks combined 

All hardwoods combined 

2 

A/D0B17 = D(a + b(17.3/H) ) 

where: DOE17 = d.0.b. at 17.3 feet, in inches 

D = d.b.h. in inches 

H = tree total height in feet 

a and b = regression coefficients 
Table 13.--Regression coefficients for estimating d.i.b. at 17.3 feet from d.b.h. and height to 

1 / 4-inch d.0.b. top, for species and species groups across the South and in seven subregionsSpecies or species group 

- -- 

Standard 

Regression error of Coefficient of Coefficient 

coefficients estimate determination of variation 

2 a b S R C.V. 

All pines combined 

Shortleaf pine 

Slash pine 

Longleaf pine 

Loblolly pine 

All major pines combined 

Sand pine 

Spruce pine 

Table Mountain pine 

Pitch pine 

Pond pine 

White pine 

Virginia pine 

All other pines 

All cypress combined 

Baldcypress 

Pondcypress 

Hemlock 

All soft hardwoods combined 

Cherry 

Red maple 

Buckeye 

Hackberry 

Sweetgum 

Yellow-poplar 

Sweetbay 

Water tupelo 

Blackgum (Upland) 

Blackgum (Lowland) 

Sycamore 

SOUTHWIDE 

-0.38934 

-0.44197 

-0.50122 

-0,44264 

-0.47347 

-0,44607 

-0.26820 

-0.33446 

-0.83950 

-0.42143 

-0.33912 

-0.18446 

-0.19186 

-0.29093 

-0,80721 

-0.64227 

-0 70573 

-0.20634 

-0.35639 

-0.14592 

-0.26620 

-0.40672 

-0.36290 

-0.34564 

-0.26821 

-0.18697 

-0.01464 

-0.24686 

-0.29903 

-0.36098 

0.99 5.45 

0.99 4.84 

0.99 5.08 

0.99 4.85 

0.99 5.15 

0.99 5.36 

0.99 5.37 

0.99 3.47 

0.99 4.70 

0.99 4.40 

0 99 4 8,9 

0.99 4.52 

0.99 3 98 

0.99 5.83 

0.99 9.22 

0.99 6.31 

0 99 9.67 

0 99 4.80 

0.99 6.71 

0.99 3.19 

0.99 5.94 

0.99 6.40 

0.99 6.57 

0.99 5.76 

0.99 4.40 

0.99 8.32 

0.99 11.23 

0.99 5.31 

0.99 7.96 

0.99 4.94 

Continued 
Table 13.--Regression coefficients for estimating d.i.b. at 17.3 feet from d.b.h. and height to 

1 / 

4-inch d.0.b. top, for species and species groups across the South and in seven subregions- -- Continued 

Standard 

Regression error of Coefficient of Coefficient 

Species or species group coefficients estimate determination of variation 

2 a b S R C.V. 

Magnolia 

Basswood 

Elm 

All hard hardwoods combined 

Beech 

Birch 

Hickory 

Pecan 

White ash 

Green ash 

White oak 

Overcup oak 

Chestnut oak 

Post oak 

All white oaks combined 

Scarlet oak 

Southern red oak 

Cherrybark oak 

Laurel oak 

Water oak 

Nuttall oak 

Willow oak 

Northern red oak 

Black oak 

All red oaks combined 

All oaks combined 

Black locust 

All hardwoods combined 

All pines combined 

Slash pine 

0.83991 -0.32901 0.484 

0.83021 -0.11653 0.509 

0.80227 -0.21286 0.741 

0.80367 -0.22663 0.757 

0.86948 -0.27754 0.495 

0.80779 -0.14043 0.754 

0.81426 -0.32340 0.615 

0.81449 -0.50486 0.909 

0.81619 -0.55831 0.589 

0.83445 -0.87195 0.701 

0.83573 -0.41990 0.568 

0.78991 -0.32951 0.851 

0.80184 -0.18959 0.572 

0.80255 -0.24130 0.514 

0.80968 -0.23903 0.658 

0.84486 -0 39323 0.410 

0 79565 -0 39576 0.498 

0 83299 -0.58875 0.501 

0 77759 -0.12847 0.418 

0.80804 -0.12146 0.433 

0 82553 -0.37213 0- 839 

0.80844 -0.39672 0.501 

0.81783 -0.26276 0.533 

0.81231 -0.34214 0.467 

0.81869 -0.33826 0.616 

0.81486 -0.29437 0.634 

0 - 77932 -0.28470 0.461 

0.80505 -0.28467 0.820 , 

GULP AND ATLANTIC COASTAL PLAIN 

0.82213 -0.36900 0.492 

0.82191 -0.50291 0.423 

0.99 5.07 

0 99 4.64 

Continued 
Table 13.--Regression coefficients for estimating d.i.b. at 17.3 feet from d.b.h. and height to 

1 / &-inch d.0.b. top, for species and species groups across the South and in seven subregions- -- Continued 

Species or species group 

Standard 

Regression error of Coefficient of Coefficient 

coefficients estimate determination of variation 

2 a b S R C.V. 

y.x 

Yellow-poplar 

Blackgum (Upland) 

Cherry 

Basswood 

All hard hardwoods combined 

Birch 

Hickory 

Beech 

White ash 

White oak 

Chestnut oak 

All white oaks combined 

Scarlet oak 

Southern red oak 0.79825 -0.41735 0.702 0 99 6.73 

Northern red oak 0.82708 -0.39037 0 555 0.99 4.26 

Black oak 0.81626 -0.37848 0.412 0.99 3.36 

All red oaks combined 0.82862 -0.40352 0.551 0.99 4.47 

All oaks combined 

Black locust 

All hardwoods combined 

All pines combined 

Shortleaf pine 

Loblolly pine 

All major pines combined 

Virginia pine 

All soft hardwoods combined 

Swee tgum 

0.81592 -0.32782 

0.77932 -0.28470 

0.81711 -0.32020 

UPPER COASTAL PLAIN 

0. 83901 -0.46136 

0.86365 -0.52919 

0.81181 -0.41128 

0.84320 -0.53546 

0.80850 -0.04927 

0.81964 -0.54616 

0.79764 -0.37185 

Yellow-poplar 0,79795 -0.26821 0.473 0 99 4.40 

All hard hardwoods combined 0.82844 -0.36415 0.588 0.99 5.02 

Hickory 0.84656 -0.48309 0 538 0.99 4.65 

Continued 
Table 13.--Regression coefficients for estimating d.i.b. at 17.3 feet from d.b.h. and height to 

I/ 4-inch d.0.b. top, for species and species groups across the South and in seven subregions- -- Continued 

Standard 

Regression error of Coefficient of Coefficient 

Species or species group coefficients estimate determination of variation 

2 a b S R C.V. y.x 

All soft hardwoods combined 

Red maple 

Sweet gum 

Yellow-poplar 

Sycamore 

Elm 

All hard hardwoods combined 

Hickory 

White oak 

Chestnut oak 

All white oaks combined 

Scarlet oak 

Southern red oak 

Water oak 

Northern red oak 

Black oak 

All red oaks combined 

All oaks combined 

All hardwoods combined 

All pines combined 

Shortleaf pine 

Table Mountain pine 

Pitch pine 

Virginia pine 

All other pines 

White pine 

Hemlock 

All soft hardwood 

Red maple 

Buckeye 

0.83137 -0.27040 0.378 

0.78729 -0.15744 0.481 

0. 79703 -0.27153 0.498 

0.81678 -0.31038 0.582 

0.82317 -0.33846 0.556 

0.81039 -0.27780 0.579 

APPALACHIAN MOUNTAINS 

0.81997 -0.24009 0.568 

0.86103 -0.4501 5 0.413 

0.87420 -0.83950 0.499 

0.81607 -0.42143 0.460 

Continued 
Table 13.--Regression coefficients for estimating d.i.b. at 17.3 feet from d.b.h. and height to 

1/ 4-inch d.0.b. top, for species and species groups across the South and in seven subregions- -- Continued 

Standard 

Regression error of Coefficient of. Coefficient 

Species or species group coefficients estimate determination of variation 

2 a b S R C.V. 

Longleaf pine 

Loblolly pine 

All major pines combined 

Sand pine 

Pond pine 

All other pines 

All cypress 

Baldcypress 

Pondcypress 

All soft hardwoods 

Swee tgum 

Yellow-poplar 

Swee tbay 

Blackgum (Lowland) 

Red maple 

Water tupelo 

All hard hardwoods combined 

White oak 

Laurel oak 

Water oak 

Willow oak 

All red oaks combined 

All oaks combined 

All hardwoods combined 

All pines combined 

Shortleaf pine 

Longleaf pine 

Loblolly pine 

All major pines combined 

Virginia pine 

-0.17844 

-0.04333 

-0 31397 

-0.41990 

-0.12847 

-0.15360 

-0.92328 

-0.18673 

-0.31532 

-0.31656 

PIE DBONT 

-0.37233 

-0.43591 

-0.74616 

-0.46704 

-0.43888 

-0.26470 

0.99 4.76 

0.99 4.21 

0.99 3.65 

0.99 4.74 

0.99 4.65 

0.99 4.72 

Continued 
Table 13.--Regression coefficients for estimating d.i.b. at 17.3 feet from d.b.h. and height to 1 / 

&-inch d.0.b. top, for species and species groups across the South and in seven subregions- -- 

Continued 

Standard 

Regression error of Coefficient of Coefficient 

Species or species group coefficients estimate determination of variation 

2 a b S R c. v. y.x 

White oak 

Chestnut oak 

Post oak 

All white oaks combined 

Scarlet oak 

Southern red oak 

All red oaks combined 

All oaks combined 

All hardwoods combined 

All pines combined 

Shortleaf pine 

Slash pine 

Spruce pine 

Longleaf pine 

Loblolly pine 

All major pines combined 

All soft hardwoods combined 

Red maple 

Swee tgum 

Yellow-poplar 

Magnolia 

Swee tbay 

Blackgum (Upland) 

Sycamore 

Elm 

All hard hardwoods combined 

Hickory 

Beech 

Green ash 

White oak 

-0 45955 

-0.02255 

-0.13141 

-0.34247 

-0.18849 

-0.39576 

-0.32460 

-0.32800 

-0.2gooi 

DEEP SOUTH 

-0.46240 

-0.40684 

-0.38227 

-0.33446 

-0.51987 

-0.57194 

-0.46694 

-0.39781 

-0.33919 

-0.54749 

-0.15831 

-0.32901 

-0.28561 

-0.39408 

-0.24913 

-0.64730 

-0.43213 

-0.65863 

-0.25684 

-0.87195 

-0.65725 

Continued 
Table 13.--Regression coefficients for estimating d.i.b. at 17.3 feet from d.b.h. and height to 

1 / &-inch d.0.b. top, for species and species groups across the South and in seven subregions- -- Continued 

Species or species group 

Standard 

Regression error of Coefficient of Coefficient 

coefficients estimate determination of variation 

2 a b S R C.V. 

Post oak 

All white oaks combined 

Southern red oak 

Cherrybark oak 

Water oak 

Laurel oak 

All red oaks combined 

All oaks combined 

All hardwoods combined 

All pines combined 

Shortleaf pine 

Loblolly pine 

Blackgum (Upland) 

All hard hardwoods combined 

Hickory 

White oak 

Post oak 

All white oaks combined 

Southern red oak 

Northern red oak 

Black oak 

All red oaks combined 

All oaks combined 

All hardwoods combined 

All soft hardwoods combined 

Hackberry 

Sweet gum 

Yellow-poplar 

Elm 

-0 37839 

-0,52448 

-0.54761 

-0.58875 

-0.16835 

-0.42645 

-0.47482 

-0.47740 

-0.41870 

ARKANSAS AREA 

-0.39221 

-0.46706 

-0.59369 

-0.33884 

-0.32461 

-0.51691 

-0.30306 

-0.37703 

-0.34736 

-0.87641 

-0.20944 

-0.37194 

-0.25516 

-0.28623 

-0.37660 

DELTA AREA 

-0 ' 50597 

-0.35631 

-0.34564 

-0.26821 

-0.43674 

0.99 

0.99 

0.99 

0.99 

0.99 

Continued 
Table 13.--Regression coefficients for estimating d.i.b. at 17.3 feet from d.b.h. and height to 

1 / 

4-inch d.0.b. top, for species and species groups across the South and in seven subregions- -- Continued 

Standard 

Regression error of Coefficient of Coefficient 

Species or species group coefficients estimate determination of variation 

2 a b S R C.V. y.x 

All hard hardwoods combined 0.78845 -0.22744 1. 170 0.99 8.92 

Hickory 0.81486 -0.35768 0,466 0 99 4.52 

Pecan 0.81348 -0.47848 0.904 0 99 6.57 

Green ash 0.83445 -0.87195 0.701 0.99 8.19 

White oak 0.85127 -0.37082 0.730 0.99 5 98 

Post oak 0.84363 -0.27550 0 535 0.99 4.83 

Overcup oak 0.79375 -0.37802 0.915 0 99 0.602 

All white oaks combined 0.79991 -0.14132 0.922 0.99 6.89 

Southern red oak 0.82427 -0.55528 0.738 0.99 6.09 

Nuttall oak 0.82546 -0.38706 0.842 0.99 5.13 

Black oak 0.802.42 -0.2474% 0.654 0.99 5.56 

All red oaks combined 0.82526 -0.45706 0.780 0 99 5.48 

All oaks combined 0.81303 -0.29398 0.865 0 99 6.27 

All hardwoods combined 0.79830 -0.34324 1. 103 0.99 8.07 

2 

"DIB17 = D(a + b(17.3/Hx) ) 

where: DIBl7 = d.i.b. at 17.3 feet, in inches 

D = d.b.h. in inches 

H = tree height to a 4-inch d.0.b. top, in feet X 

a and b = regression coefficients 
Table 14.-@ egression coefficients for estimating d.0.b. at 17.3 feet from d.b.h. and height to 

1 / 4-inch d.0.b. top, for species and species groups across the South and in seven subregionsRegression 

Standard 

error of Coefficient of Coefficient 

Species or species group coefficients estimate determination of variation 

2 a b S R C.V. 

y.x 

A11 pines combined 

Shortleaf pine 

Slash pine 

Longleaf pine 

Loblolly pine 

All major pines combined 

Sand pine 

Spruce pine 

Table Mountain pine 

Pitch pine 

Pond pine 

White pine 

Virginia pine 

All other pines 

All cypress combined 

Baldcypress 

Pondcypress 

Hemlock 

All soft hardwoods combined 

Cherry 

Red maple 

Buckeye 

Hackberry 

Swee tgum 

Yellow-poplar 

Swee tbay 

Water tupelo 

Blackgum (Upland) 

Blackgum (Lowland) 

Sycamore 

Continued 
Table 14.- egression coefficients for estimating d.0.b. at 17.3 feet from d.b.h. and height to 

1 / &-inch d.0.b. top, for species and species groups across the South and in seven subregions- -- 

Continued 

Standard 

Regression error of Coefficient of Coefficient 

Species or species group coefficients estimate determination of variation 

2 a b S R C.V. y.x 

All soft hardwoods combined 0.87085 -0.24940 0.617 0.99 5.66 

Red maple 

Sweetgum 

Yellow-poplar 

Sycamore 0.85423 -0.30796 0.536 0.99 4.78 

Elm 0.88873 -0.32550 0.778 0.99 6.85 

All hard hardwoods combined 0.90119 -0.27094 0.596 0.99 5-25 

Hickory 0 90767 -0.23831 0.653 0.99 5-59 

White oak 0.90681 -0.35780 0.603 0.99 5.36 

Chestnut oak 0.93531 -0.25518 0.402 0.99 3.19 

All white oaks combined 0.91220 -0.31989 0 594 0.99 5.15 

Scarlet oak 

Southern red oak 

Water oak 

Northern red oak 

Black oak 

All red oaks combined 

All oaks combined 

All hardwoods combined 

A11 pines combined 

Shortleaf pine 

Table Mountain pine 

Pitch pine 

Virginia pine 

All other pines 

White pine 

Hemlock 

All soft hardwood 

Red maple 

Buckeye 

APPALACHIAN MOUNTAINS 

Continued 
Table 14.- egression coefficients for estimating d.0.b. at 17.3 feet from d.b.h. and height to 

1 / 4-inch d.0.b. top, for species and species groups across the South and in seven subregions- -- Continued 

Species or species group 

Yellow-poplar 

Blackgum (Upland) 

Cherry 

Basswood 

All hard hardwoods combined 

Birch 

Hickory 

Beech 

White ash 

Whi.te oak 

Chestnut oak 

All white oaks combined 

Scarlet oak 

Southern red oak 

Northern red oak 

Black oak 

All red oaks combined 

All oaks combined 

Black locust 

All hardwoods combined 

All pines combined 

Shortleaf pine 

Loblolly pine 

All major pines combined 

Virginia pine 

All soft hardwoods combined 

Sweet gum 

Yellow-poplar 

All hard hardwoods combined 

Hickory 

Standard 

Regression error of Coefficient of Coefficient 

coefficients estimate determination of variation 

2 a b S R C.V. 

y.x 

0.88410 

0.88792 

0.89576 

0.88197 

0.88389 

0.86814 

0.89648 

0.87570 

0.88884 

0.86737 

0.87030 

0.87024 

0.90270 

0.88348 

0.87549 

0.88525 

0.88601 

0.87989 

0 89903 

0.89144 

UPPER 

0.91350 

0.92447 

0.89386 

-0.24477 0.460 

-0.27491 0.814 

-0.12522 0.313 

0.05921 0.507 

-0.15720 0.636 

-0.16330 0 737 

-0.21224 0.684 

-0.16248 0.366 

-0.14231 0.373 

-0.10314 0.783 

-0.03047 0.695 

-0.04145 0.73923 

-0.24293 0.562 

-0.29111 0 699 

-0.12313 0 556 

-0.11175 0.494 

-0.16586 0.563 

-0.11767 0.642 

-0.28617 0.545 

-0.24651 0.634 

COASTAL PLAIN 

-0.40479 

-0.29106 

-0.28198 

0 99 4.26 

0.99 2 77 

0.99 4.48 

0.99 4.04 

0.99 3.77 

0.99 4.33 

0.99 4.90 

0 99 3 85 

0.99 4.39 

0.99 3.79 

Continued 
Table 14.--Regression coefficients for estimating d.0.b. at 17.3 feet from d.b.h. and height to 1 / 4-inch d.0.b. top, for species and species groups across the South and in seven subregions- -- Continued 

Species or species group 

White oak 

Chestnut oak 

Post oak 

All white oaks combined 

Scarlet oak 

Southern red oak 

All red oaks combined 

All oaks combined 

All hardwoods combined 

All pines combined 

Shortleaf pine 

Slash pine 

Spruce pine 

Longleaf pine 

Loblolly pine 

All major pines combined 

All soft hardwoods combined 

Red maple 

Sweet gum 

Yellow-poplar 

Magnolia 

Sweet bay 

Blackgum (Upland) 

Sycamore 

Elm 

All hard hardwoods combined 

Hickory 

Beech 

Green ash 

White oak 

Standard 

Regression error of Coefficient of Coefficient 

coefficients estimate determination of variation 

2 a b S R C.V. y.x 

-0.27635 

-0.27248 

-0.24233 

-0.23880 

DEEP SOUTH 

-0.3546O 

-0.32727 

-0.25196 

-0.26088 

-0.37719 

-0.48282 

-0.35825 

-0.31332 

-0.30052 

-0.43436 

-0,08812 

-0.25550 

-0.14620 

-0.32828 

-0.12366 

-0.47202 

-0.33350 

-0.58013 

-0.18137 

-0.78803 

-0.58248 

Continued 
Table 14.-ÿÿ egression coefficients for estimating d.0.b. at 17.3 feet from d.b.h. and height to 

1 / 

4-inch d.0.b. top, for species and species groups across the South and in seven subregions- -- Continued 

Standard 

Regression error of Coefficient of Coefficient 

Species or species group coefficients estimate determination of variation 

2 a b S R C.V. 

Post oak 

All white oaks combined 

Southern red oak 

Cherrybark oak 

Water oak 

Laurel oak 

All red oaks combined 

All oaks combined 

All hardwoods combined 

All pines combined 

-0.27801 

-0 + 37932 

-0.42860 

-0.46761. 

-0.13560 

-0.29555 

-0.34417 

-0.32263 

-0.33442 

ARKANSAS AREA 

-0.26570 

Shortleaf pine 0.92503 -0.32127 0.501 0.99 3.68 

Loblolly pine 0.90788 -0.41433 0.490 0.99 3.17 

Blackgum (Upland) 0.88203 -0.32886 0 - 519 0.99 4.34 

All hard hardwoods combined 0.89107 -0.20963 0 538 0.99 4.27 

Hickory 0.91212 -0.26360 0 535 0.99 4.30 

White oak 0.89087 -0.20648 0.566 0.99 4.50 

Post oak 

All white oaks combined 

Southern red oak 

Northern red oak 

Black oak 

All red oaks combined 

All oaks combined 

All hardwoods combined 

All soft hardwoods combined 

Hackberry 

Sweetgum 

Yellow-poplar 

Elm 

-0.15412 

-0.23758 

-0.56646 

-0.13060 

-0.27623 

-0.16870 

-0.19545 

-0.25317 

DELTA AREA 

-0.47022 

-0.28625 

-0.28063 

-0.24477 

-0.25791 

0 99 5.00 

0.99 5.66 

0.99 5.53 

0.99 3.85 

0.99 5.59 

Continued 
Table 14.--Regression coefficients for estimating d.0.b. at 17.3 feet from d.b.h. and height to 

1/ 4-inch d.0.b. top, for species and species groups across the South and in seven subregions- -- Continued 

Standard 

Regression error of Coefficient of Coefficient 

Species or species group coefficients estimate determination of variation 

L 

a b S R C.V. 

All hard hardwoods combined 

Hickory 

Pecan 

Green ash 

White oak 

Post oak 

Overcup oak 

All white oaks combined 

Southern red oak 

Nuttall oak 

Elack oak 

All red oaks combined 

All oaks combined 

All hardwoods combined 

2 

"DOB17 = D(a + b(17.3/Hx) ) 

where: DOBl7 = d.0.b. at 17.3 feet, in inches 

D = d.b.h. in inches 

H = tree height to a 4-inch d.0.b. top, in feet X 

a and b = regression coefficients 
Table 15.--Regression coefficients for estimating d.i.b. at 17.3 feet from d.b.h. and height to 

7-inch d.0.b. top (softwoods) and height to +inch d.0.b. top (hardwoods), for species and species 

1 / 

groups across the South and in seven subregionsStandard 

Regression error of Coefficient of Coefficient 

Species or species group coefficients estimate determination of variation 

2 a b S R C.V. 

All pines combined 

Shortleaf pine 

Slash pine 

Longleaf pine 

Loblolly pine 

All major pines combined 

Sand pine 

Spruce pine 

Table Mountain pine 

Pitch pine 

Pond pine 

White pine 

Virginia pine 

All other pines 

All cypress combined 

Baldcypress 

Pondcypress 

Hemlock 

All soft hardwoods combined 

Red maple 

Buckeye 

Hackberry 

Sweet gum 

Yellow-poplar 

Swee tbay 

Blackgum (Upland) 

Blackgum (Lowland) 

Sycamore 

Magnolia 

Basswood 

0.99 5.18 

0.99 4.72 

0.99 4.94 

0.99 4.68 

0.99 5.08 

0 99 5.21 

0.99 4.81 

0 99 3 34 

0 99 5 31 

0.99 4.09 

0.99 4.74 

0.99 4.34 

0 99 4.00 

0.99 5.12 

0.99 9.55 

0.99 6.08 

0.99 10.34 

0.99 4.65 

0.99 6.28 

0.99 5.58 

0 99 6.07 

0.99 6.08 

0 99 5.23 

0 99 4.71 

0 99 8.05 

0.99 5.10 

0.99 7.04 

0 99 4.97 

0.99 4.87 

0.99 4.11 

Continued 
Table 15.--Regression coefficients for estimating d.i.b. at 17.3 feet from d.b.h. and height to 

?-inch d.0.b. top (softwoods) and height to 9-inch d.0.b. top (hardwoods), for species and species 

groups across the South and in seven subregionsL/--Continued 

Species or species group 

--- 

Elm 

All hard hardwoods combined 

Beech 

Birch 

Hickory 

Pecan 

White ash 

Green ash 

White oak 

Overcup oak 

Chestnut oak 

Post oak 

All white oaks combined 

Scarlet oak 

Southern red oak 

Cherrybark oak 

Water oak 

Nuttall oak 

Willow oak 

Northern red oak 

Black oak 

All red oaks combined 

All oaks combined 

Black locust 

All hardwoods combined 

All pines combined 

Slash pine 

Longleaf pine 

Loblolly pine 

All major pines combined 

Standard 

Regression error of Coefficient of Coefficient 

coefficients estimate determination of variation 

2 a b S R C.V. y.x 

0.79755 -0.05318 0.831 

0.79646 -0.05063 0.805 

0.85139 -0.03113 0.476 

0.79552 0 03199 0.659 

0.80719 -0.08518 0.632 

0 79328 -0.08161 0.880 

0.80060 -0.08996 0.488 

0.65576 0.06129 0.863 

0.82274 -0.11024 0 596 

0 77729 -0.04719 0.890 

0.79633 -0.05454 0.608 

0 79173 -0.05179 0.506 

0.79921 -0.0361 1 0. 680 

0.83047 -0.10105 0.421 

0.78385 -0.11649 0.506 

0.81509 -0.15310 0.444 

0 79576 0.00843 0.467 

0.81161 -0.02696 0.877 

0.79847 -0.11006 0.520 

0.80887 -0.06456 0.565 

0.80091 -0.09622 0.482 

0.81135 -0.11809 0.662 

0.80569 -0.07819 0.673 

0.76080 0.01117 0.541 

0.79554 -0.07264 0.922 

GULP AND ATLANTIC COASTAL PLAIN 

0.80945 -0.17312 0.619 

0.80669 -0.19519 0.463 

0.82079 -0.16556 0,432 

0.81309 -0.20403 0.621 

0.81428 -0.17615 0.516 

0.99 5.97 

0.99 4.81 

0.99 4.18 

0.99 5.28 

0.99 4.85 

Continued 
Table 15.--Regression coefficients for estimating d.i.b. at 17.3 feet from d.b.h. and height to 

?-inch d.0.b. top (softwoods) and height to 9-inch d.0.b. top (hardwoods), for species and species 

groups across the South and in seven subregionsi/--Continued 

Species or species group 

Standard 

Regression error of Coefficient of Coefficient 

coefficients estimate determination of variation 

Sand pine 

Pond pine 

All other pines 

All cypress 

Baldcypress 

Pondcypress 

All soft hardwoods 

Sweet gum 

Yellow-poplar 

Sweetbay 

Blackgum (Lowland) 

Red maple 

All hard hardwoods combined 

White oak 

Water oak 

Willow oak 

All red oaks combined 

All oaks combined 

All hardwoods combined 

All pines combined 

Shortleaf pine 

Longleaf pine 

Loblolly pine 

All major pines combined 

Virginia pine 

All soft hardwoods combined 

Red maple 

Sweet gum 

Yellow-poplar 

Sycamore 

-0.15633 

-O.11806 

-0.10647 

-0 33559 

-0.25531 

-0.20278 

-0.09136 

-0.17661 

0.01789 

-0,02270 

-0. 06817 

0.08191 

-0.15813 

-0.18705 

-0.06817 

-0.19061 

-0.12657 

-0.15922 

-0.11981 

PIEDMONT 

-0.18125 

-0.22704 

-0.22503 

-0.23215 

-0.21755 

-0.14852 

-0.09307 

0.08634 

-0.10475 

-0.11434 

0.06190 

0.99 

0.99 

0.99 

0 + 99 

0.99 

0.99 

0.99 

0.99 

0 99 

0 = 99 

0 99 

Continued 
Table 15.--Regression coefficients for estimating d.i.b. at 17.3 feet from d.b.h. and height to 

?-inch d.0.b. top (softwoods) and height to 9-inch d.0.b. top (hardwoods), for species and species 

groups across the South and in seven subregionsL/--Continued 

- - 

Standard 

Regression error of Coefficient of Coefficient 

Species or species group coefficients estimate determination of variation 

2 a b S R C.V. 

Elm 

All hard hardwoods combined 

Hickory 

White oak 

Chestnut oak 

All white oaks combined 

Scarlet oak 

Southern red oak 

Water oak 

Northern red oak 

Black oak 

All red oaks combined 

All oaks combined 

All hardwoods combined 

All pines combined 

Shortleaf pine 

Table Mountain pine 

Pitch pine 

Virginia pine 

APP other pines 

White pine 

Hemlock 

All soft hardwood 

Red maple 

Buckeye 

Yellow-poplar 

Blackgum (Upland) 

Basswood 

All hard hardwoods combined 

Birch 

0.82105 -0.12649 

0.81862 -0.11491 

0.82244 -0.08677 

0.83220 -0.16781 

0.83786 -0.16357 

0.82678 -0.13958 

0.81892 -0.01249 

0.78722 -0.11730 

0.82227 -0.06274 

0.79068 -0.05985 

0.80128 -0.14328 

0.80976 -0.09912 

0.81846 -0.12074 

0.80782 -0.09134 

APPALACHIkN MOUNTAINS 

0.81681 -0.12555 

0 85177 -0.21342 

0.82541 -0.30158 

0.80459 -0.17945 

0.83240 -0.05362 

0 80539 -0.09665 

0.79877 -0.12387 

0.79732 -0.06334 

0.81483 -0.07660 

0.82568 -0.08486 

0.82222 -0.12441 

0.81884 -0.08312 

0.77242 -0.10132 

0.81984 0.04156 

0.80386 -0.06102 

0.79552 0 03199 

0.99 5-05 

0.99 3.61 

0.99 5.31 

0 99 4.09 

0.99 3.98 

0.99 4.97 

0.99 4.34 

0 99 4.65 

0.99 5.44 

0.99 5.24 

0.99 6.07 

0.99 4.08 

0.99 6.36 

0.99 4.11 

0.99 5.22 

0.99 5.92 

Continued 
Table 15.--Regression coefficients for estimating d.i.b. at 17.3 feet from d.b.h. and height to 

7-inch d.0.b. top (softwoods) and height to 9-inch d.0.b. top (hardwoods), for species and species 

groups across the South and in seven subregionsL/--Continued 

Standard 

Regression error of Coefficient of Coefficient 

Species or species group coefficients estimate determination of variation 

2 a b S R c .v. y.x 

Hickory 

Beech 

White ash 

White oak 

Chestnut oak 

All white oaks combined 

Scarlet oak 

Southern red oak 

Northern red oak 

Black oak 

All red oaks combined 

All oaks combined 

Black locust 

All hardwoods combined 

All pines combined 

0.81611 -0.10063 0.584 0.99 4.26 

0.80475 -0.06985 0.681 0.99 5 03 

0.76080 0.01117 0.567 0.99 5.02 

0.80765 -0.06992 0.693 0.99 5.23 

UPPER COASTAL PLAIN 

0.82365 -0.17541 0.601 0.99 5.27 

Shortleaf pine 0.84961 -0.22576 0.390 0.99 3.44 

Loblolly pine 0.80195 -0.20471 o .711 0.99 5.74 

All major pines combined 0.82639 -0.21460 0.642 0.99 5.45 

Virginia pine 

All soft hardwoods combined 

Swee tgum 

Yellow-poplar 

All hard hardwoods combined 

Hickory 

White oak 

Chestnut oak 

Post oak 

All white oaks combined 

Scarlet oak 

Southern red oak 

Continued 
Table 15.--Regression coefficients for estimating d.i.b. at 17.3 feet from d.b.h. and height to 

?-inch d.0.b. top (softwoods) and height to +inch d.0.b. top (hardwoods), for species and species 

groups across the South and in seven subregionsL/--Continued 

Standard 

Regression error of Coefficient of Coefficient 

Species or species group coefficients estimate determination of variation 

2 a b S R C.V. y.x 

All red oaks combined 

All oaks combined 

All hardwoods combined 

All pines combined 

Shortleaf pine 

Slash pine 

Longleaf pine 

Loblolly pine 

All major pines 

Spruce pine 

All soft hardwoods combined 

Red maple 

Sweet gum 

Yellow-poplar 

Magnolia 

Swee tbay 

Blackgum (Upland) 

Sycamore 

Elm 

All hard hardwoods combined 

Hickory 

Beech 

Green ash 

White oak 

Post oak 

All white oaks combined 

Southern red oak 

Cherrybark oak 

Water oak 

All red oaks combined 

DEEP SOUTH 

-0.19106 

-0.23884 

-0.14487 

-0.17066 

-0.23878 

-0.19353 

-0.15396 

-0.08664 

-0.07028 

-0.09150 

-0.01441 

-0.10291 

-0.09731 

-0.06841 

-0.05756 

-0.14785 

-0.07227 

-0.17712 

-0.03975 

-0.08898 

-0.16679 

-0.02867 

-0.12871 

-0,13424 

-0.15310 

-0.01661 

-0.09030 

Continued 
Table 15.--Regression coefficients for estimating d.i.b. at 17.3 feet from d.b.h. and height to 

7-inch d.0.b. top (softwoods) and height to 9-inch d.0.b. top (hardwoods), for species and species 

groups across the South and in seven subregionsy--Continued 

Species or species group 

Standard 

Regression error of Coefficient of Coefficient 

coefficients estimate determination of variation 

2 a b S R C.V. 

All oaks combined 

All hardwoods combined 

All pines combined 

Shortleaf pine 

Loblolly pine 

Blackgum (Upland) 

All hard hardwoods combined 

Hickory 

White oak 

Post oak 

All white oaks combined 

Southern red oak 

Northern red oak 

Black oak 

All red oaks combined 

All oaks combined 

All hardwoods combined 

All soft hardwoods combined 

Hackberry 

Swee tgum 

Yellow-poplar 

Elm 

All hard hardwoods combined 

Hickory 

Pecan 

Green ash 

White oak 

Post oak 

Overcup oak 

-0.10294 

-0.08142 

ARKANSAS AREA 

-0.19899 

-0.22485 

-0.24766 

-0.06223 

-0.09801 

-0.15325 

-0.06241 

-C. 38154 

-0.09662 

-0.18002 

-0.06502 

-0.08013 

-0.08248 

-0.08506 

-0.io500 

DELTA AREA 

-0.09210 

-0.05862 

-0.14822 

-0.14414 

-0.03019 

-0.06088 

-0.11432 

-0.08167 

0.06129 

-0.08590 

-0.15238 

-0.06228 

0.99 

0.99 

0.99 

0.99 

0 99 

0.99 

0 99 

0.99 

0.99 

0.99 

0 99 

0.99 

Continued 
Table 15.--Regression coefficients for estimating d.i.b. at 17.3 feet from d.b.h. and height to 

7-inch d.0.b. top (softwoods) and height to pinch d.0.b. top (hardwoods), for species and species 

groups across the South and in seven subregionsL/--Continued 

- 

Standard 

Regression error of Coefficient of Coefficient 

Species or species group coefficients estimate determination of variation 

2 a b S R C.V. y.x 

All white oaks combined 0.78992 0.02085 0.937 0.99 6.38 

Southern red. oak 0.81186 -0.20515 0.730 0.99 5.46 

Nuttall oak 0.81110 -0.03014 0.883 0.99 5.11 

Black oak 0.80142 -0.12838 0.998 0.99 5.11 

All red oaks combined 0.81430 -0.14532 0.841 0.99 5.42 

All oaks combined 0.80397 -0.07025 0.906 0.99 6.00 

All hardwoods combined 0.78401 -0.07594 1.206 0.99 8.21 

2 yore17 = o(. + b(i7.3/Hx) 

where: DIBl7 = d.i.b. at 17.3 feet, in inches 

D = d.b.h. in inches 

H = tree height t.0 a 7-inch d.0.b. top (softwoods) or X 

9-inch d.0.b. top (hardwoods), in feet 

a and b = regression coefficients 
Table 16.--Regression coefficients for estimating d.0.b. at 17.3 feet from d.b.h. and height to 

?-inch d.0.b. top (softwoods) and height to 9-inch d.0.b top (hardwoods), for species and species 

1 i 

groups sampled across the South and in seven subregionsSpecies or species group 

Regression 

coefficients 

Standard 

error of Coefficient of Coefficient 

estimate determination of variation 

2 a b s R C.V. 

y.x 

All pines combined 

Shortleaf pine 

Slash pine 

Longleaf pine 

Loblolly pine 

All major pines combined 

Sand pine 

Spruce pine 

Table Mountain pine 

Pitch pine 

Pond pine 

White pine 

Virginia pine 

All other pines 

All cypress combined 

Baldcypress 

Pondcypress 

Hemlock 

SOUTIIWIDE 

0.89450 -0.13734 0 550 

All soft hardwoods combined 0.87204 -0.08541 0.798 

Red maple 0.88457 -0.08811 0.707 

Buckeye 0.88433 -0.10564 0.837 

Hackberry 

Sweetgum 

Yellow-poplar 

Sweetbay 

Blackgum (Upland) 

Blackgum (Lowland) 

Sycamore 

Magnolia 

Basswood 

0.99 

0 99 

0.99 

0.99 

0.99 

0.99 

0.99 

0.99 

0.99 

0.99 

0.99 

0.99 

0.99 

0.99 

0.99 

0.99 

0.99 

0.99 

0.99 

0.99 

0 99 

0.99 

0 99 

0.99 

0.99 

0 99 

0.99 

0.99 

0 99 

0.99 

Continued 
Table 16.--Regression coefficients for estimating d.0.b. at 17.3 feet from d.b.h. and height to 

7-inch d.0.b. top (softwoods) and height to 9-inch d.0.b top (hardwoods), for species and species 

groups sampled across the South and in seven subregions1'--Continued 

Species or species group 

Standard 

Regression error of Coefficient of Coefficient 

coefficients estimate determination of variation 

2 a b S R C.V. 

Elm 

All hard hardwoods combined 

Beech 

Birch 

Hickory 

Pecan 

White ash 

Green ash 

White oak 

Overcup oak 

Chestnut oak 

Post oak 

All white oaks combined 

Scarlet oak 

Southern red oak 

Cherrybark oak 

Water oak 

Nuttall oak 

Willow oak 

Northern red oak 

Black oak 

All hardwoods combined 

All red oaks combined 

All oaks combined 

Black locust 

All pines combined 

Slash pine 

Longleaf pine 

Loblolly pine 

All major pines combined 

0.85687 -0.01844 0.856 

0 86593 -0.00701 0.809 

0.88813 -0.02679 0.498 

0.86178 -0.00272 0 598 

0.88968 -0.03612 0.670 

0.85541 0.01049 0.911 

0 89433 -0.05869 0.484 

0.72220 0.10776 0 947 

0.89391 -0.08706 0.616 

0.84039 -0.00116 0.852 

0.89338 -0.02394 0.620 

0.87437 -0.03572 0.476 

0.87242 0.00488 0.694 

0.89526 -0.06894 0 475 

0.86485 -0.08856 0.544 

0 87570 -0.07148 0.484 

0.84769 0.04176 0.467 

0.85618 0 03525 0.884 

0.86700 -0.08414 0 527 

0.87259 -0.01653 0.546 

0.87871 -0.00548 0,521 

0.86260 -0.03694 0 934 

0.87427 -0.05445 0.671 

0.87280 -0.02381 0.685 

0.88246 -0.00358 0.637 

GULP AND ATLANTIC COASTAL PLAIN 

0.88235 -0.11920 0.589 

0.89933 -0.14045 4.411 

0.89352 -0.11290 0 394 

0.88325 -0.16476 0.580 

0.88870 -0.12254 0.480 

0.99 5-13 

0 99 3.77 

0.99 3.45 

0.99 4.50 

0 99 4.07 

Continued 
Table 16.--Regression coefficients for estimating d.0.b. at 17.3 feet from d.b.h. and height to 

7-inch d.0.b. top (softwoods) and height to 9-inch d.0.b top (hardwoods), for species and species 

groups sampled across the South and in seven subregions"--Continued 

Species or species group 

Standard 

Regression error of Coefficient of Coefficient 

coefficients estimate determination of variation 

L 

a b S R C.V. y.x 

Sand pine 

Pond pine 

All other pines 

All cypress 

Baldcypress 

Pondcypress 

All soft hardwoods 

Sweet gum 

Yellow-poplar 

Sweetbay 

Blackqum (Lowland) 

Red maple 

All hard hardwoods combined 

White oak 

Water oak 

Willow oak 

All red oaks combined 

All oaks combined 

All hardwoods combined 

All pines combined 

Shortleaf pine 0.91030 -0.15030 0.382 0.99 3.16 

Longleaf pine 6. 91100 -0.26890 0.388 0.99 3.13 

Loblolly pine 0 89893 -0.28427 0.528 0.99 4.03 

All major pines combined 0. 90269 -6.17589 0.477 0.99 3.77 

Virginia pine 0.87348 -8.11701 0.378 8-99 3.77 

All soft hardwoods combined 0.86837 -0.07123 0.682 0.99 5.23 

Red maple 0.76189 0.08898 0.455 0.99 4.27 

Swe e tgum 

Yellow-poplar 

Sycamore 

0 86397 -0.06534 0.730 0- 99 5.60 

0.88411 -0,10933 0 . 505 0.99 3.69 

0.83300 0. oQ161 (a. 638 0 99 4.85 

Continued 
Table 16.--~egression coefficients for estimating d.0.b. at 17.3 feet from d.b.h. and height to 

7-inch d.0.b. top (softwoods) and height to 9-inch d.0.b top (hardwoods), for species and species 

groups sampled across the South and in seven subregions"--Continued 

Species or species group 

Standard 

Regression error of Coefficient of Coefficient 

coefficients estimate determination of variation 

2 a b S R C.V. 

Elm 0.89612 -0.13051 0.757 0 99 6.47 

All hard hardwoods combined 0.89780 -0.08898 0.605 0 99 4.77 

Hickory 0.90907 -0.07630 0.586 0 99 4.60 

White oak 

Chestnut oak 

All white oaks combined 

Scarlet oak 

Southern red oak 

Water oak 

Northern red oak 

Black oak 

All red oaks combined 

All oaks combined 

All hardwoods combined 

All pines combined 

Shortleaf pine 

Table Mountain pine 

Pitch pine 

Virginia pine 

All other pines 

White pine 

Hemlock 

All soft hardwood 

0.90319 -0.13027 

0.92890 -0.08733 

0.90754 -0.10717 

0.89178 -0.00164 

0.86621 -0.07982 

0.87956 -0.04742 

0.86968 0.03886 

0.90804 -0.16066 

0.88441 -0.07032 

0.89602 -0.08999 

0.88199 -0.05926 

APPALAClIIAN MOUNTAINS 

0.88205 -0.09587 

0.91722 -0.14075 

0.90043 -0.28868 

0.89487 -0.12543 

0.86754 -0.03855 

0.87039 -0.07864 

0.86316 -0.08326 

0.86920 -0.05278 

0.89060 -0.07892 

Red maple 0.88908 -0.08554 0.671 0.99 4.82 

Buckeye 0.88433 -0.10564 0 837 0.99 6.03 

yellow-poplar 0.89576 -0.03363 0.561 0 99 3-55 

Blackgum (Upland) 0.88526 -0.11044 0.903 0 99 5.70 

Basswood 0.87850 0.06035 0 565 0.99 3.90 

All hard hardwoods combined 0.87848 -0.03133 0.676 0.99 4.68 

Birch 0.86178 -0.00272 0 598 0.99 5-03 

Continued 
Table 16.- e egression coefficients for estimating d.0.b. at 17.3 feet from d.b.h. and height to 

7-inch d.0.b. top (softwoods) and height to +inch d.0.b top (hardwoods), for species and species 

groups sampled across the South and in seven subregions"--Continued 

Species or species group 

Standard 

Regression error of Coefficient of Coefficient 

coef f icients estimate determination of variation 

2 a b S R C.V. y.x 

Hickory 0.89438 -0.07682 0 732 0.99 4.91 

Beech 0.87258 -0.04166 0 337 0.99 2,11 

White ash 0.88792 -0.05736 0.436 0.99 3.39 

White oak 0.86182 0.00130 0 . 835 0.99 5.99 

Chestnut oak 

All white oaks combined 

Scarlet oak 

Southern red oak 

Northern red oak 

Black oak 

All red oaks combined 

All oaks combined 

Black locust 

All hardwoods combined 

All pines combined 

Shortleaf pine 

Loblolly pine 

All major pines combined 

Virginia pine 

All soft hardwoods combined 

0.89258 -0.03707 

0.88786 -0.12622 

0 87199 -0.03632 

0.88108 -0.01948 

0.88037 -0.03450 

0 87571 -0.02091 

0.88246 -0.00358 

0.88324 -0.05057 

UPPER COASTAL PLAIR 

0 901 57 -0.16773 

0.91688 -0.12348 

0.88459 -0.11500 

0.90103 -0.11744 

0.84730 -0.00102 

0.90145 -0.15631 

Swee tgum 0.87869 -0.07452 0.628 0.99 4.88 

Yellow-poplar 0 90397 0.00711 0.370 0.99 2.35 

All hard hardwoods combined 0.90030 -0.08087 0.585 0 99 4.31 

Hickory 0.91091 -0.04887 0.491 0.99 3.70 

White oak 0.91329 -0.12951 0.591 0.99 4.28 

Chestnut oak 0.88341 0.11844 0.328 0.99 2.40 

Post oak 0.88656 -0.09893 0.556 0.99 4.40 

All white oaks combined 0.90764 -0.10112 0 554 0 99 4.09 

Scarlet oak 0.89654 -0.06428 0.681 0 - 99 4.87 

Southern red oak 0.88762 -0.18478 0.426 0 99 3.14 

Continued 
Table 16.- egression coefficients for estimating d.0.b. at 17.3 feet from d.b.h. and height to 

7-inch d.0.b. top (softwoods) and height to pinch d.0.b top (hardwoods), for species and species 

groups sampled across the South and in seven subregions~'--Continued 

Standard 

Regression error of Coefficient of Coefficient 

Species or species group coefficients estimate determination of variation 

2 - a b 8 R C.V. 

All red oaks combined 

All oaks combined 

All hardwoods combined 

All pints combined 

Shortleaf pine 

Slash pine 

Longleaf pine 

Loblolly pine 

All major pines 

Spruce pine 

All soft hardwoods combined 

Red maple 

Swee tgum 

Yellow-poplar 

Magnolia 

Sweetbay 

Blackgum (Upland) 

Sycamore 

Elm 

All hard hardwoods combined 

Hickory 

Beech 

Green ash 

White oak 

Poa t oak 0.87123 -O.OO~~O 0.663 0.99 5.25 

All white oaks combined 0 89907 -0.09613 0.643 0.99 4.85 

Southern red oak 0.87359 -0.11618 0.612 0 99 4-59 

Cherrybark oak 0 87570 -0.07148 0.484 0 99 3.48 

Water oak 0.87032 -0.00260 0 537 0 99 4.04 

All red oaks combined 0.87351 -0.06005 0.546 0.99 4.12 

Continued 
Table 16.- egression coefficients for estimating d.0.b. at 17.3 feet from d.b.h. and height to 

?-inch d.0.b. top (softwoods) and height to 9-inch d.0.b. top (hardwoods), for species and species 

groups sampled across the South and in seven subregions--'/Continued 

Standard 

Regression error of Coefficient of Coefficient 

Species or species group coefficients estimate determination of variation 

2 a b S R C.V. y.x 

All oaks combined 0.88172 -0.06750 0.600. 0 99 4.53 

All hardwoods combined 0.88299 -0.07351 0.608 0.99 4.76 

ARKANSAS AREA 

All pines combined 

Shortleaf pine 

Loblolly pine 

Blackgum (Upland) 

All hard hardwoods combined 

Hickory 

White oak 

Post oak 

All white oaks combined 

Southern red oak 

Northern red oak 

Black oak 

All red oaks combined 

All oaks combined 

All hardwoods combined 

All soft hardwoods combined 

Hackberry 

Sweetgum 

Yellow-poplar 

Elm 

All hard hardwoods combined 

Hickory 

Pecan 

Green ash 

White oak 

Post oak 

Overcup oak 

DELTA AREA 

0.99 

0.99 

0.99 

0.99 

0.99 

0.99 

0 99 

0.99 

0 99 

0.99 

0.99 

0.99 

Continued 
Table 16.- egression coefficients for estimating d.0.b. at 17.3 feet from d.b.h. and height to 

?'-inch d.0.b. top (softwoods) and height to 9-inch d.0.b top (hardwoods), for species and species 

groups sampled across the South and in seven 8ubregions"--Continued 

Standard 

Regression error of Coefficient of Coefficient 

Species or species group coefficients estimate determination of variation 

2 a b S R c .v. y.x 

All white oaks combined 

Southern red oak 

Nuttall oak 

Black oak 

All red oaks combined 

All oaks combined 

All hardwoods combined 

2 

'/DOBl7 = D(a + b(17.3/Hx) ) 

where: DOBl7 = d.0.b. at 17.3 feet, in inches 

H = tree height to a 7-inch d.0.b. top (softwoods) or X 

9-inch d.0.b. top (hardwoods), in feet 

a and b = regression coefficients 
Table 17.--Average d.i.b. at 4.0 and 7.0 inches d.0.b. (softwoods) and at 4.0 and 

1/ 9.0 inches d.0.b. (hardwoods)- 

Species or 

Stem diameter inside bark where stem measures-- 

(Average and standard deviation) 

7.0 inches d.0.b. (softwood) 

species group 4.0 inches d.0.b. 9.0 inches d.0.b. (hardwoods) 

All pines combined 

Shortleaf pine 

Slash pine 

Longleaf pine 

~oblolly pine 3.6 + 0.1 6.4 + 0.2 - 

All major pines combined 

All other pines combined 

Sand pine 

Spruce pine 3.6 2 0.1 6.4 - + 0.1 

Table Mountain pine 

Pitch pine 

Pond pine 

White pine 

Virginia pine 

All cypress combined 

Baldcypress 3.6 2 0.1 6.5 2 0.1 

Pondcypress 3.4 2 0.2 6.2 + 0.3 - 

Hemlock 3.6 2 0.1 6.3 2 0.1 

All soft hardwoods combined 3.5 2 0.2 8.0 2 0.3 

Red maple 

Buckeye 

Hackbe rry 

Sweet gum 

Yellow-poplar 

Sweetbay 

Blackgum (Upland) 

Blackgua (Lowland) 

Sycamore 

Magno 1 i a 

Basswood 

Elm 

7.9 2 0.2 

8.6 - + 0.1 

8.2 + 0.2 

8.1 + 0.2 - 

8.1 - + 0.2 

Continued 
Table %?.--Average d.i.b. at 4.0 and 7.0 inches d.0.b. (softwoods) and at 4.0 and 

9 .O inches d. o. b. (hardwoods)y--Continued 

Stem diameter inside bark where stem measures-- 

(Average and standard deviation) 

Species or 7.0 inches d.0.b. (softwood) 

species group 4.0 inches d.0.b. 9.0 inches d.0.b. (hardwoods) 

All hard hardwoods combined 

Beech 

Birch 

Hickory 

Pecan 

White ash 

Green ash 

White oak 

Overcup oak 

Chestnut oak 

Post oak 

All white oaks combined 

Scarlet oak 

Southern red oak 

Cherrybark oak 

Water oak 

Nuttall oak 

Willow oak 

Northern red oak 

Black oak 

All red oaks combined 

All oaks combined 

Black locust 

All hardwoods combined 

yper use in equations 4. 5. and 6. 
*c.cca waa & 

-4hhO 

a(d4C.) ad6 CdOE 

w Md (dCP.4 

do04 

m L;I L;I 'CC 
Table 18.-st egression coefficients for estimating topwood ratios used to expand volume to a 7-inch d.0.b. top (softwoods) or to a 9-inch 

d.0.b. top (hardwoods) to volume to a 4-inch d.0.b. top, by species and species groups'/--Continued 

- -- - 

Topwood ratio - inside bark Topwood ratio - outside bark 

Species or species group Coefficients Statistics Coefficients Statistics 

- 2/ - 3 / - 2/ - 3/ 

2 2 a b c MSE R a b c MSE R 

Swee tbay 2485.43000 -2.77553 -0.86911 0.100 0.71 582.78000 -2.16738 -0.81731 0.092 0.77 

Blackgum (Upland) 894.12000 -1.93752 -1.14822 0.063 0.84 883.16000 -1.93753 -1.12364 0.070 0.83 

Blackgum (Lowland) 14231.48000 -4.26925 -0.38234 0 .085 0.83 11456.51000 -4.05755 -0.43561 0.091 0.83 

Sycamore 3184.46000 -2.25465 -1.12228 0.077 0.88 3029.23000 -2.20819 -1.13561 0.076 0.89 

Magnolia 1061 47000 -1.94681 - 1.19023 0.097 0.77 831.04000 -1.72652 -1.26013 0.098 0.78 

Basswood 13286 54000 -2.79296 -1.19864 0.046 0.87 8339.96000 -2.66620 -1.14255 0.049 0.86 

Elm 590.650"~ -1.20817 -1.49539 0.055 0.89 510.72000 -1.12455 -1.48817 0.058 0.89 

All hard hardwoods combined 1825.80000 -2.43971 -0.99275 0.065 0.79 1568.59000 -2.37061 -0.98418 0.068 0.79 

Beech 257.76000 -1.84770 -0.86672 0.045 0.69 235.85000 -1.78718 -0.87668 0.046 0.68 

Birch 10417.39000 -3.70789 -0.58295 0.079 0.85 7095. 10000 -3.45634 -0.63156 0.081 0.85 

Hickory 

Pecan 

White ash 1124.84000 -0.68661 -1.99037 0.066 0.88 1057.85000 -0.68648 -1.95678 0.069 0.88 

Green ash 782.40000 -1.06622 -1.66719 0.045 0.94 626.05000 -0.93812 -1.66882 0.049 0.94 

White oak 2142.11000 -2.71150 -0.84808 0.054 0.83 1789.90000 -2.63067 -0.83755 0.056 0.83 

Overcup oak 369.19000 -2.55005 -0.47367 0,048 0.84 309.79000 -2.48819 -0.44524 0.049 0.85 

Chestnut oak 1940.09000 -2.53246 -0.97033 0.050 0.74 1606,29000 -2.38996 -0.99773 0.052 0.73 

post oak 1864.13000 -2.42265 -1.07396 0.058 0.77 1309.47000 -2.27359 -1.05712 0.059 0 77 

All white oaks combined 1539 24000 -2.69777 -0.79071 0.057 0.78 1214.70000 -2.58072 -0.78690 0.059 0.78 

Scarlet oak 710,94000 -2.10508 -0.96103 0.041 0.78 578.14000 -2.04308 -0.93710 0.042 0.77 

Southern red oak 3419.94000 -2.45803 -1.19112 0.068 0.81 2838.68000 -2.39290 -1.17271 0.071 0.80 

Cherrybark oak 

\D 

0.82020 0.063 0.78 

Continued 

Table 19.--Accuracy of volume estimates obtained by using form-class segmented-profile equations and of volume estimates obtained by using 

Max and Burkhart's segmented-profile equation. Accuracy based on actual and simulated field measurements of loblolly pine, yell~~-p~plar, 

and white oak 

Averane absolute difference (observed-~redicted) and standard deviation 

Total Stemwood volume from stump to-- 

Equation and stem measurements st emwood Hgt to 9-in Hgt to 7-in Hgt to 4-in 

used to predict stem volume volume 4.5 feet 17.3 feet d.0.b. top d.0.b. top d.0.b. top 

-------------------percent------------------- 

LOBLOLLY PIRE 

Form class model with observed measurements 4.1 + 3.5 5.4 + 4.2 2.4 + 2.3 3.3 + 3-5 3.7 + 4.4 - - 3.7 2 3.3 

Max-Burkhart model with observed measurements 8.8 + 8.0 6.6 + 5.1 5.4 + 4.9 7.0 + 6.1 7.5 + 6.4 8.5 7.4 - - 

Form class model with D and DOBl7 observed and DIBD 

and DIB17 estimated with equations (7) and (8), 

respectively 5.4 + 4.6 6.4 + 5.2 4.1 + 3.5 4.7 + 4.3 5.0 + 4.7 5.1 + 4.3 - 

Form class model with DO817 measured to an average 

of + 0.2 inch 6.0 + 4.9 6.4 + 5.2 5.0 _t 4.4 5.4 2 4.8 5.7 + 4.6 - 4.4 + 3.6 - 

Form class model with form class estimated to an 

average of + 2 units and used to estimate DIBl7 5.4 + 4.1 6.4 + 5.2 3.7 + 2.9 4.9 + 4.1 5.1 2 4.4 5.2 + 3.9 - 

Porm class model with DIBl7 estimated using regional 

equation (9) and D and H 7.9 + 6.9 6.4 + 5.2 5.3 + 4.4 6.8 + 5.7 7.3 + 6.2 7.8 + 6.6 - - 

Form class model with average form class for pole 

and sawtimber used 9.6 + 8.6 6.3 + 5.2 5.5 + 4.7 7.2 + 6.1 8.2 + 6.8 9.0 + 7.8 

YELLOW-POPLAR 

Form class model with observed measurements 3.7 + 2.8 4.9 + 3.9 2.1 + 1.9 2.9 + 2.7 3.4 + 395 3.4 + 2.7 

Max-Burkhart model with observed measurements 7.2 + 5.2 5.9 + 4.7 4.0 - + 3.5 5.8 2 4.6 6.1 + 4.8 - 6.7 + 4.9 

Form class model with D and DOBl7 observed and DIBD 

and DIB17 estimated with equations (7) and (8), 

respectively 4.4 + 3.5 - 5.4 + 4.6 3.5 2 2.8 3.9 + 3.5 4.2 - + 4.0 4.2 + 3.3 - 

Continued 

Table 20. --Accuracy of volume estimates obtained by using form-class segmented-profi le equations and known d .b oh. and total 

height* known d.b.h. and height to 4-inch d.0.b. top, and known d.b.h. and height to 7-inch or pinch d.0.b. top 

Average absolute difference (observed-predicted) and standard deviation 

Equation 

Diameter D.b.h. and total height D.b.h. and height to =$-inch top D.b.h, and height to 7- or 9-inch top 

inside bark at Stemwood volume from stump to-- Stemwood volume from stump to-- Stemwood volume from stump to-- 

d.b.h. and 1'7.3 fty Saw-log top 4-inch top Saw-log top 4-inch top Saw-log top 4-inch top 

Observed 

Estimated 

Observed 

Estimated 

Observed 

Estimated 

LOBLOLLY PINE 

YELLOW-POPLAR 

WHITE OAK 

'Inside-bark diameter at d.b.h. estimated using equation (7) and inside-bark diameter at 17.3 feet estimated using 

equation (9) for total height model and equation (11) for height to fixed d.0.b. model.