Site Index for Loblolly Plantations on

Cutover Sites in the West Gulf Coastal Plain

T. W. Popham, D. P. Feduccia, T. R. Deli,

W. F. Mann, Jr., and T.E. Campbell

SUMMARY

Functions used previously to derive height-age

relationships for southern pines are compared in

order to develop new site index curves for loblolly

pine plantations on cutover sites in the lower West

Gulf.

Additional keywords: Pinus taeda, height

growth.

INTRODUCTION

Site index permits the timberland owner or

manager to classify forest land by its productive

capacity. Initial planting density, thinning regimes,

cutting cycles, and rotation lengths can be adjusted

according to the site index. Existing site index

curves are not suitable for loblolly pine (Pinus

taeda L.) planted on cutover sites in the West Gulf.

Curves for naturally regenerated loblolly (U.S.

Forest Service 1929, Zahner 1962, Trousdell and

others 1974) show a steady increase in estimated

site index when measurement is repeated. The

same is true of the Coile and Schumacher (1964)

curves for planted loblolly on drainage classes

d, -d,. Site curves from Lenhart (1971) and

Smalley and Bower (1971) are for loblolly planted

on old fields. The Lenhart (1971) curve has heights

greater at early ages and lower at older ages while

the Smalley and Bower (1971) curve has heights

lower at older ages than observed averages for

plantations on cutover sites.

Myers’ (1977) yield program for planted loblolly

computes heights by combining Lenhart’s (1971)

old-field curve for ages 3 to 25 and Farrar’s (1973)

curve for natural stands for ages 25 and beyond.

For site indices 30 to 100 (index age 25) and ages

up to 70, Myers’ program predicts taller trees than

any of the anamorphic loblolly curves we investigated and for site indices 60 to 100 (index age

25) of the Trousdell and others (1974) polymorphic

curves. Our paper presents new curves for

estimating site index and height growth of loblolly

pine plantations on cutover sites in the lower West

Gulf Coastal Plain. The height-age relationship

presented here was used in a system to generate

yield tables in Feduccia and others (1979).

METHODS

A total of 787 age and height determinations

were available from 293 permanent plots

geographically distributed as shown in figure 1.

Plots were measured from one to six times at

intervals of 1 to 5 years. The height value used for

each plot observation was the average of the

dominant and codominant trees on the plot. Plots

were located in plantations on cutover sites having

no establishment problems or accidents that

retarded growth. The age and site index distribution of the observations are shown in table 1.

Two basic mathematical models are frequently

used to determine site index for the southern pines

(table 2). Models 1 a, 1 b, 1 c, 1 d, and 2a were fitted

to our data. The fitted regression of height on age

Southern Forest Experiment Station/T-10210 U.S. Postal Services Bldg., 701 Loyola Avenue, New Orleans. La 70113

Forest Service, U.S. Depsrtment of Agriculture.

Servmg Alabama, Arkansas, Louisiana, Mississippi, Eastern Oklahoma, Tennessee, Eastern Texas.
Figure 1 -Geographic location of 293 plots (numbers enclosed in boxes); 787 observations (numbers not enclosed in boxes).

Popham is Mathematical Statistician; Feduccia, Research Forester; Dell, Mathematical Statistician; Mann, Chief Silviculturist; and

Campbell, Silviculturist. All are employed by the Southern Forest Experiment Station, Forest Service-USDA, except Feduccia,

who is assigned to the Southern Station by the Louisiana Office of Forestry.

2
Table 1 .-Number of observations classified by age and site index (index age 25)

Site Index

Age < 45 45-50 50-55 55-60 60-65 65-70 > 70 Total

5-7 6 ____ 1 1 7 7

8-l 2 7 1 9 1 6 5 8

13-17 7 3 1 7 46 6 2 1 1

18-22 1 9 1 6 7 4 40 4 6

2 5 2 1 0 2 8 2 7 9 ____

3 0 2 1 6 3 8 1 1 2

3 5 ____ 2 1 0 3 9 1 5 3

40 1 3 3 4 1 9 3

4 5 4 4 1 2 3 1

9 3 1

1 4 6 0

3 149

9 195

____ 7 6

____ 6 9

___. 6 9

____ 6 9

6 9

Total 2 3 2 7 114 316 191 8 1 3 5 787

was required to approximate the data center of

mass over the range of ages. Also, on plots

measured more than once, site index of plots when

they were older had to be consistent with the site

index estimated when the plots were younger. This

consistency was evaluated for each model by a

combination of statistical procedures. The site

index computed for a plot when it was older was

plotted over the index computed for an earlier age

in pairs of successive observations on a plot. A

simple linear regression was fitted through the

points to give a visual impression of possible bias.

A chi-square procedure (Freese 1960) was used to

evaluate the consistency of site index determination at progressing ages.

have the greatest weight in fitting the relationship

of height to age. Farrar (personal communication)’

suggests weighted regression with the square of

age as the weight. When fitting the relationship

with the square of age as weight, it was impossible

to distinguish between the models by using

statistical criteria. Model 1 c was selected because

it best approximated the data center of mass for the

older plots.

Remeasurement data were insufficient for a

polymorphic approach to site curves as

recommended by Curtis (1964). so anamorphic

curves were used.

RESULTS AND DISCUSSION

The coefficients for model 1 c, fitted by weighted

regression, are:

b,= 2.24283

b, = -21.0977

b,= 316.282

b,= -2443.84

b,= 6318.86

The regression lines were well below the

average height of the older plots when the models

were fitted using unweighted regression. The

longer a stand occupies a site the more accurately

it represents the growth potential of the site.

Obtaining data from age classes 30 to 50 years is

difficult because of the scarcity of older plantations. Logically, the oldest data collected should

Site index for a given height and age iscomputed

by equation 1 (fig. 2) and height for a given site and

age is computed by equation 2 (fig. 2).

Estimates of site mdexor height beyond 45years

‘Robert M. Farrar, Jr. Research Forester, Southern Forest

Experiment Station, Monticello, Ark.

3
Table 2.-Frequently used models for relating height to age in southern pines

MODEL REFERENCE

I. Height=lOfbo+bl (function Of Age’)or Log,,Height=b,+b, (function of Age)

(la) H=lO’botbriA) or Log,,H=bc+b, /A; Zahner (1962), Coile

& Schumacher (1964),

b, and b, parameters to be estimated; H is observed height at age A.

(lb) H=lO’bO+bli,,% or Log,cH=b,+b,/fl; b,, b,, H, and A same asmodel (la)

Lenhart (1971)

Smalley & Bower

(1971)

(1~1 H=,o’bo+b,/A+b~/A*+b3’A3+b4/n4, or Log,,H=b,+b,/A+b,/A2+b3/A3+b4/A4;

b,, b,, H, and A same as model (la).

Farrar (1973)

(Id) H=b,+b, (Log,,A); b,, b, , H, and A same as model (la). Larson & Moehring

(1972)

)_. Height=a(l-e-r’blAge))c ; a, b, and c parameters to be estimated. Pienaar & Turnbull

Chapman-Richards generalization of Von Bertalanffy’s equation. (1973)

(2a) H=a(l-e -b’A))c; a, b, and c parameters to be estimated, H is observed Bailey and others

height at age A. (1973)

(2b) H=a( 1-ewbAF; Where a=b, +b,S, b=b, +b,S+b, S2, H and A are same as model Graney & Burkhart

(2a) and S=site index, 5 parameters to be estimated. (1973)

(2~) H=a(l-embA)* ; wherea=b,+b2S, b=b,+b4S+b,S2, m=b,+b,S+b,S2, Trousdell and others

H and A are same as model (2a), and S=site index, (1974)

8 parameters to be estimated.

are an extrapolation beyond our data. The model

cannot be used below age 6. The function reaches

a minimum between 5 and 6 and goes to infinity as

age approaches 0. Evaluation of site quality from

observations of plots less than 10 years old cannot

take into account long-term environmental conditions. Some situations, such as computer

simulation, require computing a height for a

specific site index regardless of age. The FORTRAN

computer subprogram (fig. 3) provides for computing height when the age is less than 6 by linear

interpolation between 0 height at age 0 and height

at age 6 for the specific site index.

The data used in exploring the height-age

relationship represent a broad area and a variety of

conditions. The chosen function should, on the

average, be good. Computer programs capable of

linear and non-linear least-squares regression

with weighting are readily available. Development

of specific relationships using local data sets is

more feasible than in the past.

To generate site index or height tables with our

model, a computer program by Farrar (1975) can be

modified easily by substituting the coefficients

b,, b,, b, , b, for those in line SOH 123. Also, line

PRT 106 should be changed to remove M. P. 50

from the printed output.

Curves for site indices 30 to 80 (index age 25)

where generated using equation 2 (fig. 2). The

curves are shown in figure 4.

4
Equation 1.

S,=H, (IO)

Equation 2.

where:

AP zplantation age (the number of growing I =reference or index age (plantation age to

seasons since the seedlings were planted), which site quality is referenced),

HD=average height of dominant and codominant

trees at any given Ap,

S, =site index, the average height of dominant

and codominant trees at a given reference

age.

Flgure Z.-General equations for computing site index given height and age (equation 1) or height given site index and age

(equation 2).

SUkRUUI’IijE KTSI (CO,AI,X,SH,I,AL)

c--

C-- CCjEE IS A REAL ARRAY OF SIZE 4 I\HICH COtiTAIN S TKE F"ODEL COEFFICIENTS

c-.- AI IS 'THE; IabEX ACE

C-- X 15 ACT: AS A REAL VARIAdLE

C-- Str IS EITi-iBh 'PI16 SITE Ii40EX OR THE HEIGti?

C-- I IS AN ItifiICAI'OR VALUE, 1. COMPUTATIOiv OF HEIGHT GIVEN SITE INDEX

c-- -1. CCt.;PUTATION OF SITE INhEX GIVEN HEIGHT

2-- AL IS ThE LLAS?' IIv'I'ECRAL AGE A'p WICH FUKCTIOb SHOULD BE EVALUATED

;3-- ~~I'IHOUT IPiVOKIfiG ItvTERPOLATIQi OPTION.

C-- A.LL AktlGCIPXtu’lS ARE REAL VARIABLES.

C--

REAL CO(4),AX,X,SH,I,AL

\/I.=CO(1)/AI+CG(2))AI**2+Cd(3)/AI**3+CO(4)/AI**4

IF (X.Gt.AL) GO TC 10

IF (I.LT.0) co TO 20

L'2=CO(1)/AL+CO(2)/AL**2+CO(~)/AL**3+CO(4)/AL**4

'ISH=(X*(SE*l.O.**(VZ-Vl))))/AL

SH=TSh

kE1'URDj

1c L2=CO(l)/X +cc(2)/x**2 +co( 3)/X”“3 +cc(4) /x**4

~ys~~z-s[!*l(j. ** (I * (V2-Vl) )

si7=1’c; 11

EE’l;li;;q

2 0 Sfi=(;*

RETU F.iJ

E hU

Figure 3.-Computer subprogram to compute height or site Index given the other and age. CO(l). CO(2). CO(3). CO(4) should be set

equal to b,. b2, b3, b, respectively. AL should be set equal to 6.

5
- 7 0

aa

aa

V

60

c

I

a

J 50

I

40

30

20

10 I

..............

........ .... ... .............. . . ... .... .. ......... .. .. .... .. .... ....

........

................ I

10 15 20 25 30 35 40 45 50

A G E

60

65

Figure 4.-Loblolly site index curves (index age 25); plantations on cutover sites.

6
LITERATURE CITED

Bailey, R. L., W. F. Mann, Jr., and T. E. Campbell.

1973. Slash pine site index in the West Gulf. U.S.

Dep. Agric., For. Serv. Res. Note SO-l 69, 4 p.

South. For. Exp. Stn., New Orleans, La.

Coile, T. S., and F. X. Schumacher.

1964. Soil-site relations, stand structure, and

yields of slash and loblolly pine plantations in

the southern United States. 296 p. T. S. Coile,

Inc., Durham, N.C.

Curtis, R. 0.

1964. A stem-analysis approach to site-index

curves. For. Sci. IO:241 -256.

Farrar, R. M., Jr.

1973. Southern pine site index equations. J. For.

71:696-697.

Farrar, R.M., Jr.

1975. Southern pine site-index computing

programs. U.S. Dep. Agric., For. Serv. Res.

Note SO-197, 8 p. South. For. Exp. Stn., New

Orleans, La.

Feduccia, D. P., T. R. Dell, W. F. Mann, Jr., T. E.

Campbell, and B. H. Polmer.

1979. Yields of unthinned loblolly pine plantations on cutover sites in the West Gulf

region. U.S. Dep. Agric. For. Serv. Res. Pap.

SO-148 88 p. South. For. Exp. Stn., New

Orleans, La.

Freese, Frank.

1960. Testing accuracy. For. Sci. 6:139-l 45.

Graney, D. L., and H. E. Burkhart.

1973. Polymorphic site curves for shortleaf pine

in the Ouachita Mountains. U.S. Dep. Agric.,

For. Serv. Res. Pap. SO-85, 12 p. South. For.

Exp. Stn., New Orleans, La.

Larson, E. H., and D. M. Moehring.

7

1972. Site index curves for longleaf pine in east

Texas. Dep. For. Sci. Res. Note No. I,3 p. Tex.

A&M Univ., Dep. For. Sci., College Station,

Tex.

Lenhart, J. D.

1971. Site index curves for old-field loblolly pine

plantations in the interior West Gulf coastal

plain. Tex. For. Pap. No. 8, 4 p. Sch. For.,

Stephen F. Austin State Univ., Nacogdoches,

Tex.

Myers, C. A.

1977. A computer program for variable density

yield tables for loblolly pine plantations. U.S.

Dep. Agric., For. Serv. Gen. Tech. Rep. SO-l 1,

31 p. South. For. Exp. Stn., New Orleans, La.

Pienaar, L. V., and K. J. Turnbull.

1973. The Chapman-Richards generalization of

Von Bertalanffy’s growth model for basal area

growth and yield in even-aged stands. For. Sci.

19:2-22.

Smalley, G. W., and D. R. Bower.

1971. Site index curves for loblolly and shortleaf

pine plantations on abandoned fields in

Tennessee, Alabama, and Georgia highlands.

U.S. Dep. Agric. For. Serv. Res. Note SO-l 26,6

p. South. For. Exp. Stn., New Orleans, La.

Trousdell, K. B., D. E. Beck, and F. T. Lloyd.

1974. Site index for loblolly pine in the Atlantic

coastal plain of the Carolinas and Virginia.

U.S. Dep. Agric., For. Serv. Res. Pap. SE-l 15,

11 p. Southeast. For. Exp. Stn., Asheville, N.C.

U. S. Dep. Agric. For. Ser.

1976. Volume, yield, and stand tables for

second-growth Southern pine. U.S. Dep.

Agric. Misc. Publ. 50. 202 p. Rev. [I929 ed.]

Zahner, Robert.

1962. Loblolly pine site curves by soil groups.

For. Sci. 8:104-l 10.

U.S. GOVERNMENT PRINTING OFFICE: 1979-675466