United States

Department of

Agriculture

Forest Service

Loblolly Pine Growth and

Yield Prediction for Managed

Southern Forest

Experiment Station West Gulf Plantations

New Orleans,

Louisiana

Research Paper

SO-236

V. C. Baldwin, Jr. and D. P. Feduccia
Baldwin, V.C., Jr. and Feduccia, D.P. 1987. Loblolly pine growth and yield 

prediction for managed west gulf plantations. Res. Pap. SO-236. New Orleans, 

LA: U.S. Department of Agriculture, Forest Service, Southern Forest Experiment 

Station. 27 p.

ERRATA

Equation (6) and equation (7) on page 6 are both missing one instance of the gamma function that is 

necessary.

( ) 2 (1/ 1) (2/ 1)

2 2 2 E X = a + abΓ c + + b Γ c + (6)

2

2/

2

93

1/

2 2 93

(2.65926)

( ) (2/ 1)

(2.65926)

2 ( ) (1/ 1)

( ) a

a X a c X a c

X E X qmd c c+

− Γ +

+

− Γ +

= = (7)

Equation (12) on page 6 and equation (13) on page 8 each contain and error in the exponent term. The 

equations should read as follows:

A

qmd X HD TS e

0.70266 0.25968 0.45967/

2.14462( ) ( )

−

= (12)

A X HD TS e0.71401 0.22932 0.45967/

93 2.24213( ) ( )

−

= (13)

Equation (19) on page 10 should read as follows:

X a X b HD b BA a BA b 2.63243 0.766348 0.6102( ) 5.144246( ) /( )

1, = + 1, + − (19)

In Table 10., page 14, the third and fourth dependent variables should be:

TDWob

TDWib.
SUMMARY

A growth and yield prediction system is presented for use in thinned or

unthinned loblolly pine plantations in the west gulf region. The equations

predict cubic- and board-foot volume, green-weight, and dry-weight yields per

unit area of wood only or wood with bark of entire tree boles, boles to any top

diameter limit, and branches. Green and dry weight of foliage can also be

predicted. Total stand yields for weight or volume are partitioned into l-inch

diameter classes to forecast stand and stock tables for all aboveground tree

components for any stage of plantation development from ages 10 through 45.

The data for this system of equations came from 859 measurements of thinned

and unthinned long-term research study plots on cutover sites located in east

Texas, Louisiana, and southern Mississippi. A computer program COMPUTE

P-LOB (Comprehensive Outlook for Managed Pines Using simulated Treatment Experiments-Planted Loblolly Pine) that produces the yield tables can

be obtained from the authors.

ACKNOWLEDGMENTS

The Southern Forest Experiment Station is indebted to the following organizations for their contributions and assistance in obtaining data for this study:

Boise Cascade, DeRidder, LA

International Paper Co., Harrisburg, TX, and Colfax, LA

Georgia Pacific Corp., Meadville, MS and Bastrop, LA

Kisatchie National Forest, Pineville, LA

Southwestern Timber Co., Jasper, TX

Rice Land and Lumber Co., Merryville, LA

Cavenham Forest Industries, DeRidder, LA and Bogalusa, LA

Louisiana Office of Forestry, Woodworth, LA

We also recognize Dr. Mike R. Strub for some earlier cooperative work on

this project, Mr. Robert B. Ferguson’s programming efforts over the last

2 years, and Dr. Eugene Shoulders for persistency in keeping the biometric

applications in line with silvics principles. Other scientists were at one time

responsible for the studies that provided the data for this modeling effort. They

are Dr. Hans G. Enghardt, Mr. Thomas E. Campbell, and Mr. William F.

Mann, Jr.

Partial funding for this work was provided through a cooperative agreement

with the U.S. Department of Energy and administered by the Tennessee Valley

Authority (contract number TV-64328A).

July 1987
Loblolly Pine Growth and Yield Prediction

for Managed West Gulf Plantations

V. C. Baldwin, Jr. and D. P. Feduccia

INTRODUCTION

Loblolly pine (Pinus taeda L.) is the most important

commercial softwood species in the South and the

most widely planted southern pine. Managers of

loblolly pine plantations need accurate and complete

predictions of tree component growth and yield by

weight, as well as volume, to formulate flexible management policies and predict expected monetary returns for numerous product alternatives. There is a

critical need for this information on cutover and prepared sites in the west gulf region.

Recently, a yield prediction system for thinned

loblolly pine plantations in this region was published

by Matney and Sullivan (1982). However, this data

base consisted only of old-field plantation study data.

Other thinned loblolly pine plantation models

(Daniels and Burkhart 1975, Cao and others 1982,

Burkhart and Sprinz 1984) utilized either old-field or

cutover land data, but those data were from the

Southeast region of the United States. Only Coile and

Schumacher (1964) used some cutover site data from

the west Gulf region in the development of their yield

equations.

A growth and yield prediction system is presented

that provides both weight and volume yields of aboveground tree components by diameter classes for lo- to

45year-old thinned or unthinned loblolly pine plantations on cutover sites of the west gulf region. This

system expands the earlier work of Feduccia and others (1979) and Strub and others (19811, providing accurate yield forecasts for cutover sites and serving as

an interim guide for yields in site prepared plantations.

METHODS

Data

Study plots in unthinned and thinned loblolly pine

plantations were established on cutover longleaf pine

(Pinus palustris Mill.) forest land. In general, frequent wildfires burned the idle lands and prevented

natural regeneration and hardwood brush invasion.

On some areas, the predominant heavy grass rough

was burned before planting; on others, it was not. The

established plantations had good initial survival and

minimum levels of insect, disease, or other problems.

Data for unthinned stands came from control plots

located in thinning studies and from supplementary

plots installed to include specific site, age, and initial

planting density combinations not well represented in

the existing studies. The unthinned plantation data

came from 85 unthinned research plots and from 167

before-thinning measurements on thinned plantation

research plots.

Thinned stand data came from four long-term studies located in central Louisiana. The thinning interval in all these studies was 5 years unless insufficient

growth had occurred during that period. Figure 1

gives the geographic coverage, and tables 1 through 7

provide more detailed background information about

the data and summarize the distribution of the observations. Of the 167 thinned stand plots, all were

thinned from below except 12 plots that were row

thinned.

Diameter growth of the residual trees after row

thinning was not significantly different from diameter growth on the residual trees on comparable plots

that were thinned from below during the time period

covered by these data. Therefore, all the thinned

stand data were combined and treated the same in

this modeling effort.

The average height of dominant and codominant

trees was obtained on each plot at each mesurement

to determine site index. Diameter at breast height

(d.b.h.) to the nearest 0.1 inch was measured for each

tree on the plot. Additionally, individual volume sample trees were measured for total height, height to the

base of the full live crown, and upper stem outside

bark diameters. Where available, these trees were

selected in proportion to the total number within the

diameter class.

Trees removed in thinnings were selected and

marked by the study leaders. In most cases, felling

was done by loggers either employed or contracted by

V. C. Baldwin, Jr. is principal mensurationist with the Southern Forest Experiment Station, USDA-Forest Service, 2500 Shreveport

Highway, Pineville, LA 71360; D. P. Feduccia is staff forester with the Louisiana Department of Agriculture and Forestry, Alexander State

Forest, P. 0. Box 298, Woodworth, LA 71485.
HARRISON

TERREBONNE

CALCASIEU

CAMERON

VERMILION

UNTHINNED PLOTS

Kq THINNED & UNTHINNED PLOTS

Figure l.-Geographic location by parish or county of the thinned and unthinned plantation study plots.
Table l.-Planted loblollypine spacing and thinning studies in the west gulf region thatprovided data for thegrowth

and yield prediction system

Age first Site

thinned index Survival at

or Age at last range Planting first Number of Residual No. of

Study measured measurement (base 25) density measurement thinnings densities plots’

-------- years _________ Feet Treeslacre Percent BA21acre

1 2 0 4 5 53-67 400-2700 40-74 6 70-100 6 5

(4)

2 17 32 56-72+ 300-1200 69-85 4 60-120 73

(15)

3 15-22 20-27 56-72+ 800-1200 68-78 2 60-130 z

4 17 17 67-72+ 908 48-86 1 50-90 12

5 5-45 15-36 40-72+ 100-1400 30-95 0 . . . (62)

lThe number of unthinned plots are in parentheses.

2BA: basal area.

Table 2.-Distribution of unthinned stand observations by plantation age and planting density

Age

class 5250 251-500

Planting density class (trees per acre)

501-750 751-1000 1001-1250 1251-1500 21500 Total

Years ------------------------------------------Number ________________________________________--

3-7 8 4 4 16

8-12 8 7 8 16 39

13-17 8 5 4 39 2 6 29 156

18-22 47 21 27 26 18 6 145

23-27 2 4 13 2 2 13 5 77

28-32 18 16 9 12 4 5 9

33-45 19 6 5 5 35

Total 2 4 173 107 105 85 27 6 527

Table 3.-Distribution of unthinned stand observations by plantation age and site index

Age

class

Years

Base age 25 site index class (feet)

542 43-47 48-52 53-57 58-62 63-67 68-72 73-77 ~78 Total

___________________________________ Number ___________________________________

3-7 1 6 8 1 16

8-12 13 8 12 6 39

13-17 4 3 6 18 26 55 3 0 13 1 156

18-22 4 5 19 50 28 27 8 1 3 145

23-27 5 2 7 19 17 21 5 1 77

28-32 1 1 2 11 13 21 9 1 5 9

33-45 1 1 2 9 10 7 5 35

Total 15 12 3 6 107 9 4 145 71 36 11 527
Table 4.-Distribution of unthinned stand observations by planting density and site index

Planting

density

class

Base age 25 site index class (feet)

542 43-47 48-52 53-57 58-62 63-67 68-72 73-77 278 Total

Trees _____________.____________________ Number ___________________________________

per acre

1250 3 12 9 2 4

251-500 12 3 5 37 29 41 2 8 12 6 173

501-750 1 4 19 16 42 12 8 5 107

751-1000 3 2 13 23 15 30 13 6 105

1001-1250 3 2 16 31 2 6 6 1 85

1251-1500 1 8 12 3 3 27

21500 2 4 6

Total 15 12 36 107 94 145 71 36 11 527

Table 5.-Distribution of thinned stand observations by plantation age and site index

Age

class 547 48-52

Base age 2.5 site index class (feet)

53-57 58-62 63-67 68-72 273 Total

Years ________._._______________________ Number __________________________________

13-17 5 15 2 8 17 5 70

18-22 4 13 37 31 31 2 0 6 142

23-27 3 9 36 29 2 9 19 5 130

28-32 3 9 31 15 5 63

33-38 3 9 3 2 16 4 6 4

3945 3 9 32 16 5 65

Total 16 4 9 173 122 102 5 6 16 534

Table B.-Distribution of thinned stand observations by residual density after thinning and site

index

Residual

basal area

class 547 48-52

Base age 25 site index class (feet)

53-57 58-62 63-67 68-72 273 Total

Ft.21acre ---------------------------------Number _________________________________

555 1

56-65 5

66-75 2 13 38

76-85 8 6 53

86-95 5 14 33

96-105 14 2 9

106-115 1 1 4

116-125 1 9

2126 1

1

13

11

3 4

3 0

2 0

4

9

17

12

19

5

28

3

15

3

2

21 5 61

2 78

7 2 129

1 8 8

1 1 5 107

1 14

13 3 50

1 5

Total 16 49 173 122 102 5 6 16 534
Table 7.-Distribution of thinned stand observations by planting density and residual density after thinning

Planting

density Residual basal area class (ft? per acre)

class 555 56-65 66-75 76-85 86-95 96-105 106-115 116-125 2126 Total

Treeslacre

251-500 2 3 4 24 4 6 2 4 33 2 10 175

501-750 16 18 3 0 16 33 5 20 1 139

751-1000 4 12 17 5 1 3 9

1001-1250 10 7 15 7 18 4 16 4 81

1251-1500 1 17 18 20 10 4 7 0

21501 8 8 4 8 2 30

Total 2 61 78 129 8 8 107 14 50 5 534

the cooperating forest industries. The cutting and removal operations were performed with minimal residual tree damage.

Moment-Percentile Estimation Procedure

The three-parameter Weibull function (Bailey and

Dell 1973) was selected as a model to describe the

distribution of diameters. The probability density

function is

f(x) = (c/b)[(x-a)/blc-l e-[(x-a)iblc

foraL0, b>O, c>O, alx,

= 0 elsewhere,

(1)

where:

a = location parameter,

b = scale parameter,

c = shape parameter,

X = random variable representing d.b.h. in inches,

and

e = exponential function.

The cumulative distribution function is

F(x) = 1 - e-k-a)hfe

The ith noncentral moment of X is given by

(2)

i

m

E(X’) = x’f(x)dx,

a

and the pth percentile of x is

(3)

X,=a+b [-in(e)1

(lid

(4)

where X, is that diameter such that p percent of the

trees in the stand are smaller, and In is the natural

logarithm.

Rather than predict maximum likelihood or percentile estimates of the Weibull parameters as functions

of stand characteristics (age, site index, trees per acre,

and so forth) (Smalley and Bailey 1974, Dell and others 1979, Feduccia and others 1979, Baldwin 1982,

Little 1983), a parameter recovery technique (Matney

and Sullivan 1982, Cao and others 1982, Bailey and

others 1981,1982) was chosen to obtain the scale and

shape parameters and to directly estimate the location parameter. This system is based on prediction of

two percentiles and the second moment of the distribution.

In selecting moments and/or percentiles to describe

the distribution of diameters in a given stand, it is

reasonable to choose values that locate the tails of the

distribution and to utilize some measure of central

tendency. The first percentile (X1), the ninety-third

percentile (X9,), and the quadratic mean diameter

(Xqmd, which is the square root of the second moment

of the diameter distribution), or basal area (BA, which

is a constant times the second moment of the diameter

distribution times the number of trees per unit area in

the stand) were chosen to be predicted.

The first percentile was selected because it was an

estimate of the “a” Weibull parameter (the minimum

diameter of the distribution). Although it is rather

poorly predicted in practice, direct prediction of the

minimum diameter was necessary in order to insure

the natural progression of minimum stand diameter

over time. The ninety-third percentile was chosen to

tie down the upper tail of the diameter distribution

(Zanakis 1979). Finally, the quadratic mean diameter

was selected as the measure of central tendency because it is commonly used in forestry, is directly related to BA, and can be accurately predicted.

Estimates of the Weibull parameters are obtained

as follows:

1. The “a” parameter is set equal to k.X1. It was

found k = 0.60 gives the best prediction from

these data.

2. Equation (4) is solved for “b”, given p = 93 and

predicted values of X,, and a, which yields:

b = (X,, - a)/[-ln(.07)l(1’c), (5)

5
and this expression is substituted into the equation for E(X2). In its solved form it is (from equation (3) with i = 2)

E(X2) = a2 + 2 abI(l/c + 1) + b2(2/c + 1). (6)

The resulting expression is:

X2qmd = E(X2) =

2a (Xs, - a)IYl/c + 1)

(2.65926)1’c

+ (X9, - aI2 (2/c + 1)

(2.65926)2’c

+ a2 (7)

where I(=) = the gamma function evaluated at

the point(m).

3. Equation (7) is set equal to zero and is solved by

numerical techniques to obtain an estimate, c, of

the shape parameter.

4. Finally, c is substituted back into equation (5) to

obtain an estimate of the scale parameter b.

Thus with estimates of a, b, and c, the Weibull

distribution of diameters in that stand can be

completely described. This fundamental procedure is repeatedly utilized to describe diameter

distributions in unthinned stands, residual

stands after thinning, and thinned stands at any

particular age desired by the user.

Growth and Yield Prediction System Options if only TP is known, or by

This prediction system allows a user to begin the

process by: starting and ending with an unthinned

stand, starting with an unthinned stand and ending

with a stand thinned one or more times, or starting

with a previously thinned stand and ending with a

stand thinned one or more times.

Required input information when starting with an

initially unthinned stand includes stand age from

planting (A), average height of the dominant and

codominant trees (HD), and surviving trees per acre

(TS). If HD or TS is unknown, then site index (SD,

basal area per acre (BA), or trees planted per acre (TP)

are input variables that can be substituted for the

required site and density measures.

TS = [o ()2P&y.J (HD)l.40533 e0.91934/A BA-l]-2.08056 (10)

if only BA is known, where A, HD, and BA are initial

age, initial average height of the dominants and

codominants, and initial basal area per acre, respectively.

Given this initial information, the current stand

can be described as mentioned before. The stand diameter attributes Xi, Xqmd, and Xss are predicted as

follows:

When starting with a previously thinned stand, the

system requires A, HD, and TS. As in the unthinned

case, an estimate of SI can be substituted for HD.

Furthermore, if an estimate of TS is not known, it can

be predicted by providing the stand age and the residual trees surviving (TS,) at the time of the last thinning. Figure 2 summarizes the prediction system

process.

x1 = 2.14462 (HD)0.70266 (TS)-0.36282 e-1.96895/A (11)

n = 527 FI = 0.63 SE = 1.04 in,

Xgmd = 2.14462 (HD)0.70266 (TS)-0.25968 e-O.459671A (12)

n = 527 FI = 0.91 SE = 0.60 in,

‘FI = Fit Index = {lG[Z(Yi - ~i)‘]/[C(Yi -WI}

2S~ = Standard error of the estimate

PROCEDURES AND EQUATIONS

Yield Prediction in Unthinned Stands

If height of the dominant and codominant trees is

not available as an input, it is predicted using a given

site index function. The following site index equation

is solved for dominant height:

HJ) = SI [2.14g15 (1 - e-O.O25O42 A)]O.755862

n = 1061 FI1 = 0.78 SE2 = 6.23 ft

where:

(8)

SI = site index (feet) at base age 25,

HD = average height (feet) of dominants and

codominants,

A = plantation age (years),

e = exponential function.

Figure 3 illustrates the characteristics of site index

function for various index values for base age 25.

If initial survival (TS) in terms of trees per acre is

not known, the variable can be predicted using the

following equation derived from Feduccia and others

(1979):

TS = TP/{EXP [A, (0.013480 In (TP)

+ 0.00139956 (HD)

- 0.01937002 (HD).5)1} (9)
Initial unthinned stand inputs

*Height of dominants and codominants

or site index

*Stand age

*Trees per acre, or

Basal area per acre, or

Trees planted per acre

LUBLOLLY PINE PLANTATION GROWTH AN0 YIELD PREOICTION SYSTEM

Initial thinned stand inputs

*Height of dominants and

codominants or site index

*Stand age

*Trees per acre, or

Residual trees per acre after

last thinning and age last

thinned

Recover Weibull Parameters

and output for initial conditions

if desired

Project unthinned stand

I

Thin the stand to the

residual BA or TS

desired

I

Project thinned stand

I

Predict

HO2 ,TS, JIMIN ,QMO, ,P932

at A2

Predict

H02,TS2,0flIN2.QM02, P932

Recover Weibull Parameters Recover Weibull parameter

and output desired volume, and output desired volume

weight information by weight information by

diameter classes diameter classes

Recover Weibull Parameters

and output desired volume,

weight information by

diameter classes

~ Project

growth

o f

unthinned

stand

Thin

the

stand

I 1

* Preferred inputs

Project growth of

thinned stand

Project

growth

o f

thinned

stand

I *

Figure 2.-Schematzc diagram summarizing the operation of the yield prediction system.
110

--xi-l Predicting Stand Attributes After Thinning

100 -

4

80 -

I

2 0 I I I I I

1 0 1 5 2 0 25 30 3 5 4 0

PLANTATION AGE (YEARS)

Figure 3.-Heightof dominants and codominants by planation age

for site indices 40-80.

X9, = 2.24213 (HD) 0 71401 (TS)-O.22932 e-O.45967/A (13)

n = 527 FI = 0.91 SE = 0.74 in

This system of equations was constrained to insure

that Xi 5 Xqmd 5 Xg3. The constraining was accomplished in this case by using the same model form and

predictor variables for each equation. It was insisted

that during the fitting process comparable coefficients

in equation (11) were always 5 the comparable coefficients in equation (12) and that comparable coefficients in equation (13) were always 2 the comparable

coefficients in equation (12). With estimates of Xi,

Xqmd, and x93, the Weibull parameters can then be

estimated.

Predictions of future stand attributes and, hence

future stand table information in unthinned stands,

are accomplished first by projecting TS from Ai to A2

using the following equation:

TS2 = 100 {(TS,/100)-0s7372

+ (0.01859 - 0.3912OSI) [(A2/10)2.11g47

_ (A,/10)2.“947]}~‘.14454 (14)

n = 224 FI = 0.95 SE = 37 trees/acre

where: TSi, TSs = number of trees surviving per acre

at times Al and A,, respectively.

Equation (8) is then employed to obtain an estimate

HD2 at A2, and then these predictions of HD,, TS2, and

Aa are substituted for HD, TS, and A in equations (11)

- (13) to obtain the new predictions of Xl, Xqmd, and

X9, at A2.

Figures 4 through 7 give examples of the behavior

of these functions over time for selected site index and

initial density values.

8

The residual stand after thinning is determined by

prediction of “thinned” values of Xl, Xqm& X9,, TS,

and BA, followed by recovery of the new Weibull

parameters, as already explained.

Many types of thinning could easily have been modeled and built into the prediction system. However,

since these data represent stands essentially thinned

from below, only that thinning option was included in

this yield prediction system.

The low thinning in the study plots was not strictly

a process of removing only the suppressed and intermediate trees until the desired leave-tree basal area

per acre was obtained. Spacing, stand uniformity, and

stand vigor were also factors of equal weight. In some

cases, especially during the first thinning, codominants or even dominants were removed if they were

deformed or diseased, or if large “holes” would have

otherwise been left in the stand.

Graphical examination of the diameter distributions before and after thinning showed the most

change occurred in both shape and location after the

first thinning, the next greatest after the second thinning, and so forth. It was determined that the data, at

least for thinnings beyond the second, should be combined. In some cases, the data beyond the first thinning should be combined. The attribute (Xi, X,,& X9,)

equations for these groups were tested using an analysis of covariance procedure (Freese 1964, Milliken

1982) to see if there was some statistical, as well as

visual, justification for combining or separating some

or all of the equations. The tests3 indicated Xl, and

Xqmd predictions would be much less variable if there

was one set of equations to accomplish this for the first

thinning and another set for all subsequent thinnings. The tests also showed that Xl prediction would

be less variable and Xqmd predictions slightly less

variable if there was also a separate set of equations

for the second thinning, as well as a set for the first

thinning and a set for all subsequent thinnings. In all

cases there were no significant differences for X9, predictions. For the sake of simplicity, only two sets of

equations were chosen: one to predict the residual

stand after the first thinning and another set to predict the residual stand after all subsequent thinnings.

3The test of the hypothesis that the regressions (to predict X,,

Xqm~, Xga after a thinning) for the first thinning should be kept

separate from the others rather than one overall regression be used,

yielded calculated F4,eos values of 16.11, 14.94, 2.21 for XI, Xqmd,

and Xo,, respectively. The test of the hypothesis that the regressions for the second thinning should be kept separate from the 2nd

through last thinnings rather than the 2nd through last thinning

regressions be combined into one overall regression, yielded calculated F4,493 values of 7.67, 3.30, 0.86 for XI, Xqmd, and Xaa respectively.
Figure 4.--Surviving trees per acre by plantation age for unthinned

loblolly pine planted at four initial densities,

-10 15 20 25 30 35 40

PLANTATION AGE (YEARS)

(SITE 60 FOR BASE AGE 25,

Figure 5.-Predicted diameter growth relationships over time for

unthinned loblolly pine stand (site index 60) with survival at age 10 of 400 trees per acre.

Input information is typically based on unthinned

stand attributes that have been provided by the user

or predicted from appropriate equations given in the

previous section. The target density for each thinning

may be in terms of residual stand basal area per acre

or residual trees per acre. Equations 15 through 17

and 19 through 21, which follow, are based on an

assumed residual BA target. If a residual TS target is

chosen, either equation 18 or 22 is utilized to predict

BA following the thinning. This value is then used in

the previously mentioned equations as if it were the

target BA. The b and a subscripts in the following

equations reference before and after thinning conditions; otherwise the definitions for the variables are

as before:

I. First Thinning

X1,, = 1.28767 Xl,b - 0.410403(BA),/(BA),, (15)

I*-

-.----

-.-.--

-A---

4-

zl-

~(~/--------

/e/.----

I I I I I

1 0 15 20 25 30 35 140

PLANTATION AGE (YEARS)

(SITE 60 FOR BASE AGE 25,

Figure 6.-Predicted diameter growth relationships over time for

unthinned loblolly pine stand (site index 60) with survival at age 10 of 600 trees per acre.

01 I I I I 1 I

IO 15 20 25 30 35 40

PLANTATION AGE (YEARS)

(SITE 60 FOR BASE AGE 251

Figure 7.---Predicted diameter growth relationships over time for

unthinned loblolly pine stand (site index 60) with survival at age 10 of 800 trees per acre.

n= 173 R2 = (0.94j4 SE = 0.96 in,

Xqmd,a = 1.069587 Xqmd,b - 0.350918(BA)$(BA),, (16)

n = 173 R2 = (0.99) SE = 0.36 in,

Xs3,a = 0.95074 Xs3,b + 0.017485(HDjb

-0.298543(BA)$(BA)b (17)

n = 173 R2 = (0.99) SE = 0.45 in,

4CoefEcient of Determination (R2) values enclosed in parentheses

were calculated using an uncorrected sum of squares value since

there was no constant term in those equations.
BA, = BA,Jl - (1 - TS,/TSb)0.83888]0.71395

n = 173 FI = 0.85 SE = 7.9 ft2

II. Subsequent thinnings

X1,, = 2.63243 + 0.766348X1,b

(18)

- E~144246(BA),/(BA)~ (19)

n = 501 R2 = 0.82 SE = 1.17 in,

Xv&a = 1.278159 + 0.953873Xq,d,1, + 0.008981(HD)b

- 1.265008(BA),/(BA)b (20)

n = 501 R2 = 0.98 SE = 0.29 in,

X93,a = 1.084635 + 0.972118X93,b - 0.67333(BA),/(BA),(21)

n = 501 R2 = 0.96 SE = 0.48 in,

BA, = BAb[l - (1 - TS,/TS&)0.85566]0.56963 cm

n = 501 FI = 0.95 SE = 3.5 ft2

In those cases where the residual density is specified as basal area per acre, the number of residual

trees after thinning is obtained directly from the relationship

(TS), = (BA),/0.005454(Xq,d,a)” (23)

where Xqmd , is predicted using equation (16) or a (201,

as appropriate.

Thinned Stand Predictions

Equations in the thinned stand section of the yield

system take either predicted or user supplied afterthinning stand information at age A, and project

these values into the future to time A, to provide

stand table predictions at the new age. The same

stand diameter and height attributes as used elsewhere are also predicted here, and these values are

used to obtain Weibull parameters for description of

the new stand.

The equations for prediction of diameters at a second age in thinned stands are

Xl,, = [-529.8956 + 059995(TS,)

+ 5298956(A,/A,) - 0.59995(TS),(A2/A,)

+ (A,/A,)(X, 1)3.39763]1/3.39763 (24

n = 534, FI = 0.88, SE = 0.97 in,

10

Xqmd,2 = [ - 109.9872 + 0.12169(TS1) + 109.9872(A2/A1)

- 0.12169(TS1)(A2/A1)

+ (&/A1)(xqmd,l)2~3ggg8]1’2~3ggg8 (25)

n = 534, FI = 0.98, SE = 0.33 in,

Xg3,2 = [ - 146.8410 + 0.15597(TS1) + 146.8410(A2iA1)

- 0.15597(TS1)(A2/A1)

+ (A2/A1)(Xg3,,)2.33778]1’2.33778

n = 534, FI = 0.97, SE = 0.48 in.

where

(26)

Xi,i, Xi,z = smallest diameter tree at time A,,

and at time AZ, respectively,

x qmd,l 7 Xqmd,2 = quadratic mean diameter at time

A,, and at time A,, respectively,

x93,1, x93,2 = 93rd percentile diameter at time A,,

and at time A2, respectively.

The equation for prediction of survival in thinned

stands is

TS2 = 100{(TS1/100)-1~066gg + (0.00941

+ 15.43171SI) [A2/10)o.2g683

_ (A,/10)0.29683]}-0.93722 (27)

n = 534 FI = 0.98 SE = 15.6 trees/acre

TSi = initial trees surviving per acre.

In figures 8 through 10, the behavior of these functions is illustrated for one site index value assuming

some common post-first thinning densities and no further thinning.

It must be noted here that equations 24, 25, and 26

are not time invariant. In other words, given an

ordered time sequence ti, t,, t3, predictions for values

of the variables at time t3 based on initial values at

time t, (t,-+t,) will not be exactly the same as those at

time t, that were projected from those at time t2,

which were based on those at time ti (tl-+t2+t3). Time

invariant equations, which are desirable, were developed and tried, but the precision of predictions from

the equations presently given, when used in conjunction with equation 27, was much better than the precision of the predictions from the time invariant set of

equations.

Nevertheless, this improved precision can be lost if

the projection interval length differs much from 5

years, the data measurement interval length. Therefore, to achieve the most reliable and consistent pre-
I I I I

I

15 20 25 30 35 40

PLANTATION AGE (YEARS)

(SITE 60 FOR B&SE AOE 25)

Figure 8.-Predicted diameter growth relationships over time for

loblolly pine stand (site index 60) thinned once at age 15

to 300 trees per acre.

___----

____-----

___----

___---

___----

___---

__/--

Y __/--

pi 6 /---- _.__A---- _----

0 ; ___c_c-----

4- ./--

._.A--

.A--

e0 I

15 20 25 30 35 40

PLANTATION AGE (YEARS)

(SITE 60 FOR MSE IlaC 25,

Figure B.-Predicted diameter growth relationships over time for

loblolly pine stand (site index 60) thinned once at age 15

to 500 trees per acre.

- 93d PERCENTILE 0 B H.

___---

___---

__/-- __/-- __/--

-.--

____c_---------

/~c/------ __----

,.A-.

I I I

2 0 25 30 35

PLANTATION AGE (YEARS)

(SITE 60 FOR B&SE AGE 25)

4 0

dictions with this system of equations, after-thinning

growth projection intervals should be in multiples of

5 years with the final projection, if required, done over

the remaining years.

Volume and Weight Prediction

Stand tables are generated at any age by apportioning the total number of trees surviving into l-inch

diameter classes according to the predicted Weibull

distribution for that age. The average total height of

all trees within a diameter class is predicted with the

following equations:5

H = exp11.203241 + 0.751234 ln(HD) - 1.767749/A

+ 0.048913 ln(TS/D)

+ 9.057581/(A)(D) - 3.113997/D] Cm

n = 7872 FI = 0.94, SE = 3.45 ft,

for trees in unthinned stands, and

H = expl1.124364 + 0.80562 In (HD) - 3.880531/A

+ 0.049332 ln(TS/D)

+ 42.279443/(A)(D) - 4.816993/D] (29)

n = 6007 FI = 0.90 SE = 3.34 ft,

for trees in thinned stands, where:

H = mean predicted height of a tree, in feet,

D = d.b.h., in inches, represented by the midpoint of

a diameter class.

Given the mean height and midpoint of the diameter class for all the predicted numbers of trees, the

following measurements are calculated for each average tree: cubic foot volume, green weight, or oven-dry

weight of the total stem or stem to a merchantable top

diameter limit, either inside or outside bark. This

quantity is then multiplied by the predicted number

of trees per acre in that diameter class to obtain the

volume or weight per acre for each diameter class.

Finally, the stand averages are obtained by summation over all diameter classes.

Board-foot volume for trees with d.b.h(o.b.) 2 10

inches to an o.b. top diameter of 8 inches is also predicted. The user may elect to use either the Doyle,

Scribner, or International l/4-inch log rules.

Figure lO.-Predicted diameter growth relationships over time for

loblolly pine (site index 60) thinned once at age 15 to

700 trees per acre.

5Equations 28 and 29 are presented in arithmetic form with FI

and SE in arithmetic units although the equations were fitted in

logarithmic form!,

11
This procedure requires predictions of i.b. diameters at various log heights and also the prediction of

height to the B-inch (o.b.) top diameter, of each average tree in each diameter class L 10 inches. Our stem

taper data were fitted to the Max and Burkhart (1976)

model in order to provide equations for these predictions. The model is presented below and the parameter coefficients and supporting statistics (Baldwin and

Feduccia 1987) are given in table 8:

d2

- = b,(X - 1) + b2(X2 - 1) + bJa, - Xj211

D2

+ b4(a2 - Xj212 (30)

where:

Ii =

[

1, ifX5ai

0, if X > ai

i = 1,2

d = stem diameter i.b. or o.b. (inches) at any given

height, h,

D = d.b.h. (inches) o.b.,

X = h/H,

h = height (feet) at which diameter is to be determined (%H),

H = tree total height (feet),

ai = join points estimated from the data and

bi = coefficients estimated from the data.

There are separate equations for height or diameter

prediction of trees from unthinned stands (or trees

from stands thinned less than 5 years previously) and

for trees from stands thinned 5 or more years earlier.

The volume and weight model selected was that of

Schumacher and Hall (1933). It is

In (Y) = bi + b2 In (D) + b, In (H) (31)

where bi, bat bs are coefficients to be estimated from

the data, and Y represents either cubic-foot volume,

green weight, or dry weight of appropriately defined

tree components.

Table 8.-Regression coefficients for a stem-taper model useful in predicting upper stem diameters at a specified

height given breast-height diameter and total tree height.’

Dependent

ratio2 b

Unthinned stands

dob2/D2 -8.07778

dib2/D2 -4.58266

Thinned stands

dob2/D2 -13.31391

dib2/D2 -7.43322

‘The model is:

b

4.02542

2.24195

6.73098

3.74079

Parameter estimates

b3 b

>3.65499 229.739

-2.34978 138.546

-6.65501 203.959

-4.03111 191.149

al a2

0.89406 0.05703

0.80645 0.05980

0.91195 0.06035

0.85190 0.04833

Statistics3

FI SE

0.95 0.11

0.97 0.07

0.96 0.08

0.95 0.07

-$ = bl(X - 1) + b2(X2 - 1) + b3(a1 - Xl2 I, + b4(a2 - Xl2 I2

where: Ii =

[

1, ifXsai

0, if X > ai

i = 1,2

d = stem diameter Lb. or o.b.

D = d.b.h. (inches) o.b.,

X = h/H

h = height (feet) at which diameter is to be determined (sH),

H = tree total height (feet),

ai = join points estimated from the data, and

bi = coeffkients estimated from the data.

2dob = diameter o.b. at any given height, h.

dib = diameter i.b. at any given height, h.

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

3FI = (1 -[C(Yi - Pi)2]/‘[Z(Yi - Y)‘]}

where: Yi =

Jo

D2 $ and Y,= di.

SE = Standard error of the estimate in original units.
As explained in Baldwin (1987) and Baldwin and

Feduccia (19871, this model was best when fitted separately to cubic-foot volume stem data from thinned

stands and from unthinned stands. It also worked well

when utilized to develop equations to fit both weight

and volume of various crown components with unthinned and thinned stand tree data combined. However, an age variable, A2, was added to provide more

precise predictions of total stem green and dry weight

from combined thinned and unthinned stand data.

Therefore, combined data from both thinned and

unthinned plantations were fitted to Schumacher and

Hall’s model to predict the following yield components:

(1) cubic-foot volume, green weight, and oven-dry

weight of branch wood and branch bark, and

(2) green and dry weight of the foliage.

Combined data were also fitted to this model, with

the age variable added, to predict green-weight and

oven-dry weight of the main stem. To precisely predict

cubic-foot volume (o.b. and i.b.) of the main stem, separate equations using the Schumacher and Hall

model were developed from the thinned stand data

and from the unthinned stand data. Coefficients for

all of these equations and accompanying fit statistics

are found in tables 9 through 11.

Merchantable cubic-foot volume and green and dry

weight of the main stem (i.b.or o.b.) to any top diameter limit (i.b. or o.b.1 are obtained from equations developed from the following ratio model (Van Deusen

and others 1981, Parresol 1983):

R = exp[b,(dbz/Db3)l

where:

(32)

R = predicted ratio of merchantable to total

volume (cubic feet) or weight (green or

dry weight in pounds),

bi, b2, b3 = coefficients estimated from the data.

The coefficients, from Baldwin (1987) and Baldwin

and Feduccia (19871, are given in table 12.

Testing

To avoid unneccessarily weakening the development data set, a subset of the development data was

not withheld for testing purposes; instead it was decided to later validate against truly independent data

sets. However, to make sure the combined system of

equations behaved well. as a unit, the completed

growth and yield predictions system was tested

against the data used to develop it. The tests verified

that predicted values were close to those observed.

The prediction phases tested were: initial prediction in an unthinned stand, growth prediction in an

unthinned stand, residual stand after thinning, and

growth prediction in a thinned stand. In each case

Table 9.-Regression coefficients for total stem volume’

Dependent Parameter estimates

variable2 bl b b3

Unthinned stands

TVob -5.731735 1.896449 1.010252

TVib -6.897192 1.836827 1.245844

Statistics3

FI SE c v

0.99 1.93 11.2

0.98 1.96 13.6

Thinned stands

TVob -5.816087

TVib -6.835331

2.036340 0.953537 0.99 2.93 10.8

2.040995 1.150022 0.98 3.50 15.6

‘The model is:

In(Y) = b1 + b21n(D) + b&(H)

where:

Y = predicted stem volume (cubic feet) from a 6-in stump to the stem

tip,

D = diameter outside bark (inches) at 4.5 feet,

H = total tree height (feet), and

br, b2, ba = coefficients estimated from the data.

2TVob = total stem volume outside bark.

TVib = total stem volume inside bark.

3Fit Index (FI) = (1 - [C(Yi - Pi)2]/[C(Yi - yj2]}

SE = Standard error of the estimate in original units.

CV = Coefficient of variation in percent.
Table lO.-Regression coefficients for total stem weight equations’

Dependent

variable2 b,

Parameter estimates

b2 b3 b4

Statistics3

FI SE CV

TGWob -2.06033 1.93926 1.05077 .000061 0.99 153.4 11.4

TGWib -2.53232 1.96524 1.12691 .000060 0.99 152.9 12.4

TGWob -3.31353 1.91029 1.19118 .000076 0.99 70.1 10.5

TGWib -4.20913 1.87667 1.38064 .000088 0.99 69.0 11.8

‘The model is:

In(W) = b; + b21n(D) + b&(H) + b4A2

where:

W = predicted stem volume (pounds) from a 6-in stump to the stem tip,

D = diameter outside bark (inches) at 4.5 feet,

H = total tree height (feet),

A = age from planting, and

b;, b2, ba, b4 = coefficients estimated from the data.

2TGWob = total stem green weight outside bark.

TGWib = total stem green weight inside bark.

TDWob = total stem dry weight outside bark.

TDWib = total stem dry weight inside bark.

3Fit Index (FI) = {l - [B(Yi - Pi)2]/[~(Yi - Y)‘]}

SE = Standard error of the estimate in original units.

CV = Coefficient of variation in percent.

Table Il.-Regression coefficients for crown green and dry weight equations1

Dependent

variable2

bo

Parameter estimates

bl b2 FI

Statistics3

SE CV

CGWW 1.735217 3.492293 - 1.243386 0.90 61.5 41.2

CDWW 0.379049 3.454388 - 1.088445 0.90 28.5 41.3

CGWB 1.203148 3.023912 - 1.136030 0.85 14.6 36.9

CDWB 0.264828 3.033934 -1.109824 0.86 6.9 38.2

CGWF 3.652443 2.864732 - 1.454774 0.86 25.1 32.4

CDWF 2.796233 2.912819 -1.474651 0.85 11.4 33.5

‘The model is:

In(W) = bo + brln(D) + b&(H)

where:

W = predicted weight (pounds) of crown component,

D = diameter outside bark (inches) at 4.5 feet,

H = total tree height (feet), and

bo, br, b2 = coefficients estimated from the data.

2CGWW = crown green weight of wood.

CDWW = crown dry weight of wood.

CGWB = crown green weight of bark.

CDWB = crown dry weight of bark.

CGWF = crown green weight of foliage.

CDWF = crown dry weight of foliage.

3Fit Index (FI) = (1 - [C(Yi - Pi)2]/[C(Yi - Y)2]}

SE = Standard error of the estimate in original units.

CV = Coefficient of variation in percent.

14
Table 12.-Regression coefficients for volume and weight ratio equations1

Dependent

variable2

Unthinned stands

MVoblTVob

MVib/TVib

MGWobTGWob

MGWib/TGWib

MDWob/TDWob

MDWibTDWib

Thinned stands

MVoblTVob

MViblTVib

MGWob/TGWob

MGWib/TGWib

MDWob/TDWob

MDWib/TDWib

Parameter estimates Statistics 3

bo bl b FI SE

-0.799015 4.975752 4.686168 0.98 0.048

-0.938014 4.950338 4.706034 0.98 0.049

-1.153726 4.911545 4.723876 0.97 0.050

-1.171351 4.957184 4.772917 0.97 0.055

-0.842507 5.128205 4.854891 0.97 0.060

-0.932732 5.101845 4.857412 0.96 0.059

-1.718906 5.261784 5.262902 0.97 0.053

-2.177444 5.239462 5.314077 0.97 0.057

-2.058914 5.124867 5.170415 0.97 0.050

-2.075039 5.171997 5.218171 0.97 0.056

- 1.875204 5.346034 5.397755 0.96 0.060

- 2.020278 5.367307 5.436636 0.97 0.057

iThe ratio model is:

R = exp[bo(db1/Db2)],

where:

R = predicted ratio of merchantable to total volume (ft3) or weight (pounds),

d = upper stem diameter limit (inches, o.b.)

D = diameter o.b. (inches) at 4.5 feet, and

bo, bi, b2 = coefficients estimated from the data.

2 MVob = Merchantable volume outside bark.

TVob = Total volume outside bark.

MVib = Merchantable volume inside bark.

TVib = Total volume inside bark.

MGWob = Merchantable green weight outside bark.

TGWob = Total green weight outside bark.

MGWib = Merchantable green weight inside bark.

TGWib = Total green weight inside bark.

MDWob = Merchantable dry weight outside bark.

TDWob = Total dry weight outside bark.

MDWib = Merchantable dry weight inside bark.

TDWib = Total dry weight inside bark.

3Fit Index (FI) = {l - [Z(Yi - Pi)2]/[~(Yi - Q2]}

SE = Standard error of the estimate in original units.

predicted values of stand and yield table variables

were compared with their respective observed values.

Mean predicted, mean observed, correlation coefficient, mean difference, and mean percent difference

statistics were calculated. Results of these tests are

found in tables 13 through 17. Note that with the

general exception of the two lowest percentiles (Xi

and Xi,), which are highly variable, nearly all the

other stand and yield table variables were predicted

within +-5 percent of the observed values.

These statistics, along with the Fit Index and

Standard Error of the estimate statistics presented for

each separate prediction equation within the system,

indicate that the entire system accurately predicts

growth and yield within the stands from which it was

developed. This system should provide good results

when used to make predictions in similar loblolly pine

plantations.

Validation of the unthinned stand prediction system is in process, and a later publication will report

these results and any necessary system updates if required. Validation of the thinned stand system will be

accomplished as soon as an independent data set is

available.

DISCUSSION AND RESULTS

Trends

Prediction trends for unthinned plantations and

thinned plantations and some comparisons of results

between those two management alternatives are

noted. In most cases, 700 trees per acre planted (about

15
Table 13.-Comparison of some observed versus predicted stand and yield table variables for initial

values in an unthinned stand

Parameter

Xl6

x10

x17

x24

x50

x63

X82

x93

x97

X qmd B A

VOL

Mean Mean Correlation Mean Mean percent

predicted1 observed2 coefficient3 difference* difference5

3.48 3.34 0.80 0.14 19.84

4.97 4.79 0.84 0.18 6.82

5.51 5.47 0.90 0.03 2.47

5.92 5.96 0.92 -0.04 0.81

7.13 7.25 0.95 -0.12 -0.69

7.70 7.82 0.95 -0.11 -0.63

8.69 8.75 0.96 -0.06 0.05

9.61 9.66 0.96 -0.05 0.08

10.26 10.45 0.93 -0.20 -1.22

7.33 7.37 0.96 -0.04 0.17

127.92 130.26 0.92 -2.33 1.11

3298.0 3317.0 0.97 -9.04 -1.38

lMean predicted value = F = Z P,in

2Mean observed value = b = I: Oi/n

3Correlation coefficient = r =

X[(Pi - P)(Oi - 011

~/B(Pi - P)‘Z(Oi - 0)’

*Mean difference = d = B (Pi - OJn

5Mean percent difference = %d = lOO/nC(Pi - Oi)/Oi

sxi, i = l-97, are the ith percentile values of the variable X.

X ,& = Quadratic mean diameter (in).

BA = Basal area per acre (ft?

VOL = Total ft3 volume.

Table 14.-Comparison of some observed versus predicted stand and yield table variables for

unthinned plantations after growth over 4-6 year time periods.

Mean Mean

Parameter predicted1 observed2

Xl6 4.07 4.33

x10 5.62 5.67

x17 6.21 6.39

x24 6.66 6.91

x50 7.99 8.33

x63 8.61 8.96

X82 9.69 10.03

x93 10.70 11.11

x97 11.40 11.96

X qmd 8.20 8.48

B A 130.6 136.7

TS 396.3 394.3

H D 56.7 59.3

VOL 3616.3 3913.3

IMean predicted value = P = C Pi/n

Correlation Mean Mean percent

coefficient3 difference* difference5

0.69 -0.26 -1.94

0.74 -0.05 -1.32

0.84 -0.18 -1.54

0.86 -0.25 -2.40

0.90 -0.34 -3.43

0.91 -0.35 -3.34

0.92 -0.34 -2.86

0.92 -0.41 -3.33

0.89 -0.56 -4.46

0.92 -0.29 -2.95

0.83 -6.18 -3.46

0.98 2.00 1.32

0.83 -2.5 -3.00

0.90 -297.0 -5.20

2Mean observed value = 0 = C Oi/n

3Correlation coefficient = r =

E[(Pi - P)(Oi - -611

~/z(Pi - F)2C(Oi - 0)2

4Mean difference = d = Z: (Pi - OiYn

5Mean percent difference = %d = lOO/nZ(Pi - Oi)/Oi

exi, i = l-97, are the ith percentile values of the variable X.

X qmd = Quadratic mean diameter (in).

BA = Basal area per acre (ft2).

VOL = Total ft3 volume.

TS = Trees surviving per acre.

HD = Mean height (ft) of dominant and codominant trees.

1 6
Table E.-Comparison of some observed versus predicted stand and yield table variables immediately following the first thinning

Parameter

Xl6

x10

x17

x24

x50

x63

x32

x93

x91

Xqmd

TS

HD

VOL

Mean Mean Correlation Mean Mean percent

predicted’ observed2 coefficient3 difference4

difference5

3.99 3.45 0.74 -0.21 24.99

5.25 4.71 0.80 -0.36 13.70

5.72 5.50 0.86 -0.08 4.62

6.10 6.02 0.90 -0.03 1.41

7.24 7.26 0.95 -0.10 -0.81

7.80 7.79 0.96 -0.01 -0.34

8.78 8.68 0.97 -0.11 -1.4

9.73 9.56 0.96 -0.17 2.08

10.41 10.21 0.91 -0.19 2.36

7.48 7.34 0.96 -0.14 2.33

332.2 351.2 0.97 - 18.98 -3.68

50.7 50.8 0.99 -0.11 -0.30

2279.4 2356.1 0.96 -76.6 -2.94

‘Mean predicted value = ?; = X Pi/n

2Mean observed value = G = C Oi/n

3Correlation coefficient = r =

X[(Pi - F)(Oi - G)]

~~(Pi - P)28(Oi -~)’

4Mean difference = ;i = Z (Pi - Oi)/n

5Mean percent difference = %d = lOO/nX(Pi - Oi)/Oi

6Xi, i = l-97, are the ith percentile values of the variable X.

Xqmd = Quadratic mean diameter (in).

BA = Basal area per acre (ft2).

VOL = Total ft3 volume.

TS = Trees surviving per acre.

HD = Mean height (ft) of dominant and codominant trees.

Table 16.-Comparison of some observed uersus predicted stand and yield table variables immediately following all thinnings after the first thinning

Parameter

Mean

predicted1

Mean

observed2

Correlation

coefficient3

Mean

difference4

Mean percent

difference5

Xl6 6.97 7.82 0.87 -0.85 -6.33

x10 8.60 8.53 0.93 0.06 2.8

x17 9.17 9.12 0.95 0.05 1.17

x24 9.61 9.56 0.96 0.05 0.50

x50 10.89 10.76 0.98 0.13 0.73

X63 11.49 11.32 0.98 0.17 1.23

X82 12.52 12.34 0.99 0.18 1.36

x93 13.48 13.48 0.99 0.00 0.09

x37 14.15 14.20 0.95 -0.05 0.07

Xwd 11.04 10.93 0.99 0.11 0.91

TS 151.0 152.3 0.99 -1.32 -1.56

HD 68.1 68.3 0.99 -0.21 -0.29

VOL 2926.4 2978.4 0.96 -52.0 -1.77

‘Mean predicted value = I’ = X Pi/n

2Mean observed value = B = C Oiin

3Correlation coefficient = r =

B[(Pi - P)(Oi - O,]

v/B(Pi - F)2X(Oi -G)2

4Mean difference = d = C (Pi - Oi)/n

5Mean percent difference = %d = lOO/nZ(Pi - Oi)/Oi

6Xi, i = l-97, are the ith percentile values of the variable X.

Xqmd = Quadratic mean diameter (in).

BA = Basal area per acre (ft2).

VOL = Total ft3 volume.

TS = Trees surviving per acre.

HD = Mean height (ft) of dominant and codominant trees.

1 7 I
Table 17.-Comparison of some observed versus predicted stand and yield table variables for

plantations after a 5-year growth period following thinning

Parameter

Mean Mean

predicted1 observed2

Correlation

coefficient3

Mean

difference4

Mean percent

difference5

Xl6

x10

x17

x24

x50

X63

x82

x93

x91

Xqmd

B A

T S

HD

VOL

6.10 6.92 0.91 -0.81 -5.96

7.78 7.81 0.94 -0.03 2.03

8.39 8.49 0.96 -0.10 -0.02

8.88 9.01 0.97 -0.13 -0.79

10.28 10.38 0.98 -0.09 -0.88

10.95 11.00 0.98 -0.05 -0.45

12.12 12.08 0.98 -0.04 -0.40

13.22 13.24 0.98 -0.02 -0.03

14.00 13.97 0.96 -0.02 0.37

10.51 10.53 0.99 -0.01 -0.03

102.5 102.5 0.93 -0.88 -0.82

204.1 204.1 0.99 -1.87 -0.75

67.3 68.0 0.96 -0.67 -0.94

3421.9 3493.9 0.90 -72.0 -2.1

‘Mean predicted value = p = C P(n

2Mean observed value = G = B Oi/n

3Correlation coefficient = r =

Z[(Pi- PXOi - O)l

d/x(Pi - F)2Z(Oi- Gj2

4Mean difference = d = B (Pi - Oil/n

5Mean percent difference = %d = lOO/nZ(Pi- Oi)/Oi

aXi, i = l-97, are the ith percentile values of the variable X.

Xqmd = Quadratic mean diameter (in).

BA = Basal area per acre (ft?.

VOL = Total ft3 volume.

TS = Trees surviving per acre.

HD = Mean height (ft) of dominant and codominant trees.

B- by B-ft spacing) was assumed on lands of site index

(base age 25) of 50 and 70 feet. After prediction of

initial stand conditions at age 10, projections were

made over 2 or 3 year intervals to age 40 for unthinned stand examples or to age 50 for thinned stand

examples. In the thinned stand examples, the site 70

plantation was thinned back to 80 square feet of basal

area at ages 15, 22,30, and 40 years. Thinning of the

site 50 plantation was delayed until age 22, when it

was thinned the same as the higher site plantation.

Unthinned Plantation

Survival.-On both sites the survival decreased

less with increasing age (fig. 11). In the early years,

survival was highest on the higher site. However, because of intensified competition on the better site, at

about age 17 survival became better on the poorer

site. The latter relationship remained for the growth

period.

Mean Diameter.-The average gain in mean diameter for the site index 70 plantation over the site

index 50 plantation was 2.04 inches by age 40 (fig. 12).

Basal Area .-Basal area of all trees increased with

increasing site index (fig. 13) but increased more

18

rapidly on the high site. Basal area culminated by age

40 in the site index 70 plantation but had not culminated in the site index 50 planations.

Total Stem Volume Yield.-Total stem cubic-foot

(o.b.) yields did not culminate before age 40 on either

site, but the high-site volume was on average 2,855

cubic feet per acre more than on the low site (fig. 14).

Mean and Periodic Annual Increment. -Total stem

cubic-foot (0.b.) volume mean annual increment

(MAI) culminated at about age 24 in the site index 70

plantation and at about age 27 in the site index 50

plantation. The higher site stands peak MA1 was

about 125 cubic feet per acre per year greater than the

peak MA1 in the lower site stand (fig. 15).

Thinned Plantation

Survival. -In this example, the stand was thinned

before the survival crossover occurred, as mentioned

in the previous section. After both stands were

thinned at least once, there were about 155 fewer

trees per acre in the higher site stand than in the

lower site stand. This relationship persisted through

age 50, but the magnitude of the difference decreased

over time because the rate of survival was better on
200 1

I I I I

IO 15 20 25 30 35

PLANTATION AGE (YEARS)

Figure Il.-Predicted survival trends within an unthinned loblolly

pine stand (site index 50) and an unthinned loblolly

pine stand (site index 70) both planted with 700 trees

per acre.

I” 13 zo 25 30 35 40

PLANTATION AGE (YEARS)

Figure 12.-Predicted quadratic mean diameter trends within an

unthinned loblolly pine stand (site index 50) and an

unthinned loblolly pine stand (site index 70) both

planted with 700 trees per acre.

I I 1

80 15 20 25 30 35 40

PLANTATION AGE (YEARS)

Figure 13.-Predicted basal area per acre trends within an unthinned loblolly pine stand (site index 50) and an unthinned loblolly pine stand (site index 70) both planted

with 700 trees per acre.

0

I I I I

IO 15 20 25 30 35

PLANTATION AGE (YEARS)

Figure 14.-Predicted total cubic foot volumeper acre trends within

an unthinned loblollypine stand (site index 50) and an

unthinned loblolly pine stand (site index 70) both

planted with 700 trees per acre.

s 250 ?i

= 200

cu

5 \ \

3 150- \

k

‘\

./‘-------. \

t--w. \

y1 loo- .’

./ _________ --------- --Y=,,---_-____

---- ----__ l-L_

B

___---

-*Y.\*

--- SlTE70 P n / .i. \:

0

I I I I I

10 15 20 25 30 35

PLANTATION AGE (YEARS)

Figure 15.-Predicted mean and periodic annual cubic foot volume

increment within an unthinned loblollypine stand (site

index 50) and an unthinned loblolly pine stand (site

index 70) both planted with 700 trees per acre.
the high site (fig. 16). Notice that in the site index 70

plantation after the first thinning and in the site

index 50 plantation after the second thinning mortality had nearly stabilized.

Mean Stand Diameter.-Quadratic mean diameter

averaged 2.98 inches higher on the high site than on

the low site. The difference was smaller in the early

years but consistently increased over time (fig. 17).

Since the thinning technique was a modified low thinning, as explained earlier, the average diameter increased with each thinning. The larger increases occurred in the latter thinnings, because spacing and

stand clean-up would have then essentially been

achieved, and a more accurate low thinning would be

practiced.

Basal Area .-After each stand had been thinned at

least once, basal area growth was only slightly higher

in the high-site stand than in the low-site stand (fig.

18). This result was unexpected but not inconsistent

with our data. The fewer larger trees did not greatly

compensate in basal area for the greater number of

smaller trees in the lower site index stand. There was

essentially no statistical relationship between site

index and basal area growth after a stand had been

thinned. The linear correlation between these variables was only r = 0.046.

Total Stem Volume Yield.-Total cubic foot (o.b.1

standing volume was always higher in the higher site

plantation than in the lower site plantation (fig. 19).

This was true even after all thinnings. Not only was

there 1,060 cubic feet per acre more total volume on

the high site at age 50, but here was 2,571cubic feet

per acre more volume removed through all of the thinnings in the higher site plantation.

UNTHINNED, THINNED PLANTATION

COMPARISON

In the unthinned plantation (site index 701, the age

40 survival was 236 trees per acre as compared to 103

trees per acre (before the final thinning) in the

thinned plantation at that age. The unthinned plantation had almost double the total volume of the thinned

plantation-7,745 cubic feet per acre as compared to

4,278. However, the average diameter of the trees in

the thinned plantation (at age 40) was about 2 inches

greater than those in the unthinned plantation. If one

considers the cumulative total volume removed in the

first three thinnings, the total volume either used or

available for use before thinning at age 40 in the high

site stand was 3,627 + 4,278 = 7,905 cubic feet per

acre. This is about 160 cubic feet per acre more volume than in the site index 70 unthinned stand at age

40.

20

An Example

To illustrate the application and utility of the prediction system, a relatively simple but realistic example should be considered. Given an existing unthinned

loblolly pine plantation that is presently 15 years old,

an inventory of the stand reveals there are 500 surviving trees per acre, and the average height of the

dominant and codominant trees is 45 feet. The user

desires full stand and stock table volume output to

describe the present stand. He then wants to thin the

stand back to a residual basal area per acre of 70

square feet, see what the stand looks like after the

thinning, and obtain a projection of what the thinned

stand will look like 5 years later. Stand and stock

table volume output is desired after the thinning and

at the end of the projection period. Also, a table completely summarizing the timber removed during the

thinning is requested. Board-foot volume using the

International l/kinch rule is chosen. Furthermore,

the same stand and stock table information in terms

of green weight is requested. A merchantable top diameter of 4 inches is selected for all the output.

The following scenario demonstrates how this system obtains the desired information.

Since HD = 45 feet is given, equation (8) is solved

for SI obtaining 61 feet.

Equations (ll), (121, and (13) are solved next giving

Xi = 2.9 inches, Xqmd = 6.4 inches, and Xs, = 8.4

inches.

This information is then used in equations (51, (61,

and (71, following the procedure explained on p. 5, 6.

This produces Weibull parameter estimates of

a = 1.718, b = 5.010 and c = 3.357.

Given the Weibull parameters and TS, equation (2)

is used to distribute TS into l-inch diameter classes.

Now assuming each diameter class represents the

midpoint diameter (i.e., the quadratic mean diameter)

for that class, equation 23, rearranged to estimate

BA, is invoked within each class to obtain BA for each

of those diameter classes.

The average height of the trees within each class is

obtained from equation (28) in this case.

Given all of this information, equations (301, (31),

and (321, with appropriate coefficients from tables 8

through 10, are used to obtain cubic-foot volume,

board-foot volume, and green-weight estimates

within each diameter class.

Finally, the stand totals for each output category

are obtained by summation. Figures 20 and 21 are

outputs from a computer program, COMPUTE PLOB (Ferguson and Baldwin 19871, which performed

the calculations for this procedure. The tables describe the initial stand before thinning. Note that due

to rounding of fractional to whole numbers, some

columns of figures do not add to the totals indicated in

the output tables.

Next, the stand is thinned. This is accomplished by
600, I

0 I I

10 1 5 2 0 2 5 3 0 3 5 4 0 4 5 50

PLANTATION AGE (YEARS)

Figure 16.-Predicted survival trends within a loblolly pine stand

(site index 50) and a loblolly pine stand (site index 70)

both planted with 700 trees per acre and thinned back

to 80 square feetper acre of basal area at ages 15,22,30

and 40.

41 I I I I I I I 1

10 15 2 0 2 5 3 0 35 4 0 45 50

PLANTATION AGE (YEARS)

Figure 17.-Predicted quadratic mean diameter trends within a

loblolly pine stand (site index 50) and a loblolly pine

stand (site index 70) both planted with 700 trees per

acre and thinned back to 80 square feet per acre of basal

area at ages 15,22, 30 and 40.

taking the values of X1, Xqmd, Xss, TS, and BA, which

are now defined as Xi,,, Xqmd,b, TSb, and BAb, and

placing them into equations (15), (16), (171, and (23) to

obtain X, a = 3.4 inches, Xqmd,a = 6.6 inches,

X 93,a = 8.6 ‘inches, TS, = 293 trees per acre, and

BA, = 70 square foot per acre (the given target basal

area). Then equations (51, (61, and (7) are solved again

to obtain new Weibull parameter estimates of

a = 2.057, b = 4.897, and c = 3.363. Finally, the stand

and stock tables (figs. 22, 23) are generated in the

same manner as explained previously. The desired

tables to summarize the volume and green weight of

the trees removed in the thinning (figs. 24, 25) are

simply obtained by term-by-term subtraction of the

70

6 0

IO 15 2 0 25 30 35 4 0 45

PLANTATION AGE (YEARS)

Figure 18 .-Predicted basal area per acre trends within a loblolly

pine stand (site index 50) and a thinned loblolly pine

stand (site index 70) both planted with 700 trees per

acre and thinned back to 80 square feet per acre of basal

area at ages 15,22,30 and 40.

4,500

SITE

I /- I

4 1,500

i

/

b ? /

4 1,000

/

/

500 1

I I I I I I I I

10 15 20 25 30 35 4 0 45 50

PLANTATION AGE (YEARS)

Figure lg.-Predicted total cubic-foot volume per acre trends within

a loblolly pine stand (site index 50) and a loblolly pine

stand (site index 70) both planted with 700 trees per

acre and thinned back to 80 square feet per acre of basal

area at ages 15,22,30 and 40.

comparable after-thin tables from the before-thin tables.

In the final step the values of Xi,+, Xqmd,+, Xss,+ and

TS, (now defined as Xi,i, Xqmd,i, Xsa,i, TSi) are placed

in equations (241, (251, (261, and (27), respectively.

Given that A = 15 and the projections of these values

are desired at time A = 20, Xr,s = 4.8 inches,

Xqmd,a = 8.0 inches, X,,,, = 10.4 inches, and TS = 272

trees per acre were obtained. Once again equations

(51, (61, and (7) are solved to obtain Weibull parameter

estimates of a = 2.877, b = 5.563 and c = 3.254. The

stand and stock tables (figs. 26, 27) are then generated and completely describe the predicted stand at

age 20.

0

21 I
LOBLOLLY PINE

BEFORE THINNING INFORMATION

(PER ACRE)

AGE= 15

DOMINANT HEIGHT= 45.0 FEET

QUADRATIC MEAN DBH= 6.389 INCHES

___^________________----------------------------------------------------------- ___________--____-__-----------------------------------------------------------

CUBIC FOOT VOLUME OF STEMS INTER.l/$

DBH STEMS BASAL AV. TO AN O.B. TOP DIAMETER OF B.F. VOL.

CLASS AREA HT. 0 INCHES 4 INCHES 8 INCHES %-IN. TL)P

------------ ------------ ------------

in. no. %: ft. o.b. i.b. o.b. i.b. o.b. i.b. i.b.

-----------------------.-.---------------------------- --------------------------

t

1 5 .7 29

A:: 6::

0 . 0 . 0 . 0 . 0 .

4.5 35 0 .

5 13.5 39 200. 10:: 12:: 0 .

127 24.9 42 397. 449. 327. 0 . 0 .

112 29.9 44 496. 610. 452. 0 . 0.

65 22.7 46

; 24

392. 497. 0 .

10.6 48 251. 190. 244. 10:: 7::

IO 5

11 1

2.7 49 65. 50. $. 49: ;;. 29.

.: 53 16. 12. . 12. . 9 . 47.

--------------_---------------------------------- ___L_I____-------___-----------

500 110.3 2426. 1805. 2061. 1523. 158. 116. 202.

---------------.-~---------------------.------~--------------------------======= _________--__^______----------------..__________________----------------

SI(BASE AGE 25)~ 61 FEET; 93RD PERCENTILE= 8.423

WEIBULL PARAMETERS: "A"= 1.71%; "B"= 5.010; "C"= 3.357

Figure 20.-Predicted volume measure (per acre) stand/stock table for an unthinned loblolly pine

plantation.

LOBLOLLY PINE

BEFORE THINNING INFORMATION

GREEN WEIGHT(POUNDS)

(PER ACRE)

AGE= 15

DOMINANT HEIGHT- 45.0 FEXT

QUADRATIC MEAN DBH= 6.389 INCHES

____________-____-__----------------------------. ____________-_____-------------------------------~~~ ___..___ --_-.- --ZlLL- . __._.--__ _ _ _ _ _ _ ::

TOTAL TOTAL WEIGHT TOTAL WEIGHT WEIGi:T CC

CROWN O F O F MERCH STEFI

DBH STEMS BASAL AV. WEIGHT WOODY BOLE 4"

CLASS AREA HT. W/FOL. COMPONENT TOP DIA.

---___-------- -------------- we-------------

in. no. ::: ft. o.b. o.b. i.b. o.b. i.b. o.b. i.b.

_____-__-_^_ -_____--_________---. . _ _ _._ .--.-em__ - ---- ----------------------------

3 1 5 .7 29 173. 651. 525. 561. 465. 1.

4792. 3959. 4141. 3510. 92;: 774.

15912. 13334. 13616. 11705. 8082. 6950.

7 112 29.9 44 11292:

31857. 26959. 26889. 23356. 21570. 18775.

40535. 34524. 33577. 29387. 3018%. 2646%.

8 65 22.7 46 9494. 32455. 2780%. 26454. 23312. 24997. 22057.

9 24 10.6 4% 4839. 15967. 12425. 11029.

1 0

: 2.7 4g

1377. 4261. 3287. 2929.

11 .7 50 365. 1069. 814. 72%.

____________________-----------------------------------------------------------

500 110.3 40977. 147499. 125475. 122249. 106839. 102292. 89711.

==================TE========_===============================~::=:~~========~=~=====

SI(BASE AGE 25)~ 61 FEET; 93RD PERCENTILE= 8.423

WEIBULL PARAMETERS: "A"= 1.71%; "B"z 5.010; "C"r 3.357

Figure 21.-Predicted weight measure (per acre) standlstock table for an unthinned loblolly pine

plantation.

22
LOBLOLLY PINE

RESIDUAL STAhTD -- AFTER THINNING

(PER ACRE)

AGE= I5

DOMINANT HEIGHT= 45.0 FEET

QUADRATIC MEAN DBHr 6.613 INCHES

=================r====_E=__Z=================~=:=:=~=~~~~~~~~:~==~:~:=~:~===========

CUBIC FOOT VOLUME OF STEMS INTER.1/4

DBH STEMS BASAL AV. TO AN O.B. TOP DIAMETER OF B.F. VOL.

CLASS AREA HT. 0 INCHES 4 INCHES 8 INCHES 8-1~. TOP

--u--a------ -----------m -----------_

in. no. ::: ft. o.b. i.b. o.b. i.b. o.b. i.b. i.b.

--------------------------------------------------------------~.,.-------------

i 2: 2.0 .2 29 3:: 3 . 0. 0. 0 . 0 . 0 . 0 .

35

1::: 6::

0 . 0. 0 .

2 74 52 14.5 7.1 39 42 144. 0 .

7 7 1 19.0 44 E

231.

2%:

190. :: E:

3;:

315. 387. 286. 0": 0 . 0.

9" ;; I;.;

212.7

;;

52 16. 1

271. 143. 344. 183. 258. 139. 8:'

31:

5:'

23:

rl 0.

:: 4 I 50 43 40. 12. 51. 16. 33. 12. 12L

'I. 9 . 47. ------------------------------~----~----------------"--------------------------

_______2~3__69:3_______15_31:___i/411___133e~____~~~:----~~~~-----~~~--~_-_171:__ -----__--------_------------------------------------------------------.--------

SItBASE AGE 25)= 61 FEET; g3RD PERCENTILE= 8.607

WEIBULL PAPAMETERS: "A"= 2.057; "B"= 4.897; "C"= 3.362

Figure 22.-Predicted volume measure (per acre) stand/stock table of a loblolly pine plantation

following its first thinning.

LOBLOLLY PINE

RESIDUAL STAND -- AFTER THINNING

GREEN WEIGHT(POUNDS)

(PER Am)

AGE= 15

DOMINANT HEIGHT= 45.0 FEET

QUADRATIC MEAN DBHz 6.613 INCHES

________________________________________-------------------~------------------- ____________________-----------------------------------------------------~-----

TOTAL TOTAL WEIGHT TOTAL WEIGHT WEIGHT OF

CROWN O F MERCH STEM

DBH STEMS BASAL AV. WEIGHT WOODY BE& 4"

CLASS AREA HT. W/FOL. COMPONENT TOP DIA.

::: ft. o.b.

-----------^-- -------------- ____-----------

in. no. o.b. i.5. 0. b. i.b. o.b. i.b.

__------------~__~~~~~~~ ~~~

t 253

.2 29 217. 175. 187. 155. I.

2.0 35 2113. 1751. 1832. 1553. 410. 34::

5 52 7.1 39 2085. 8358. 7004. 7152. 6148. 4245. 3650.

6 74 14.5 42 4832. 18562. 15708. 15668. 13609. 12568. 10940.

25696. 21885. 21286. 18629. 19137. 16779.

22469. 19252. 18314. 17306. 1527C'.

11375. 10319. 9626. 93'9. 8272.

IO 4 2.2 49 1102. 3408. 2gb6. 2682. 2343.

II 1 .7 50 365. 1069. 926. 824. 737. 2E:-. 728.

________----------------------------------- ------------------------------------

293 63.3 26323. 93873. 79966. 77571. 67895. 65429. 58324.

________________________________________--------------------------------------- __________________--____________________---------------------------------------

SI(BASE AGE 25)~ 61 FEET; g3RD PERCENTILE= 8.607

WEIBULL PARAMETERS: "A"= 2.057; "B"= 4.897; "C"= 3.362

Figure 23.-Predicted weight measure (per acre) standlstock table of a loblolly pine plantation

following its first thinning.

23
LOBLOLLY PINE

STAND COMPONENT REMOVED BY THINNING

(PER ACRE)

AGE= 15

DOMINANT HEIGHT= 45.0 FEET

QUADRATIC MEAN DBH- 6.024 INCHES

------------_----_-_---------.._--.-__________________________________------~~- --------_.-- _ _----__ --__---_-_.. ,___________ - ____ -__- _____ -_- _______ -----__-- __.__

CUBIC FOOT VOLUME OF STEMS INTEi?.1/4

DBH STEMS BASAL AV. TO AN O.B. TOP DIAMETER OF B.F. VOL.

CLASS AREA HT. 0 I?!CXS !: fNCHEs 8 INCHES S-IN. TOP

------------ --m--------- -----------

in. no. Fz: ft. o.b. i.b. o.b. i.b. o.b. i.b. i.b.

--------------------___I_______________ - - _ - --_.-... L__. _. - _ - L -- -------.-----------

3 .5 29 8 . 5 . 0 . 0 . 0 . 0 .

4 2.5 35 47. 33. 0 . 0 . 0 . 0 .

2

131.

1%

86. 60.

:: ::

0 .

224. 187. 137. 0 .

7 4 1 11.0 4 4 243. 181. 223. 166. 0 . 0 . 0 .

8 2 0 7.0 4 6 160. 121. 153. 114. 0 . 0.

9 6 2.7 4 8 63. 47. 61. 46. $1 20.

1 0 1 .5 49 13. 10. 13. 10. 8 . 6 . 3::

Figure 24.-Volume measure (per acre) stand/stock table of the bole wood and bark material

removed during the first thinning of a loblolly pine plantation.

LOBLOLLY PINE

STAND COMPONENT REMOVED BY THINNING

GREEN WEIGHT(POUNDS)

(PER ACRE)

AGE= 15

DOKINANT HEIGHT- 45.0 FEET

QUADRATIC %A:: DE:= 5.024 INCHES

---------------_-----~------ ---- ----- ------ --------. _-- -. ___-.______.-_______------------------------------- -_ _____________ _ __..___---_ - ____..____ - --------------

TOTAL TOTAL 'dE:GHT TOTAL WEIGHT WEIGHT OF

CRO'JvI.‘ O F O F MERCH STEH

DBH STE% BASAL AV. WEIGHT WOODY BOLE 4 "

CLASS AREA HT. W/ FOL. COMPONENT TOP DIA.

in. no. ::: ft. o.b.

-------------- -------------- ___-----------

o.b. i.b. o.b. i.b. o.b. i.b.

__-----------___---------------------------------------------------------------

3 IO .5 23 115. 434. 350. 374. 310.

29 2.5 35 655. 1957.

51:: 1.

432.

;: 10.4 6.4 39 42 3461. 1864. 5557. 9747. 3837. 9002. 3300.

7 41 11.0 44 4133.

8 20 7.0 46 2921.

9 6 2.7 48 1210. 2757.

10 1 -5 49 275. 597. 65:. 5%.

____________-___I____I__________________________-_-------------------.--------

207 41.0 14654. 53626. 45509. 44678. 38944. 35863. 31387.

__________________________ ___- _------- _ . .._ - _____ -.--_--_-._--- ____. t==:=::::r------------------ _ __-_ -_------- - _ ____ - _-_____._ - --.__ --------- -----

Figure 25.-Weight measure (per acre) stand/stock table of the wood and bark material removed

during the first thinning of a loblolly pine plantation.
LOBLOLLY PINE

NO THINNING THIS YEAR

(PER ACRE)

AGE= 20

DOMINANT HEIGHT= 53.5 FEET

QUADRATIC MEAN DBH= 8.042 INCHES

------------------------------------------------------------~------------------ -------------------------------------------------------------------------------

CUBIC FOOT VOLUME OF STEMS INTER.l/4

DBH STEMS BASAL AV. TO AN O.B. TOP DIAMETER OF B.F. VOL.

CLASS AREA HT. 0 INCHES 4 INCHES a INCHES &IN. TOP

-L---------- ------------ --------^_--

in. no. Fk!: ft. o.b. i.b. o.b. i.b. o.b. i.S. i.b.

---------------------------------__I--c----c-------------------------_________

4 .3 39 7. A

19 2.6 44 55. 4:: 35: ".

0 . 0 . 0 .

1;::

0 . 0 . 0 .

38 7.5 48 174. 129. 142.

56 15.0 51 373. 280. 341. 253. t : i:

0 .

0 .

61 21.3 53 418. 529. 398. 0 . 0 . 0 .

1:

49 21.6 55 446. 571. 434. 232. 164. 0 .

29 15.8 56 334. 430. 329. 257. 189. 1111.

1:

12 7.9 57 223. 171. 221. 170. 162. 122. 701.

; 2.4 58 68. 52. 67. 52. 55. 42. 240.

13 .9 59 27. 21. 27. 21. 24. 18. 103.

----------------------------------------------------------------~-----------

_______~'__95:3_____--~~~:---~~~~:---~~~~:---~~~~:----~~~:----~~~:----~~~~~-- _____--________----------------------------------------------------------------

SI(BASE AGE 25)= 61 FEET; 93RD PERCENTILE= 10.391

WEIBULL PARAMETERS: "A"= 2.877; "B"= 5.563; "C"= 3.254

Figure 26.-Predicted volume measure (per acre) stand/stock table of a loblolly pine plantation

5 years after its first thinning.

LOBLOLLY PINE

NO THINNING THIS YEAR

GREEN WEIGHT(POUNDS)

(PER Am)

AGE= 20

DOMINAhT HEIGHT= 53.5 FEET

QUADRATIC MEAN DBH= 8.042 INCHES

______--_________----------------------------------------------------------~-~~ ______-___-______-_-____________________--------------------------------------.

TOTAL TOTAL WEIGHT TOTAL WEIGHT WEIGHT OF

CROWN O F MERCH STEM

DBH STEMS BASAL AV. WEIGHT WOODY BEE 4"

Cm AREA HT. W/FOL. COMPONENT TOP DIA.

::: ft. o.b.

------------- --________---- -_------^------

in. no. o.b. i.b. o.b. i.b. 0.5. i.b.

4 4 .3 39 405. 338. 361. 308.

5 1 9 2.6 44 62 3370. 2870. 2998. 2601. 16%: 14%

6 3il ?I5 4 8 10619. --' 9122. 9%5. 8209. 7377. 6492.

7 5 6 15.0 5 1 2;;:. 22720. 19674. 19813. 17536. 17801. 15789.

8 61 21.3 5 3 33855. 29473. 29114. 25934. 24613.

9 4 9 21.6 5 5 'B;Y$:

6658:

35972. 31473. 30554. 27378. 26614.

1 0 2 9 15.8 5 6 27085. 23764. 22607. 20339. 20010.

11347. 10252.

3433. 3112.

1364. 1241.

________________----------- --------------w..__-.--.-C--_--.--,--C---------- . .. . “.

272 95.3 34954. 154004. 134297. 131093. 117038. 122498. 1095Z'l.

_______------._ ___________. ., ______ ..v..-^ =--=~~.---I========ITII :: :=~:---TfTT_-,====================

SI(BASE AGE 25)~ 61 FEET; 93RD PERCENTILE= 10.391

WEIBULL DqD""ETERS: * 1 hY.2 “A”= 2.877; "B"= 5.563; "C"= 3.254

Figure 27.-Predicted weight measure (per acre) standlstock table of a loblolly pine plantation

5 years after its first thinning.

2 5
Computer Program

A computer program, COMPUTE P-LOB Comprehensive Outlook For Managed Pinessing simulated

Treatment Experiments-Planted Loblolly Pine, does

all of the required calculations and produces the desired yield tables. It is written in FORTRAN 77 and in

BASIC. At the time of this publication, compiled or

text versions in FORTRAN are available for Digital

Equipment Corporation PDPll/series computers,

Data General MV series computers, IBM and IBM

compatible personal computers, and Hewlett Packard

9800 series computers using the FORTRAN software.

Compiled and text BASIC versions are available for

the IBM and IBM compatible personal computers.

Copies of the program are available from the authors.

A companion publication to this one (Ferguson and

Baldwin 1987) is a User’s Manual for the prediction

system. It completely describes the computer software

and gives more examples of program uses. A complete

listing of the FORTRAN code is given.

LITERATURE CITED

Bailey, R. L.; Abernathy, N. C.; Jones, E. P., Jr. 1981.

Diameter distribution models for repeatedly

thinned slash pine plantations. In: Barnett, J. P.,

ed. Proceedings of the biennial southern silvicultural research conference; 1980 November 6-7; Atlanta, GA. Gen. Tech. Rep. SO-34. New Orleans,

LA: U.S. Department of Agriculture, Forest Service; Southern Forest Experiment Station; 115-126.

Bailey, R. L.; Dell, T. R. 1973. Quantifying diameter

distributions with the Weibull function. Forest Science. 19(2): 97-104.

Bailey, R. L.; Pienaar, L. V.; Shiver, B. D.; Rheney,

J. W. 1982. Stand structure and yield of siteprepared slash pine plantations. Research Bulletin

291. Athens, GA: Univeristy of Georgia, College of

Agriculture Experiment Station; 83 p.

Baldwin, V. C., Jr. 1982. A procedure to obtain evenaged forest stand structure and volume predictions

using aerial photographic information. In: Brann,

T. B., House, L. O., IV., Lund, H. G., eds. In-Place

Resource Inventories: Principles and Practices, Proceedings of a National Workshop; 1981 August 9-

14; Orono, ME. SAF 82-02. Washington, DC: Society of American Foresters; 308-314.

Baldwin, V. C., Jr. 1987. Green and dry weight equations to predict the aboveground tree components of

planted loblolly pine in the west gulf region. Southern Journal of Applied Forestry. ll(4): (in press).

Baldwin, V. C., Jr.; Feduccia, D. P. 1987. Cubic-foot

volume, volume-ratio and stem profile equations for

planted loblolly pine in the west gulf region. Publication in process.

26

Brister, G. H.; Clutter, J. L.; Skinner, T. M. 1980. Tree

volume and taper functions for site-prepared plantations of slash pine. Southern Journal of Applied

Forestry. 4(3): 139-142.

Burkhart, H. E.; Sprinz, P. T. 1984. Compatible cubic

volume and basal area projection equations for

thinned old-field loblolly pine plantations. Forest

Science. 30(l): 86-93.

Cao, Q. V.; Burkhart, H. E.: Lemin, R. C., Jr. 1982.

Diameter distributions and yields of thinned

loblolly pine plantations. Publication No. FWS-l82. Blacksburg, VA: School of Forestry and Wildlife

Resources, Virginia Polytechnic Institute and State

University; 61 p.

Clutter, J. L.; Harms, W. R.; Brister, G. H.; Rheney,

J. W. 1984. Stand structure and yields of siteprepared loblolly pine plantations in the lower

Coastal Plain of the Carolinas, Georgia, and north

Florida. Gen. Tech. Rep. SE-27. Asheville, NC: U.S.

Department of Agriculture, Forest Service; Southeastern Forest Experiment Station; 173 p.

Coile, T. S.; Schumacher, F. X. 1964. Soil-site relations, stand structure, and yields of slash and

loblolly pine plantations in the Southern United

States. Durham, NC: T. S. Coile, Inc.; 296 p.

Daniels, R. F.; Burkhart, H. E. 1975. Simulation of

individual tree growth and development in managed loblolly pine plantations. Publication No.

FWS-5-75. Blacksburg, VA: School of Forestry and

Wildlife Resources, Virginia Polytechnic Institute

and State University; 69 p.

Dell, T. R.; Feduccia, D. P.; Campbell, T. E.; Mann,

W. F., Jr.; Polmer, B. H. 1979. Yields of unthinned

slash pine plantations on cutover sites in the west

gulf region. Res. Pap. SO-147. New Orleans, LA:

U.S. Department of Agriculture, Forest Service,

Southern Forest Experiment Station; 84 p.

Feduccia, D. P.; Dell, T. R.; Mann, W. F., Jr.; Campbell, T. E.; Polmer, B. H. 1979. Yields of unthinned

loblolly pine plantations on cutover sites in the west

gulf region. Research Paper SO-148. New Orleans,

LA: U.S. Department of Agriculture, Forest Service, Southern Forest Experiment Station; 88 p.

Ferguson, R. F.; Baldwin, V. C., Jr. 1987. Users manual for COMPUTE-PLOB-a program for predicting growth and yield of loblolly pine plantations.

Publication in process.

Freese, F. 1964. Linear regression methods for forest

research. Res. Pap. FPL-17. Madison, WI: U.S. Department of Agriculture, Forest Service, Forest

Products Laboratory; 136 p.

Little, S.N. 1983. Weibull diameter distributions for

mixed stands of western conifers. Canadian Journal

of Forestry Research. 13(l): 85-88.

Matney, T.G.; Sullivan, A. D. 1982. Compatible stand

and stock tables for thinned and unthinned loblolly

pine stands. Forest Science. 28(l): 161-171.
Max, T. A.; Burkhart, H. E. 1976. Segmented polynomial regression applied to taper equations. Forest

Science. 22(3): 283-289.

Milliken, G. A. 1982. Nonlinear statistical models.

Arlington, VA: The Institute for Professional Education; 351 p.

Parresol, B. R. 1983. A volume and taper prediction

system for bald cypress in Lousiana. Baton Rouge,

LA: Louisiana State University, School of Forestry

and Wildlife Resources; 135 p. M.S. thesis.

Schumacher, F. X.; Hall, F. D. S. 1933. Logarithmic

expression of timber-tree volume. Journal of Agricultural Research. 47(g): 719-734.

Smalley, G. W.; Bailey, R. L. 1974. Yield tables and

stand structure for loblolly pine plantations in Tennessee, Alabama, and Georgia highlands. Res. Pap.

SO-96. New Orleans, LA: U.S. Department of Agriculture, Forest Service, Southern Forest Experiment Station; 81 p.

Strub, M. R.; Feduccia, D. P.; Baldwin, V. C., Jr. 1981.

A diameter distribution method useful in compaticable growth and yield modeling of thinned stands.

In: Barnett, J. P. ed., Proceedings of the biennial

southern silvicultural research conference; 1980

November 6-7; Atlanta, GA. Gen. Tech. Rep. SO34. New Orleans, LA: U.S. Department of Agriculture, Forest Service, Southern Forest Experiment

Station; 127-130.

Van Deusen, P. C.; Sullivan, A. D.; Matney, T. G.

1981. A prediction system for cubic foot volume of

loblolly pine applicable through much of its range.

Southern Journal of Applied Forestry. 5(4): 186-

189.

Zanakis, S. H. 1979. A simulation study of some simple estimators for the three-parameter Weibull distribution. Journal of Statistical Computation and

Simulation. g(2): 101-116.

27
Baldwin, V. C., Jr. and Feduccia, D. P. 1987. Loblolly pine

growth and yield prediction for managed west gulf plantations. Res. Pap. SO-236. New Orleans, LA: U.S. Department

of Agriculture, Forest Service, Southern Forest Experiment

Station. 27 p.

Complete description, including tables, graphs, computer

output, of a growth and yield prediction system providing

volume and weight yields in stand and stock table format. An

example of system use is given along with information about

the computer program, COMPUTE P-LOB, that operates -

the system.

Additional keywords: Pinus tuedu L., volume predictions,

weight predictions, unthinned or thinned plantation yields,

Weibull distribution, taper curves, site-index prediction, survival prediction, diameter distribution moments, parameter

recovery, problem-free sites.