Forest Service 

Southern Forest 

hern P 

Experiment Station 

New Orleans, 

Louisiana 

General Technical Report 

SO-48 

September, 1983 

Richard W. Guldin and Robert M. Farrar, Jr. 
SUMMARY 

A program is described that permits computation of site index in the field 

using a Texas Instruments model TI-59 progra able, hand-held, batterypowered calculator. Based on a series 06 equations developed by R.M. Farrar, 

Jr., for the site index curves in USDA hfisceflaneous Publication 50, the 

program can accommodate any index base age, tree age, and height within wide 

limits for the four principal southern pine species: loblsI%y (Pinus taeda L,), 

longleaf (P. gsalustrls Mill,), shortleaf (P, enehinata Mill.) and slash pine 

(P. ellcottzz Engelm.), Small errors in estimating average stand age or height 

cause large errors in estimating site index, especially for young stands. The 

program is used to explore the sensitivity of site index estimates to age and 

height errors. 
Computation of Southern Pine Site Index 

Using a TI-59 Calculator 

Richard W. Guldin and Robert M. Fanar, Jr. 

Forest management is influenced by the productivity of the tract supporting the timber, Site index 

- the expected average height of the dominant and 

codominant stems in a stand at a reference base age 

- is a measure of the productive capacity sf the land 

for a given species, Traditional methods of computing site index require lengthy calculations back at 

the office. To determine approximate site index of 

southern pine stands in the field, foresters have often 

relied upon ocular interpolation of the curves for 

index base age 50 presented in Miscellaneous Publication 50 (USIDA Forest Service 1976). But ocular 

interpretation of site index differences for young 

stands is very difficult and translation to other index 

base ages is also difficult with the curves. 

This report contains a listing of the program for a 

Texas Instruments model TI-59 calculator1 that alfiows foresters to compute site index quickly and accurately in the field, The program also enables foresters to translate indexes to different base ages, to 

compare expected heights ad different ages on the 

same site, and to compare site indexes implied by 

differing heights sf trees the same age, Finally, a 

sensitivity analysis of site index estimates is reported that illustrates the inaccuracy resulting from 

small errors in determining stand age and stand 

height. 

PROGRAM BACKGROUND 

Farrar (1973) expressed the site index, curves 

in Miscellaneous Publication 50 as equations having 

the form : 

Log(SI) - Log (ATH) '- bi[L- IBA - ATA ---- '1 

+ 9 1 b2[(-)2 - (-----)q IB A ATA 

where Log = logarithm, base 10 

SI = site index 

ATH = average total height of the dominant 

and co-dominant trees in a stand 

IBA = site index base age 

ATA = average total age-from-seed of the 

dominant and co-dominant trees in 

the stand 

Farrar (1975) later developed a FORTRAN program to calculate site index (or height) arrays from 

inputs of index base age, average tree age and average 

height (or site index). 

The calculator program presented here (appendix, 

Program Listing) uses coefficients Farrar (1975) 

developed to describe site index curves in Miscellaneaus Publication 50- Thus, the same limitations regarding age, site index, and average height apply 

(table 1). 

The User Instructions contain five basic steps (appendix). Tho frst step initializes the program" parameters and prepares the calculator for one of the 

next four steps, each a different program option. 

Step b : Program f nitializatiora 

During initialization, the calculator memory is L.. 

'The use of trade, firm, or corporation names in this report partitioned between storage for program steps and 

is for the information and convenience of the reader, Such 

use does not constitute official endorsement or apprsrral 06 for constants rand the program is entered into calthe product or firm by the USDA to the exclusion af others culator If the memory k not partitioned 

which may be suitable. properly, the program cannot be loaded, Program 

Richard 'iV. Guldin is Principal Economist, Southern Forest Experiment Station, Forrest Service - USDA, at New Orleans, 

LA. Robert M. Farrar, Jr, is Principal Mensuratitanist, Southern Forest Experiment Station, Forest Service --- USDA, Monticello, AR, in cooperation with the Department of Forestry and the Arkansas Agricultural Experiment Station, University of 

Arkansas at Montieello. 
Table 1.-Limits for species equationsL 

Lobfolly Longfeaf Shortleaf Slash 

Age limits (years) 10-80 15-100 10-100 10-60 

SI limits, base 

age 50 (feet) 60-.120 40-120 40-100 60-100 

1Frorn Farrar (1975, table 1). 

execution begins with the constants for the desired 

species being retrieved from storage and positioned 

in the general equation sulrtroutine. The program 

moves automatically to step 2 after completing initialization. 

Step 2 t: Site Index: Cafeulation 

This step, the subroutine labeled E inside the program, automatically calculates the average total age 

and average total height of the stand at the sampling 

point from the ages and heights of individual trees, 

The calculator display prompts the user for data 

using a numerical code. %Vhen the display contains 

1111lt%ZI11, the next datum needed is the site index 

base age; 2222222222, the tree age; 3333333333, the 

tree height, Ages and heights for a minimum of 10 

dominant and codominant trees should be measured 

and entered. The display flashes the number of trees 

already entered before prompting the user for the 

next age. A zero is entered for tree age after the data 

for all trees at a sampling point are entered, causing 

the program to prepare for index calculation. The 

program asks for the index base age, then computes 

average age, average height; and site index of the 

stand, The average age and average height flash in 

the display and site index is displayed. If the calculator is attached to a PC-100 printer, the results 

are also printed. 

From Step 2, the user can branch to any of the 

next three steps by entering the appropriate letter 

(A$, or C), If the cafculation of site index is desired 

at another sample location in the stand, press 

""RUN/ST0P9? and the program will recycle and prepare for the first tree age at the next sample location. 

Previously calculated site indexes, average ages or 

average heights are not stored in calculator memory. 

For a different species, go back to step 1.4. 

Step 3 : Height Projection 

This step, the subroutine fabeled A inside the program, calculates an expected height for each age 

specified by the user, given site index and index base 

age, the inverse of step 2, Step 3 can also be used to 

convest from one index base age to mother. For 

example, a particular stand of longleaf pine may have 

a site index of 70, base age 25, At age 50, the dominant and codominant trees rxrould have an average 

height of 110 feet. Because age 50 can also be considered an index. base age, the height at this age becomes the site index - 110 feet, 

When the program displays 4444444444, enter site 

index, After entering the age for which height is 

desired, the program calculates expected height. 

Press ''RUNi'STOP" to recycle for another age, All 

the variables entered are also printed if a BC-100 

p~nter isattached. 

Step 4 : Height Vector. 

This step, the subroutine labeled I3 inside the program, calculates a vector of expected average heights 

of dominant and eodominant trees for a vector of 

average stand ages. The user specifies site index, base 

age, and the increment between ages when heights 

are desired. The program prompts 5555555555 for 

the age increment in years, The program begins at 

age 10 (15 for longleaf) and continues computing 

heights for each age until the upper age limit is 

reached (table I). When the upper age limit is 

mached, 9896543210 is displayed, Both the age and 

height vectors are printed if a PC-100 printer is 

attached. 

Step 5 : Site Index Vector 

The site index vector, the subroutine labeled C 

inside the program, is similar to the height vector. 

Tbe user specifies the stand age, index base age, 

height increment and the maximum height desired. 

The program calculates the site index associated 

with each height, beginning at 10 feet, for the specified average stand age. The program prints 999 for 

output if site index is less than 10 feet or greater 

than 170 feet. The end of the vector is marked by 

987654321, The height and site index vectors are 

both printed if a PC-100 printer is attached. 

IJsil~g the Program 

Foresters should thoroughly familiarize themselves 

with the program before using it in the field the first 

time. The following 10 operations should be performed. 

1. Keystroke the program (appendix) into the machine after properly partitioning the memory. 

2. Write 2 sets 06 cards for the program. 

3. Clear the memory' 
4. Reload the recorded program, 

5, Run a complete listing (2ND LIST and TNV 2ND 

LIST) of the recardeb and reloaded progmm, 

6, Verify keystroke accuracy against Program Listing 

(appen&x). 

7, Gsrrect any mistakes, 

8. Rewrite both sets of cards, if neeessay, 

9, Run the test problems (appendix) do verify that 

the program is working properly. 

10. Use a data set you have previously analyzed and 

compare the program's results with your prior results, 

SEllerPSPa"l[VITY ANALYSIS 

Users must bear in mind the age limitations inherent in Miscellaneous Publication 50 (IISBA Forest Service 1976). The ages specified for loblolly, 

shortleaf, and slash pine are ring counts to pith froan 

cores taken at dbh, plus 3 years. For longleaf pine, 

age is ring count to pith from cores taken at dbh, 

plus 7 years. All of the data came from naturally regenerated, second-growth stands. Consequently, the 

ages are al estimated cge-from-seed. Users should 

calculate the ages of their trees the same way. 

Using the program for plantations can create problems, In the first place, the height growth patterns 

depicted by the site index curves for natural stands 

may not match the patterns in plantations, especially 

plantations on old field or prepared sites. Assuming 

that the curves are suitable, there is still another 

problem. When a plantation is established, the 1-0 

(bare-rooted) seedlings planted are already 1 year 

old from seed. Tbus, when a plantation is 25 years 

old, the trees are actudy 263 years kom seed. Common practice presumes that the average height of 

dominant and codominant trees in a plantation 25 

growing seasons after planting is the site index with 

an index base age of 25 years. But this presumption 

creates a one year height growth error in this program. The height of a stand planted 25 years pmviously is the site index only if the index base age is 

26 or the seedlings planted were grown in containers 

and were less than 6 months old when planted. Thus, 

the presunzption that average plantation height 

equals site index is only coswct for plantations 24 

years after establishment with 1-0 (bare-root) seedlings. 

Serious errors are created Pvhen evaluating site 

quality based on young, fast-growing stands if the 

year" difference in age-from-seed versus age-fromestablishment is ignored, For example, suppose the 

average height of dominant and csdominant trees in 

a loblolfiy pine plantation kl years from seed (10 

years after establishment) is 36 feet. Site index, base 

age 50 for 1% years and height 36 feet is 80. But if 

the age is mistakenly entenjicl as 10, based on the 

age since establishment, site index for a height of 36 

feet is 96, The error of one year induces a 20 percent 

error in. site index (fig, f ) . Pf these overestimates of 

28 30 48 

AGE-FROM-- SEED (YEARS) 

Fimse 1,-Site index perce~tage overestimate resulting from a one-year aging error, SISO = 88 for eaeh 

species. 
site index are used as arguments in some stand volume and growth predictors to estimate present and 

future volumes, they obviously cause overestimates 

of both volumes and growth. The problem becomes 

most acute when young, fast-growing stands are on 

the verge of merchantability and when the log-rule 

being used, such as the Doyle Rule, penalizes small 

stems, Under these conditions, overestimating site 

index by 10 to 20 percent can lead to overestimating 

future growth and yield by 33 to 50 percent over 20 

to 30 year rotations (Feduccia et.al. 1979). Economic 

evaluations of investments in possible intermediate 

treatments founded on such overestimates of site 

index will conclude that higher rates-of-return will 

be earned than will actually occur. Consequently, 

landowners may over-invest in stand treatments and 

inefficiently allocate scarce management funds. 

Foresters should take care when comparing their 

own plantations with published yield tables or with 

growth and yield models that vary with site index. 

They should determine whether the published information was constructed using age-from-seed or agefrom-estabfishment and which age is implied in the 

site index base age. Then, this program can he used 

to properly enter the published plantation yield 

tables or utilize published equations for comparison, 

In the authorsbxperiences, field foresters using 

clinometers tend to overestimate tree heights by 2 

to 10 percent compared to actual heights measured 

with a Gape after felling. It is often difficult to actually see the true tree top because closed crown 

canopies or intervening branches near the top of the 

tree can obstruct the measurer's vision. Consequently, heights taller than those actually existing 

are often recorded. However, in contrast to the misspecification of age, height errors are not compounded. Site index is only raised by the same percentage as the percent height error. 

The nilture of the errors flows directly from the 

form of the estimating equation. Because ages are 

used in the exponent of the equation, the equation 

is much more sensitive to aging errors than height 

estimation errors. But, overestimating actual heights 

compounds the problem of determining site index for 

plantations when the year that seedlings spend in the 

nursery is ignored. 

Sound data collection procedures should eliminate 

the age and height estimation errors. If accurate data 

are used, this program will provide site indexes and 

height growth projections far superior to results 

from ocular interpolation of curves without hawing to 

retreat to the office for computations. 

LITERATURE CITED 

Farrar, R.M., Jr. Southern pine site index equations. 

J. For. 71:696-697; 1973. 

Farrar, R.M., Jr. Southern pine site-index computing 

program. Res. Note SO-197. New Orleans, LA: 

U.S. Department of Agriculture, Forest Service, 

Southern Forest Experiment Station; 1975. 7 p. 

Feduccia, D.P., Dell, T.R., Mann, NT.F., Jr., Campbell, T.E., and Polmer, I3.F. Yields of unthinned 

loblolly pine plantations on eutover sites in the 

west gulf region. Research Paper SO-148. New 

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

1979.88 p. 

USDA Forest Service. Volume, yield, and stand 

tables for second-growth southern pines. Misc. 

Publ. 50. Washington, DC: U.S. Department of 

Agriculture, Forest Service; 1929 (rev. 1976). 

202 p. 
Appendix 
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User Instruelions 

Step Procedure ENTER Press Display 

INITIAI~IZIE: THE PROGRAM PARAMETERS 

Partition the calculator. 6 

Load the progrm, reading card sides 1 to 4, side # 

Efed;in execution. 

Sekct the species desired: A" =LL loblolly; E3' = longleaf; 

C" =;: shortleaf; and Dk slash 

SITE INDEX GALCULATIOMa 

Enter the present tree age (PTA). PTA 

Enter the present tree height (HT) . HT 

Do steps 2.1 and 2.2 for dl n sample trees. 

After entering the fast sample tree height, enter O for 

the next ETA, 0 

Enter the index base age (IBA) desired. IBA 

To prepare the program for calculating site index at a 

new sample location, If a new species is desired, 

go to step 1.4 

HEIGHT PROJECTION 

Enkr site index (531). S I 

Enter index base age (XBA), LEA 

Enter the stand age (SA). . S A 

Recycle the program for the next stand age. 

HEIGHT VECTOR 

Enter site index (Sf), ST 

Enter index base age (ZBA) . kBA 

Enter age increment (AI) . The program continues A1 

until upper age limits are reached. 

SITE INDEX WGTOR 

Enter index base age CLBA) IBA 

Enter the average tree age (ATA) ATA 

Enter height hcrement (HTI). HT% 

Enter maximum height (HTMAX), The program eonlinues HTMAX 

to HTMAX. I& an SI outside the range 10 < SZ < 178 

is computed, the program prink 9999999999. The end 

is marked 987654321. 

2ND OP 17 

INV 2ND WRITE 

RST R/S 

2ND (letter) 

Rf S 

RIS 

A 

RIS 

R/S 

a/s 

RIS 

B 

R/S 

RIS 

RfS 

e 

RIS 

RIS 

RIS 

RIS 

479.59 

side # 

9876543210, 

111111111l. 

Site Index 

4444344444, 

11111lP1l1* 

2222222222, 

Expected HT 

2222222222. 

4444444444. 

Ibkkllla1L. 

5555555555. 

Ages &, Heights 

9816543210. 

IlllllIIll. 

2222222222. 

6666666666. 

777777179'9. 

Weights and 

Site Indexes 

get to step 2.0 witbout going through step 1, press E from anywhere in the program. 
Program Test Problems 

Step Action 

Initialize the program 

Partition the calculator 

Load the program by reading cards 

Begin execution 

Select loblolly pine (A') 

Calculate site index using the data (E) 

PTA -- 16,15,18,17,16,17,15,16,16,17 

WT - 47,42,51,47,43,48,43,45f44149 

Repeat 2.1 and 2.2 for all 10 trees 

Enter 0 for PTA after WT = 49 

Enter XBA - 25 

Display flashes the average age. 

Display flashes the average height: 

Display stops flashing, SI appears: 

Calculate expected stand heights (A) 

Enter SI = 80 

Enter XBA = 25 

Enter SA = 18 

Expected hieight is displayed 

Recycle for next SA: RIS 

Enter SA = 27 

Expected height is displayed 

Calculate a height vector (B) 

Enter SI = 70 

Enter IBA = 30 

Enter AX = 10 

The display flashes 

and printer prints: 

The end marker appears: 

Calculate an SI vector (C) 

Enter IBA = 50 

Enter ATA =: 67 

Enter HTI = 20 

Enter HTMAX = 200 

The display flashes 

and printer prints: 

The end marker appears: 

Printer Calculator 

tape display 

3333333333. 

1, 2, 1,2, , 10. (& 

9 10 2222222222. 

1111111111. 

25 

16 16 

46 46 

68 68 

44444M444. 

80 111111111P. 

25 2222222222. 

18 

60 60 

2222222222. 

27 

85 85 

4444444444. 

70 1111111111. 

30 5555555555. 

10 

PTA = 10 20 30 40 50 68 70 80 

HT = 23 50 70 84 93 100 104 108 

9876543210. 9876543210. 

1111111111, 

50 2222222222. 

67 6666666666. 

20 7777777777. 

200 

HT = 10 30 50 70 90 110 130 150 170 190 

SI =s 999 27 45 63 81 100 118 136 154 999 

9876543210, 9876543210, 
Guldirn, Richard \V., and Farrar, Robert M. Jr. ComputaLion of southern pine site index using a TI-59 calculator, 

U.S, Department of Agriculture Forest Service, General 

Technical Report SO-48. South. For. Exp, Stn. New 

Orleans, La. 8 p. 1983. 

A program is described that permits computation of site 

index in the field using a Texas Instruments model TI-59 

programmable, hand-held, battery-powered calculator. Based 

on a series of equations developed by R.M. Farrar, Jr,, for 

the site index curves in USDA Miscellaneous Publication 50, 

the program can accomodate any index base age, tree age, 

and height within wide limits for four principal southern pine 

species. 

Keywords: Growth, timber management, loblolly pine, longleaf pine, shortleaf pine, slash pine, computer program, plantation, dendrochronology.