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, battery- powered 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 produc- tivity 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 comput- ing 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 Publi- cation 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 al- fiows foresters to compute site index quickly and ac- curately in the field, The program also enables for- esters to translate indexes to different base ages, t o 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 re- ported 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) '- b i [ L - IBA - ATA ---- ' 1

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

where Log = logarithm, base 10 S I = 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 pro- gram 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 Miscellan- eaus Publication 50- Thus, the same limitations re- garding age, site index, and average height apply (table 1).

The User Instructions contain five basic steps (ap- pendix). Tho f r s t step initializes the program" par- ameters 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 cal-

the 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, Monti- cello, 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 ini- tialization.

Step 2 t: Site Index: Cafeulation

This step, the subroutine labeled E inside the pro- gram, automatically calculates the average total age and average total height of the stand a t 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 a t 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 cal- culator 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 a t another sample location in the stand, press ""RUN/ST0P9? and the program will recycle and pre- pare 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 pro- gram, 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 dom- inant and codominant trees rxrould have an average height of 110 feet. Because age 50 can also be con- sidered an index. base age, the height a t this age be- comes 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 ~ n t e r is attached.

Step 4 : Height Vector.

This step, the subroutine labeled I3 inside the pro- gram, 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 a t 10 feet, for the speci- fied 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 per- formed. 1. Keystroke the program (appendix) into the ma-

chine 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 re- sults,

SEllerPSPa"l[VITY ANALYSIS

Users must bear in mind the age limitations in- herent in Miscellaneous Publication 50 (IISBA For- est Service 1976). The ages specified for loblolly, shortleaf, and slash pine are ring counts to pith froan cores taken a t dbh, plus 3 years. For longleaf pine, age is ring count to pith from cores taken a t dbh, plus 7 years. All of the data came from naturally re- generated, second-growth stands. Consequently, the ages are a l estimated cge-from-seed. Users should calculate the ages of their trees the same way.

Using the program for plantations can create prob- lems, 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 ac tudy 263 years kom seed. Com- mon 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 pro- gram. The height of a stand planted 25 years pm- viously 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) seed- lings.

Serious errors are created Pvhen evaluating site quality based on young, fast-growing stands if the year" difference in age-from-seed versus age-from- establishment is ignored, For example, suppose the average height of dominant and csdominant trees in a loblolfiy pine plantation k l 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 3 0 48

AGE-FROM-- S E E D ( Y E A R S )

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 vol- ume 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 infor- mation was constructed using age-from-seed or age- from-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. I t is often difficult to act- ually see the true tree top because closed crown canopies or intervening branches near the top of the tree can obstruct the measurer's vision. Conse- quently, heights taller than those actually existing are often recorded. However, in contrast to the mis- specification of age, height errors are not com- pounded. Site index is only raised by the same per- centage 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., J r . 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., Camp- bell, 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, For- est 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

Program Listing

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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 D k 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 i s 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 R I S

A R I S R/S a/s RIS

B R/S R I S RfS

e R I S R I S R I S RIS

479.59 side #

9876543210,

111111111l. Site Index

4444344444, 11111lP1l1* 2222222222,

Expected HT 2222222222. 4444444444. I b k k l l l a 1 L . 5555555555.

Ages &, Heights 9816543210. I l l l l l I I l l . 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 H T = 23 50 70 84 93 100 104 108

9876543210. 9876543210. 1111111111,

50 2222222222. 67 6666666666. 20 7777777777. 200

H T = 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 . Computa- Lion 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, long- leaf pine, shortleaf pine, slash pine, computer program, plan- tation, dendrochronology.