United States 

Agriculture 

User's Guide for the Northern 

Forest Service Hardwood Stand Models: 

Northeastern Forest 

Experiment Station SIMSAP and SIMTIM/ 

Research Paper NE-606 Dale S. Solomon @ Richard A. Hosmer 
Abstract 

SIMSAP and SlMTlM are computer programs that have been developed to simulate the stand growth and development of natural and treated even-aged northern 

hardwood stands. SIMSAP begins with species distributions by quality classes in 

sapling stands after regeneration. SIMTIM, the poletimber-sawtimber-harvest 

phase, uses stocking guides based on quadratic mean stand diameter, number of 

trees, and basal area per acre of trees in the main crown canopy. Using available 

data, the connecting phases of the models have been tebted to determine the 

effects of silvicultural treatments (or no treatment) on long-term stand response. 

The models are coded in FORTRAN 77 and are available on mainframe and IBM 

compatible microcomputers with a minimum of 256 K. 

The Authors 

DALE S. SOLOMON joined the Northeastern Forest Experiment Station in 1962. 

He has been engaged in mensurational research on the growth and yield of 

northern species in the Northeast at the Station's laboratories at Durham, New 

Hampshire, and Orono, Maine. 

RICHARD A. HOSMER joined the Northeastern Station in 1980. He is employed 

as a computer programmer at the Station's laboratory at Orono, Maine. 

Manuscript received for publication 6 April 1987. 

Northeastern Forest Experiment Station 

370 Reed Rd., Broomall, PA 19008 

September 1987 
Introduction 

SIMSAP and SlMTlM form a forest stand growth model for 

even-aged northern hardwood stands (Solomon 1977a, 

Solomon and Leak 1986). The models can be applied to 

northern hardwood stands across New England to simulate 

growth beginning with a sapling stand (SIMSAP), continuing to a poletimber-sawtimber stand, and terminating at a 

user-specified quadratic mean stand diameter or stand age 

(SIMTIM). 

The major species from the northern hardwood stands 

across New England used to construct the models were: 

Yellow birch 

Sugar maple 

White ash 

Paper birch 

Red maple 

Beech 

Aspen 

Hemlock 

Red spruce 

Betula alleghaniensis Britton 

Acer saccharum Marsh. 

Fraxinus americana L. 

Betula papyrifera Marsh. 

Acer rubrum L. 

Fag us grandifolia Ehrh. 

Populus tremuloides M ichx. 

Tsuga canadensis (L.) Carr. 

Picea rubens Sarg. 

The programs that were used to construct the models have 

been modified to allow interactive input data to be stored 

,#or later use. The user is prompted for information after 

which the data are checked for reasonable values. Both 

models are written in FORTRAN 77 and have on-line 

instructions available. SIMSAP/SIMTIM utilize MS-DOS on 

IBM PCcompatible microcomputers~ with at least 256 K or 

on any mainframe (Solomon 1986). 

SIMSAP Components 

The development of the sapling stand has been described 

as a compound exponential process (Leak 1969a) that provides a basis for determining changes in numbers of stems 

by species group during the sapling stage. Available data on 

potential quality classes are used. After a weeding treatment 

is applied, the shape of the exponential curve will change, 

thus changing the rate of mortality. Also, a pruning treatment will change the quality distribution of the stems in the 

residual stand. 

The initial stand information needed is the site index and 

species composition. The site index is defined as height of 

sugar maple at base age 50, and species composition is 

expressed as a percentage of the basal area in the initial 

stand at 1 inch d.b.h. 

1 The use of trade, firm, or corporation names in this publication is for the information and convenience of the 

reader. Such use does not constitute an official endorsement or approval by the U.S. Department of Agriculture or 

the Forest Service of any product or service to the exclusion of others that may be suitable. 

The silvicultural treatments available are weeding and pruning operations. The pruning option, if specified, will prune 

all yellow birch and sugar maple crop trees less than veneer 

grade to one log length. If weeding is desired, the user must 

supply a beginning average stand diameter; upper and 

lower bounds of number of acceptable stems, within which 

limits weeding will not be canceled; number of crop trees to 

be released; average number of competitors to remove per 

crop tree; and the removal priorities of beech, yellow birch, 

sugar maple, red maple, paper birch, and white ash. 

The saplingstand phase of the model is a series of subroutines that can be categorized as: (1) determination of initial 

stem numbers and qualities, (2) computation of mortality 

patterns, (3) application of an optional weeding treatment, 

and (4) determination of diameter distribution and elimination of understory trees. 

Stem Numbers and Quality 

SIMSAP begins the sapling-stand phase by determining the 

number of stems in the stand at a quadratic mean stand 

diameter (QMD) of 1.0 inch, and proportions the stems by 

species with veneer-, sawlog-, and bulk-product potential. 

The subroutine SAPST draws an initial observation at 

random from a normal distribution that represents a stand 

with a 1.0-inch mean stand diameter and 4,922 trees per 

acre, with a standard deviation of 779 trees* (Leak 1969b, 

Marquis 1967). The species composition remains constant 

for this phase of the simulator. The range of percentage of 

trees in potential stem qualities by species has been estimated (Solomon 1974) (Table 1). The subroutine picks uniformly distributed random numbers within the indicated 

ranges and sets these equal to the proportions of veneer-, 

sawlog-, and bulk-quality stems. 

Table 1. - Ranges in the percentage of number of trees, by 

species, in various potential product classes 

Species Veneer Sawlog Bulk 

Beech 5 8 87 

Yellow birch 4-1 0 11-19 71-85 

Sugar maple 3-5 12-27 68-85 

Red maple 14 18 68 

Paper birch 7-38 25-28 34-68 

I 

I 

White ash 30 16 54 

I 

ZLeak, William B. 1967. Final report. Estimation of the 

exponential rate of tree dropout in young even-aged northern hardwoods. Durham, NH: USDA Forest Service, 

i 

Northeastern Forest Experiment Station. 10 p. 
Mortality 

The number of stems (x) in a sapling northern hardwood 

stand decreases as stand diameter increases according to a 

negative exponential probability distribution (Leak 1969a, b) 

that has the form: 

The negative exponential parameter "r," for commercial 

stems alone and for all species together, is estimated by 

subroutine RPAR. Subroutine DROP applies mortality 

losses from an initial diameter of 1.0 inch to either the 

diameter at which weeding is applied or to the 3.0-inch 

mean diameter that marks the end of the sapling stage. 

The average value of "r" for all species together is a constant 0.5685. For the commercial number of stems (CN) 

(average of 3,466 per acre), "r" can be estimated by 

(Solomon 1977a): 

r= { 0.4428 + 0.0255 (CN - 3466)/1768 for CN > 3466. 

0.4428 - 0.0682 (3466 - CN)/1768 for CN < 3466. 

If we have the initial number (N,), initial diameter (D,), and 

the final diameter (D2), the final number of stems of all 

species (N,) can be calculated in subroutine DROP from: 

Multiplying the number (N2) by the species and qualityclass proportions gives the number of trees per species and 

class. 

Silvicultural Treatments 

A user may apply the subroutine CLEAN at any specified 

mean stand diameter between 1.0 and 3.0 inches by specifying a high and low number of acceptable stems. Acceptable 

stems depend on the management and product objectives 

implemented by the forest manager. The management decision must be made for top-grade products such as millwood, sawlogs, or veneer logs. The product decisions 

would be based on a sufficient number of the desired tolerant, intermediate, or intolerant species to accomplish the 

management objective. A stand should have more than the 

minimum number of acceptable stems so that after silvicultural treatments the residual stand will be composed of the 

desired species to accomplish the management objectives. 

A stand with less than the minimum number of acceptable 

stems should be considered for regeneration. Beyond a 

maximum number of acceptable stems, sufficient quantities 

of the desired species exist and a weeding treatment is not 

required to accomplish the management objectives. The 

user may also specify the number of crop trees, species 

priorities, and number df competitors to be removed per 

crop tree. Crop trees are stems with grade 1 or 2 potential, 

and the number of trees to remove is computed by multiplying the number of crop trees times the number of trees to 

be removed around each crop tree. Also, pruning may be 

applied to the first log of all yellow birches and sugar 

maples with grade 2 potential, thereby increasing their 

potential to grade 1. 

The number of trees at the end of the sapling stage is estimated by using the exponential parameter "r" calculated by 

comparing the number of stems remaining after weeding 

with the average number in an undisturbed stand. According to the stocking guide, no mortality is expected if the 

number of stems is 400 or less (5-inch mean stand diameter). Therefore, the exponential to apply after weeding to 

project the final number of trees would be: 

r = 0.4428 (residual remaining - 400.O)/(XN - 400.0) 

with 

log,, XN = 4.016316 - 0.2273 (mean diameter) 

where XN is the average number of trees in an untouched 

stand for a given stand diameter. 

In projecting numbers of trees, no mortality losses are applied to crop trees. The negative exponential losses are applied only to those residual stems not classed as crop trees. 

Thus, the final result from subroutine CLEAN is numbers of 

stems by species and quality classes at a mean stand d.b.h. 

of 3.0 inches. 

Diameter Distribution 

In managing even-aged northern hardwoods beyond the 

sapling stage, silvicultural work is applied primarily to trees 

that make up the main crown canopy. Thus, the subroutine 

DlAMD assigns trees to diameter classes and eliminates the 

understory trees. This step results in a loss in number of 

stems, an increase in average stand diameter, and changes 

in species composition. 

On the basis of plot data from young northern hardwood 

stands about 3.0 inches mean stand diameter (Leak 1969a), 

the observed ranges in percentage of trees by diameter 

class have been grouped in Table 2. Subroutine DlAMD 

chooses a random observation within each range, and 

determines numbers of trees by diameter class and species. 

Then, the I-, 2-, or 3-inch (cumulative) class is dropped to 

reduce the stand to 760 trees per acre or less. This procedure brings the stand into the lower end of the northern 

hardwood stocking guide (Fig. 1) at an average diameter of 

approximately 5 inches. Beech or sugar maple designated 

as crop trees, and released by weeding, are not eliminated 

as understory. 
---- QUALITY LINE 

111l1111111~1~1'IIli 

100 200 300 400 500 600 700 800 900 1000 

TREES PER ACRE 

Figure 1 .-Stocking chart for northern hardwoods is based on trees in the main 

crown canopy. The A line is average maximum stocking. The B line is recommended minimum stocking for adequate growth response per acre. The C line 

defines the minimum amount of acceptable growing stock for a manageable 

stand. The quality line defines the stocking measure in young stands for maintaining quality stem development. 

Finally, the subroutine determines numbers of remaining 

trees by species and product class, as well as the final average diameter and basal area per acre. This information can 

Table 2. - Range in percentage of number of trees in each 

diameter class for stands with 2.5- to 3.0-inch average 

diameter, by species 

Diameter Yellow birch, 

class Beech and red maple, and Paper birch 

(inches) sugar maple white ash and others 

34-71 

20-34 

6-1 4 

1-10 

0-8 

0-3 

remainder" - 

0-54 

0-34 

3-27 

10-37 

0-34 

0-25 

0-20 

0-20 

remainder 

0-20 

0-30 

0-25 

0-25 

12-50 

0-50 

0-50 

0-1 4 

remainder 

a Remainder is the remaining percentage if the diameter 

classes do not add to 100 percent. 

serve as part of the input into the poletimber-sawtimberharvest phase of the simulator. 

Sapling MAlN Program 

The MAlN program estimates number of years required to 

reach the end of the sapling stage. These time estimates are 

based on site index and the application or nonapplication of 

weeding; computations are made by simple interpolation 

between the following site index values (Leak et al. 1969): 

Site Index Weeded (Years) Unweeded (Years) 

50 44 59 

60 38 50 

70 33 44 

80 29 40 

SIMSAP Application 

SIMSAP will prompt the user with a menu that can be used 

to determine the scope of each run. All of the input data will 

be stored on disk in a direct access file. The user is asked to 

provide the name of this file and whether it is an existing file 

or a new file. On subsequent runs the user can use this file 

to either duplicate an earlier run or make modifications to 

run the simulation under different conditions. The output 

for the run can be directed to either a disk file, a printer, or 

to the console. 
The user selects an option from the following menu: 

(1) HELP (6) WEEDING 

(2) NEW FILE (7) PRUNING 

(3) TITLE (8) RANDOM # 

(4) INITIAL STAND (9) # REPEAT RUNS 

(5) SITE INDEX (10) DISPLAY FILE 

<I 1> EXECUTE Option (5): 

All items enclosed in <> (option 11) are default values and Site Index 

will be in effect if a carriage return is entered. Entering a 

minus sign in response to any question will terminate the 

program. 

Option (1): 

Help 

Option (2): 

New File 

A summary of instructions for 

creating the input data file is 

printed on the console. After 

every 15 to 20 lines, the program 

waits for a carriage return before 

continuing. 

A new input file is to be created 

from the information contained in 

options 3 thru 9. If a file of this 

name already exists, the user will 

be given the choice of renaming 

the file, returning to the menu, or 

continuing, which will cause the 

existing file to be erased. 

When the user has specified a new input data file, only 

options 1 and 2 are available. After the file is created or if 

the file has been designated as an existing file, options 3 

thru 9 will allow modifications to that file without having to 

re-create the whole file. 

Option (3): 

Title A title of up to 80 characters will 

appear at the top of each page of 

output. 

Option (4): 

Initial Stand The user enters the percentage of 

the basal area of each species in 

the stand at 1-inch quadratic 

mean stand diameter. The species groups are: beech (BE), 

Option (6): 

Weeding 

DBH 

Max # acceptable 

stems 

Min # acceptable 

stems 

# crop trees 

# competitors 

Priority 

yellow birch (YB), sugar maple 

(SM), red maple (RM), paper 

birch (PB), white ash (WA), pin 

cherry (PC), striped maple 

(STMAP), aspen (ASP), other 

(OTH), and red maple sprouts 

(RMSP). If the percentages do 

not add to 100, the user is asked 

to reenter the percentages. 

The site index for the stand is 

based on sugar maple at base 

age 50 and must range between 

40 and 80. 

The quadratic mean stand diameter at which to start weeding 

must be between 1 .O and 3.0 

inches. 

No weeding will be applied if the 

number of acceptable stems is 

greater than this number when 

the stand reaches the weeding 

d.b.h. 

No weeding will occur if the 

number of acceptable stems is 

less than this number when the 

stand reaches the weeding d.b.h. 

The number of crop trees per 

acre to be released. 

The average number of competitors removed per crop tree to 

ensure survival of the crop tree. 

Removal priority for each species: beech, yellow birch, sugar 

maple, red maple, paper birch, 

and white ash. Priorities range 

from 1 (first) to 6 (last) and 

numbers may not be repeated. A 

zero may be used for species 

without crop trees. 
Option (7): 

Pruning (1) The released yellow birch and 

sugar maple trees less than 

veneer quality are pruned to one 

log during weeding to increase 

quality. 

(2) No pruning will be done. 

Option (8): 

Random # The random number generator in 

the model requires an odd, ninedigit number to begin. 

Option (9): 

# Repeat Runs Because of the randomness 

within the model, the stand can 

be run through several simulations and each will be slightly different. The user can use these 

results to obtain an average stand 

value. 

Option (10): 

Display File A summary of the input data will 

be displayed on the console. 

Option <11>: 

Execute The input data are then used to 

start the simulation. 

An example of creating the input data file and the subsequent simulation is shown in Table 3. The entries in italics 

are made by the user. All input is free format, that is, data 

need only be separated by one or more blanks or a comma. 

There is no need to align the entry under a column heading 

other than for the user's own convenience. At the completion of the model run, the user is asked if another simulation 

is desired with this stand. If the answer is yes (Y), the program returns to the menu. If the answer is no <N>, the user 

is asked if a simulation with a new input data file is desired. 

A Y response will return the user to entering a file name for 

the input file and a designation for the output. An N 

response will terminate the program. 

SIMSAP Output 

able range. After a weeding, the diameter at which it 

occurred is given, along with the number of crop trees by 

species, number of trees cut, and the number of remaining 

trees. 

At the end of the sapling phase, the smaller diameter 

classes that were dropped from the understory are noted 

and the final stand characteristics: number of trees, basal 

area per acre, QMD, and number of years to reach the end 

of the sapling phase are presented. For commercial species, 

the number of trees and percentage of composition are 

given by three quality classes which may be considered as 

veneer, sawlog, and bulk product. The number of trees and 

percentage of composition of the noncommercial species 

are printed without quality classes. 

SlMTlM Components 

The poletimber-sawtimber-harvest phase of the simulator 

(SIMTIM) grows the stand from the end of the sapling 

phase, approximately 4.5 inches QMD, to harvest diameter 

or rotation age. The program covers three main steps: (1) 

stand growth projection, (2) thinning and harvesting 

options, and (3) paper birch-aspen mortality. 

The overall framework of the model is a distanceindependent stand model. Input consists of site index, specifications on the thinning regime, and stand characteristics 

of age, basal area, QMD, and percentage of basal area by 

species and quality. The model projects these stand characteristics by positioning the stand within the northern hardwood stocking chart (Fig. 1) and relating stand development 

to stocking (Solomon and Leak 1986). The lines in Figure 1 

are developed from trees within the main crown canopy of 

northern hardwood stands. The main crown canopy is 

defined as all trees on the plot that are not overtopped or 

suppressed. 

The user is required to input the following information: 

Forest stand name; 

Site index between 40 and 80 for sugar maple at base 

age 50; 

Average number of trees per acre, usually between 25 

and 1,500 trees; 

Basal area per acre to the nearest tenth of a square 

foot between 20 and 130 square feet; 

Quadratic mean stand diameter to the nearest tenth of 

an inch between 4 and 16 inches; 

Species composition list; 

Stand acle - in vears: - 

The output of SIMSAP (Table 3) starts with a copy of the Final harvest age in years, and final quadratic mean 

input data. The model indicates the number of yellow birch diameter to the nearest tenth of an inch; 

and sugar maple trees to be pruned. An appropriate mes- a Specified intervals in years for report to be presented; 

sage is printed when weeding was not conducted or when Any odd nine-digit number for the mortality function. 

the number of acceptable stems was not within the allow- 
The species composition list is entered by quality classes of 

I, II, and Ill, in the following order: beech, yellow birch, 

sugar maple, red maple, paper birch, aspen, white ash, conifer, and other. There is one quality class of eight values per 

line expressed to the nearest tenth of a percent (Table 4). 

Stand Growth 

Stand growth provides the forest manager with an estimate 

of the growth of northern hardwood stands. The growth rate 

of different species may increase or decrease depending 

upon the age and density of the stand. Thus, stand growth, 

as computed from accretion, ingrowth, and mortality, is 

proportioned into species growth rate based on the residual 

basal area of the stand and stand age. Changing species 

composition does not change stand growth, but changes 

the amount of growth allotted to individual species which 

then reproportions the species composition. 

The changes in growth rates for stands growing on different 

sites are modeled as a proportion of the site index of the 

stand to site index 60 for northern hardwoods. The stand 

basal area is adjusted by that ratio since the stand growth 

within the model is based upon northern hardwood stands 

growing on a site index 60 for sugar maple base age 50. 

The amount of stocking, represented by the basal area, 

number of trees, and quadratic mean stand diameter, can be 

followed through time with the stocking chart (Fig. 1). The 

growth simulation within the model computes the number 

of trees per acre at both the A and B line. The A line represents a fully stocked stand without any form of management. The B line is based on optimum stand growth from 

different studies of northern hardwood growth. The number 

of trees at both the A and B line can be represented as a 

function of the natural logarithmic value of the quadratic 

mean stand diameter: 

A line number of trees = e (9.491 - 1.786 * In QMD) 

B line number of trees = e (9.082 - 1.887 * In QMD) 

where 

QMD = the diameter at breast height of the tree of 

average basal area. 

The C line represents a managed stand with a minimum 

level of acceptable growing stock (sawlog potential) that 

will grow to the B line in 10 years. The quality line maintains 

a higher level of basal area stocking for smaller quadratic 

mean diameters. Thinning a stand to the quality line when 

less than 6 inches in diameter provides clear bole form on 

younger, smaller high-quality species (Leak et al. 1987). 

The stand growth components of accretion and ingrowth 

(ftZ/acre/year) can be expressed as: 

Accretion = 2.153 + 0.005 (In BA) - 0.0076 (SAW) 

lngrowth = 3.200 - 0.643 (In BA) - 0.0012 (SAW) 

where 

B A = residual basal area in square feet, 

SAW = percentage of stand in sawtimber-size 

trees, 

Accretion = d.b.h. increment in basal area of trees 

present at the initial inventory, plus 

ingrowth accretion, 

lngrowth = trees that grew larger than threshold size 

(5.0 inches) between inventories. 

The R2 values were 0.73 and 0.97; the standard errors of the 

mean were 0.0187 and 0.0138, respectively. These growth 

equations are based on information from managed stands 

of northern hardwoods (Marquis 1969; Solomon 1977b, c). 

The residual basal areas ranged from 20 to 100 square feet 

per acre for these stands that were 20 to 80 years old. The 

percentage of sawtimber ranged from zero to 60. Stand 

mortality increases as the basal area and mean stand 

diameter increase and the stand grows from the B to the A 

line. The estimate of actual stand mortality is based on the 

assumption that mortality at minimum stocking (B line) is 

zero, and that mortality of a stand above the B line is in 

some way proportional to its position between the A and B 

line. 

Stand mortality = 

where 

BA = basal area of stand, 

BAB = basal area at B line for the present QMD, 

BAA = basal area at A line for the present QMD, 

GG = gross growth, 

BAGA = annual net basal area growth at A line for the 

present QMD, 

MF = mortality factor, 

X = a random exponent between 1 and 1.5. 

When X = 1, mortality is computed in direct proportion to 

the position of the stand between the A and B line. When X 

is greater than 1, the mortality rate increases as the A line is 

approached and passed. The mortality factor (MF) ranged 

from -2.5 for stands with basal area of -60 square feet per 

acre or less up to 2.0 for stands with 100 square feet per 

acre or more. 

Thinning and Harvesting Options 

The user can specify the order of removing the eight species categories from the three quality classes. The numbers 

from 1 to 24 in the 3 x 8 matrix can be arranged to indicate 

removal priority. A number can be given that specifies the 
location in the removal order for the user to switch from 

complete species-quality class removal to proportional 

removal of remaining species quality classes. This can be 

used to maintain species composition as well as quality 

within species. 

Thinning is regulated by basal area in the stocking chart 

(Fig. 2). The user options include no thinning, thin when the 

stand reaches the A line, or when the stand reaches a userspecified basal area above the B line. The user must specify 

the quadratic mean diameter to the nearest tenth of an inch 

for the first thinning to begin. The thinning is to the B line 

except when it may be regulated by the quality line up to a 

6-inch quadratic mean stand diameter. When thinning is 

controlled by the quality line, the stand is thinned to 80 

square feet for stands with quadratic mean diameters less 

than or equal to 6 inches, and then is thinned to the B line 

for stands with quadratic mean diameters greater than 6 

inches. The final harvest, specified by the user, may be 

based on time (number of years) or occur at the predetermined quadratic mean stand diameter. 

Paper Birch - Aspen Mortality 

When the stand reaches 80 years of age, simulated mortality 

of any remaining paper birch and aspen is accelerated by 

subroutine PBMORT to represent the short life span of 

these two species. Five percent of the initial amount of each 

species is removed per year, resulting in complete removal 

of both species between 80 and 100 years of age (Solomon 

and Leak 1969). Mortality losses are applied proportionally 

across all quality classes. The user has the opportunity to 

circumvent this accelerated mortality by specifying that 

paper birch and aspen be removed first in thinnings after 

age 70. Percentages of the remaining species are adjusted 

so that they continue to sum to 100 percent. 

SlMTlM Application 

SlMTlM is designed similar to SIMSAP in that it too uses a 

direct access file to store the input data and uses a menu to 

create or modify this input file. The user must provide a 

name for the input file, and specify whether it is a new or an 

already existing file. The user must specify where output is 

to go: the console, the printer, or a disk file. The menu for 

SlMTlM is presented to the user: 

(1) HELP (6) INITIAL COMPOSITION 

(2) NEW FILE (7) THINNING 

(3) TITLE (8) ROTATION 

(4) SITE INDEX (9) RANDOM # 

(5) INITIAL STAND (10) DISPLAY FILE 

<I I> EXECUTE 

TREES PER ACRE 

Figure 2.-Comparison of growth response for unthinned stands, stands thinned 

to the quality line starting at 5.0 inches quadratic mean stand diameter, and 

thinned to the B line starting at 9.0 inches quadratic mean stand diameter. 
Option (1): 

Help 

Option (2): 

New file 

Option (3): 

Title 

Option (4): 

Site index 

Option (5): 

Initial stand 

Trees per acre 

Basal area 

Mean stand 

diameter 

Option (6): 

Initial composition 

A summary of instructions will be 

printed on the console. The program will wait after every 15 to 20 

lines for a carriage return to be 

entered before continuing. 

If a file of the above specified Option (7): 

name already exists, the user will 

be given the choice of renaming Thinning 

and creating a new file, returning 

to the menu, or continuing, which Type 

will cause the existing file to be 

erased. When the input data file 

has been designated as being 

new, the user can only select 

options 1 or 2. Options 3 through 

9 allow modifications to this input 

file after it has been created. 

When 

A title of up to 80 characters that 

will appear on the top of all pages 

of output. 

The site index for the stand 

based on sugar maple at age 50 

(40 to 80). 

The average number of trees per 

acre in the initial stand (25 to 

1,500). 

The initial basal area in square 

feet per acre (20 to 130). 

The quadratic mean stand diameter to the nearest tenth of an inch 

(4.0 to 16.0). 

The initial species composition of 

the stand by eight species groups 

and three quality classes. The 

species groups are: beech (BE), 

yellow birch (YB), sugar maple 

(SM), red maple (RM), paper 

birch-aspen (PBA), white ash 

(WA), conifer (CON), and other 

(OTH). The three quality classes 

are to be defined by the user. The 

total composition for the 24 

entries must equal 100 percent. 

(0) - no thinning will be done. 

(1) - thin when the stand reaches 

the A line of the stocking chart 

(Fig. 1). 

<2> - thin at a user specified 

level above the B line. This value 

must be between 5 and 40 square 

feet. 

The user-specified quadratic 

mean stand diameter must be 

reached before the first thinning 

will occur. After the first thinning, 

control will be according to the 

option selected above. 

Residual level <1> - thin to the B line. 

(2) - for stands with a quadratic 

mean stand diameter less than 

6.0 inches the stand will be 

thinned to a quality line (Fig. 1) at 

80 square feet. For stands over 

6.0 inches, the residual level will 

be given by the B line. 

Order of removal The eight species and three quality classes are numbered from 1 

to 24 in the following manner: 

Species 

Quality BE YB SM RM PBA WA CON OTH 

class 

1 12345678 

2 9 10 11 12 13 14 15 16 

3 17 18 19 20 21 22 23 24 

The user is asked to list these 

numbers in the order that they 

want the species-quality classes 

removed. The default order is: 24, 

20, 17, 23, 18, 19, 21, 22, 16, 12, 9, 
Thin split 

Paper birch 

15,13,14,10,11,8,4,1,7,5,6,2, 

3. All numbers should be entered 

or the remaining default order 

will be used. 

A number from 1 to 24 is specified that represents a position 

within the removal order (that is, 

thin split = 12, refers to species 

quality group 15 above, the 12th 

entry in the priority list). All 

species-quality groups prior to 

this entry will be removed entirely 

until the residual level is 

obtained, while for the groups 

after this entry, only an amount 

proportional to the amount of the 

species group in the stand will be 

removed. 

Paper birch and aspen mortality 

is increased between years 80 

and 100 until all of both species 

are removed. There is an option 

which will allow the user to salvage this mortality if desired. 

(0) - For any thinning after the 

stand is 70 years old, the 

model will automatically give 

highest priority of removal to 

paper birch and aspen for 

salvage. 

<I> - The priorities remain as 

entered, thereby maintaining 

the user-specified order of 

removal. 

Option (8): 

Rotation 

Rotation age The age at which the final harvest 

is to occur. 

Harvest diameter The quadratic mean stand diameter of final harvest. The final 

harvest will be at rotation age or 

harvest diameter, whichever 

occurs first. 

Option (9): 

Random number 

Option (10): 

Display file 

Option <1 I>: 

Execute 

includes the basal area, number 

of trees per acre, and quadratic 

mean stand diameter. 

The random number generator 

within the model requires a ninedigit odd integer to begin. 

A summary of the input data will 

be displayed on the console. 

Simulation begins using the criteria contained in the input data 

file. 

An example of creating the input data file and the subsequent simulation is shown in Table 4. As with SIMSAP, all 

data may be entered free-format and are shown in italics in 

the table. At the end of the simulation the user is asked if 

the yields are to be displayed. A yes (Y) response will cause 

the standing yield, sum of thinning yields, and total yield to 

be printed on the console and simultaneously go to the 

primary output device. The program waits for a carriage 

return between tables. Next, the user is asked if they wish to 

run another simulation with this stand. If the answer is Y, the 

program returns to the menu. If the answer is no <N>, the 

user is asked if a simulation with a new input data file is 

desired. A Y response will return the user to entering a file 

name for the input file and a designation for the output. An 

N response will cause termination of the program. 

SlMTlM Output 

The output of SlMTlM (Table 4) is made up of a copy of the 

input data, intermediate reports of stand characteristics, 

intermediate thinning reports, and a final harvest report. At 

user-specified intervals, reports of the stand age; quadratic 

mean stand diameter; number of trees in the stand, at the A 

and B line; basal area of the stand, at the A and B line; and 

the percent sawtimber are all printed. 

When a thinning occurs, the age of the stand and the stand 

characteristics are given. Also presented are the number of 

trees thinned, the basal area removed, and a yield table by 

species and quality class showing the percent removed, 

square feet of basal area, cubic-foot volume and board-foot 

volume. 

Report interval A summary of the stand characteristics will be sent to the userspecified output. This summary 
At the final harvest, a summary of the stand conditions is 

printed along with the standing yield, the total yield from all 

thinnings, and the sum of the standing yield plus all thinning~. These yields are presented by species and quality 

class in units of square feet of basal area, cubic-foot 

volume, and board-foot volume. 

Square feet of basal area is converted to both cubic feet and 

board feet based on the quadratic mean stand diameter and 

site index (Leak 1980). Thus, the yields by species are 

based on the percentage of a species in the total basal area. 

The cubic feet per square foot of basal area give the total 

cubic feet; similarly, the board feet per square foot give the 

board feet. Then the board feet divided by the board feet/ 

cubic feet ratio gives the amount of cubic feet in the sawtimber yields. By subtracting this amount from the total 

yield, we can estimate the amount of cubic feet in pulp, cull, 

or extra sawtimber. 

The computer programs described in this publication are 

available on request with the understanding that the US. 

Department of Agriculture dnnot assure their accuracy, 

completeness, reliability, or suitability for any other purpose 

than that reported. The recipient may not assert any proprietary rights thereto nor represent it to anyone as other 

than a Government-produced computer program. For 

information, please write: Dr. Dale S. Solomon, USDA Building, University of Maine, Orono, ME, 04473. 

LITERATURE CITED 

Leak, William B. 1969a. Sapling stand development: a compound exponential process. Forest Science. 16: 177-1 80. 

Leak, William B. 1969b. Stocking of northern hardwood 

regeneration based on exponential dropout rate. Forestry 

Chronicle. 45 (5): 344-347. 

Leak, William B. 1980. Rapid economic analysis of northern 

hardwood stand improvement options. Res. Pap. NE-296. 

Broomall, PA: U.S. Department of Agriculture, Forest 

Service, Northeastern Forest Experiment Station. 6 p. 

Leak, William B.; Solomon, Dale S.; DeBald, Paul S. 

1987.Silvicultural guide for northern hardwood types in 

the Northeast (revised). Res. Pap. NE- RP-603, Broomall, 

PA: U.S. Department of Agriculture, Forest Service, Northeastern Forest Experiment Station. 36 p. 

Leak, William B.; Solomon, Dale S.; Filip, Stanley M. 1969. A 

silvicultural guide for northern hardwoods in the Northeast. Res. pap. NE-143. Upper Darby, PA: U.S. Department of Agriculture, Forest Service, Northeastern Forest 

Marquis, David A. 1967. Clearcutting in northern hardwoods: results after 30 years. Res. Pap. NE-85. Upper 

Darby, PA: US. Department of Agriculture, Forest Service, Northeastern Forest Experiment Station. 13 p. 

Marquis, David A. 1969. Thinning in young northern hardwoods: 5-year results. Res. Pap. NE-139. Upper Darby, 

PA: US. Department of Agriculture, Forest Service, Northeastern Forest Experiment Statih. 22 p. 

Solomon, Dale S. 1974. Simulation of the development of 

natural and silviculturaUy treated stands of even-aged 

northern hardwoods. In: Proceedings of International 

Union of Forestry Research Organizations. S4.01-04. 

Growth models for tree and stand simulation. Stockholm, 

Sweden: Sweden Royal College of Forestry. Res. Note 

30. 

Solomon, Dale S. 1977a. A growth model of natural and silviculturally treated stands of even-aged northern hardwoods. Gen. Tech. Rep. NE-36. Broomall, PA: U.S. 

Department of Agriculture, Forest Service, Northeastern 

Forest Experiment Station. 30 p. 

Solomon, Dale S. 1977b. The influence of stand density and 

structure on growth of northern hardwoods in New England. Res. Pap. NE-362. Broomall, PA: U.S. Department 

of Agriculture, Forest Service, Northeastern Forest Experiment Station. 13 p. 

Solomon, Dale S. 1977c. Growth rates of northern hardwoods under uneven-age management. Northern 

Logger. 25(8): 18, 38. 

Solomon, Dale S. 1986. A forest growth simulator for evenaged northern hardwoods. In: Proceedings, forestry 

microcomputer software symposium; 1986 June 30-July 

2; Morgantown, WV. Morgantown, WV: West Virginia 

University. p. 97-1 16. 

Solomon, Dale S.; Leak, William B. 1969. Stocking, growth, 

and yield of birch stands. In: Proceedings of the birch 

symposium; 1969 August 19-21; Durham, NH. Upper 

Darby, PA: US. Department of Agriculture, Forest Service, Northeastern Forest Experiment Station. p. 106-118. 

Solomon, Dale S.; Leak, William B. 1986. Simulated yields 

for managed northern hardwood stands. Res. Pap. NE578. Broomall, PA: U.S. Department of Agriculture, 

Forest Service, Northeastern Forest Experiment Station. 

24 p. 

~x~erimeit Station. 34 p. 
Table 3. - Sample run for SIMSAP, Version 2.0. Items in 

italics are entered by the user 

SlMSA P 

Please enter input file name: 

SARCTL 

Is input file <I> old or (2) new? 

2 

(1) HELP (7) PRUNING 

(2) NEW FILE (8) RANDOM # 

(3) TITLE (9) # REPEAT RUNS 

(4) INITIAL STAND (10) DISPLAY FILE 

(5) SITE INDEX (1 1 ) OUTPUT 

(6) WEEDING <I 2> EXECUTE 

2 

Enter title: 

SAMPLE RUN OF SIMSAP 

Enter percent composition of initial stand: 

BE YB SM RM PB WA PC STMAP ASP OTH RMSP 

8 12 16 5 16 2 18 2 3 8 10 

Site index: 

60 

Is weeding desired? 

Y 

Enter the diameter at which to begin weeding (1.0 to 3.0): 

2.5 

Maximum number of acceptable stems: 

3500 

Minimum number of acceptable stems: 

400 

Number of crop trees released per acre: 

400 

Average number of competitors removed per crop tree: 

2 

Priority of removal from 1 to 6 (zero for not a crop tree): 

BE YB SM RM PB WA 

056123 

(1) No pruning 

<2> Prune YB and SM 

<cr> 

Random number: 

98765432 1 

# of repeat runs: 

1 

(1) HELP (7) PRUNING 

(2) NEW FILE (8) RANDOM # 

(3) TITLE (9) # REPEAT RUNS 

(4) INITIAL STAND (10) DISPLAY FlLE 

(5) SITE INDEX (1 1) OUTPUT 

(6) WEEDING <12> EXECUTE 

Species comp: 

BE YB SM RM PB WA PC STMAP ASP OTH RMSP 

.08 .12 .I6 .05 .16 .02 .18 .02 .03 .08 .I0 

Site index = 60.0 

Weeding desired at d.6.h. 2.5 

Acceptable stems Crop trees Competitors 

min max released removed 

400. 3500. 400. 2. 

Priority: BE YB SM RM PB WA 

0. 5. 6. 1. 2. 3. 

YB and SM will be pruned 

Random number: 987654321 

# of repeat runs: 1 

SAMPLE RUN OF SIMSAP 

Number of yellow birch pruned = 47.4 

Number of sugar maple pruned = 19.4 

Weeding was applied at 2.5 d.b.h. 

Crop trees of BE YB SM RM PB WA ALL 

.O 75.4 41.0 45.9 185.0 26.4 373.6 

Number cut in weeding = 747.3 Number left = 1541.9 

2-INCH CLASS DROPPED 

***** 

END OF SAPLING STAGE: 

# TREES BASAL AREA AVG DBH YEARS 

769.1 85.8 4.5 38.0 

NUMBER AND PERCENT OF TREES 

COMMERCIAL SPEC1 ES 

POTENTIAL BE YB SM RM PB WA 

QUALITY 1 # 0.7 26.5 41.0 7.0 48.9 6.0 

(VENEER) O/o 0.1 3.4 5.3 0.9 6.4 0.8 

QUALITY 2 # 1.2 0.0 5.8 9.1 93.6 3.2 

(SAWLOG) % 0.2 0.0 0.8 1.2 12.2 0.4 

QUALITY 3 # 13.0 57.2 21.3 20.7 127.8 6.6 

(BULK) % 1.7 7.4 2.8 2.7 16.6 0.9 

NON-COMMERCIAL SPECIES 

RMSP ASP OTH STMAP PC 

# 133.9 33.6 89.5 22.4 0.0 

% 17.4 4.4 11.6 2.9 0.0 

Do you want another run with this data file? 

N 

Do you want to use another data file? 

<cr> 

Stop - Program terminated. 

11 

INPUT DATA 

SAMPLE RUN OF SIMSAP 
Table 4. - Sample run of SlMTlM Version 2.0 showing the 

first of 6 thinnings. Items in italics are entered by 

the user 

SlMTlM 

Please enter input file name: 

TIM. CTL 

Is input file <1> old or (2) new? 

2 

(1) HELP (7) THINNING 

(2) NEW FILE (8) ROTATION 

(3) TITLE (9) RANDOM # 

(4) SITE INDEX (10) DISPLAY FILE 

(5) INITIAL STAND (1 1) OUTPUT 

(6) INITIAL COMPOSITION <12>EXECUTE 

2 

Enter title: 

SAMPLE RUN OF SlMTlM 

Site index: 

60 

Average number of treedacre: 

1050 

Enter the basal area: 

91.0 

Mean stand diameter: 

4.0 

Age of stand: 

30 

Species composition and quality class 

BE YB SM RM PBA WA CON OTH 

Class 1 723221 5 100 

Class 2 41111031 00 

Class 3 14401001 

(0) - No thinning 

(1) -Thin when stand reaches A line 

<2> - Thin at user-specified level above B line (in ft*) 

<cr> 

Please enter the amount of square feet above the B line to 

start thinning: 

30 

Do you wish to: 

<1> thin to the B line for all diameters or 

(2) thin to 80 ft* up to stand diameter 6 and then to the B 

line? 

2 

Species composition and quality class 

BE YB SM RM PBA WA CON OTH 

1 % 7.0 23.0 22.0 1.0 5.0 1.0 0.0 0.0 

(1) (2) (3) (4) (5) (6) (7) (8) 

2 O/o 4.0 11.0 11.0 0.0 3.0 1.0 0.0 0.0 

(9) (10) (11) (12) (13) (14) (15) (16) 

Current species removal order: 

<242017231819212216129151314101184175623> 

Choose current species removal order: 

<cr> 

Please enter the thinning split number. Species that occur 

after this number in the species removal array will be 

thinned according to their proportion of the stand composition. 24 MEANS NO PROPORTIONAL THINNING WILL 

OCCUR. 

<24> 

17 

Paper Birch removal: 

(0) - paper birch and aspen are removed first in thinning 

after age 70 

<1> - operator specified removal order 

0 

Beginning thinning diameter: 

5.0 

Rotation age: 

200 

Harvest diameter of the stand: 

18.0 

Report interval in years: 

<1> 

200 

Random number: 

987654321 

(1) HELP (7) THINNING 

(2) NEW FILE (8) ROTATION 

(3) TITLE (9) RANDOM # 

(4) SITE INDEX (10) DISPLAY FILE 

(5) INITIAL STAND (1 1) OUTPUT 

(6) INITIAL COMPOSITION <12> EXECUTE 

<cr> 

INPUT DATA 

TEST OF SlMTlM 

Site index = 60.0 

Number of treedacre = 1050.0 

Basal aredacre = 91.0 

Quadratic mean diameter = 4.0 

Age of stand = 30.0 

QUALITY SPECIES 

CLASS BE YB SM RM PBA WA CON OTH TOTAL 

1 O/o 7.0 23.0 22.0 1.0 5.0 1.0 0.0 0.0 59.0 

FT2 6.4 20.9 20.0 0.9 4.6 0.9 0.0 0.0 53.7 

2 % 4.0 11.0 11.0 0.0 3.0 1.0 0.0 0.0 30.0 

FI-2 3.6 10.0 10.0 0.0 2.7 0.9 0.0 0.0 27.3 

3 % 1.0 4.0 4.0 0.0 1.0 0.0 0.0 1.0 11.0 

FT2 0.9 3.6 3.6 0.0 0.9 0.0 0.0 0.9 10.0 
Thin when stand reaches 30 ft2 above the B line and mean 

stand diameter is at least 5.0 inches. 

Quality-line thinning (thin to 80 ft2) will be used up to 

diameter 6 inches. 

Order of species class removal by priority: 

24 20 17 23 18 19 21 22 16 12 9 15 

13141011 8 4 17 5 62 3 

Thinning split number: 17 

Model starts to remove paper birch and aspen first in thinnings after age 70 

Rotation age: 200. 

Harvest diameter: 18.0 

Report interval: 200 

Random number: 987654321 

TEST OF SlMTlM 

Thinning #I 

Stand at 45 years 

Stand A line B line 

Diameter 5.5 

# trees 635.5 635.5 355.6 

Sq. ft. 104.0 103.9 58.1 

Percent sawtimber = 0. 

Thinning yields 

Number of trees thinned = 147.2 

BA thinned = 24.1 

QUALITY SPECIES 

CLASS BE YB SM RM PBA WA CON OTH TOTAL 

1 O/o 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 

FT2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 

Fr3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 

BF 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 

TEST OF SlMTlM 

STAND AT HARVEST 

Site index = 60.0 

Number of treeslacre = 49.2 

Basal area = 87.8 

Quadratic mean diameter = 18.0 

Age of stand = 122. 

Thinning began at diameter 5.0 

HARVEST YIELD 

QUALITY SPECIES 

CLASS BE YB SM RM PBA WA CON OTH TOTAL 

1 15.2 37.6 40.8 3.3 0.0 3.2 0.0 0.0 100.0 

FT2 13.3 33.0 35.8 2.9 0.0 2.8 0.0 0.0 87.8 

1FT3 357.3 883.9 959.9 77.1 0.0 75.4 0.0 0.0 2353.6 

BF 1501.9 3715.0 4034.4 324.0 0.0 316.8 0.0 0.0 9892.1 

TOTAL YIELD FROM THlNNlNGS 

QUALITY SPECIES 

CLASS BE YB SM RM PBA WA CON OTH TOTAL 

FT2 15.0 40.4 41.6 3.3 17.3 3.2 OD 0.0 120.8 

lFT3 340.6 900.0 937.4 74.8342.9 73.1 0.0 0.0 2668.9 

BF 1125.7 2883.8 3066.1 246.7 852.8 241.0 0.0 0.0 8416.0 

TOTAL YIELD 

QUALITY SPECIES 

CLASS BE YB SM RM PBA WA CON OTH TOTAL 

FT2 28.3 73.3 77.4 6.2 17.3 6.0 0.0 0.0 208.6 

1 FT3 698.0 1783.9 1897.3 151.9 342.9 148.5 0.0 0.0 5022.5 

BF 2627.6 6598.7 7100.5 570.6 852.8 557.8 0.0 0.0 18308.0 

THE TOTAL HARVEST PER ACRE (INCLUDING THINNINGS) IS: 

BASAL AREA: 253.4 

CUBIC FEET: 5677.9 

BOARD FEET: 18308.0 
Solomon, Dale S.; Hosmer, Richard A. 1987. User's guide for the northern 

hardwood stand models: SIMSAP and SIMTIM. Res. Pap. NE-606. 

Broomall, PA: U.S. Department of Agriculture, Forest Service, Northeastern Forest Experiment Station. 13 p. 

SIMSAP and SlMTlM are computer programs that have been developed to 

simulate the stand growth and development of natural and treated evenaged northern hardwood stands. SIMSAP begins with species distributions 

by quality classes in sapling stands after regeneration. SIMTIM, the 

poletimber-sawtimber-harvest phase, uses stocking guides based on quadratic mean stand diameter, number of trees, and basal area per acre of trees 

in the main crown canopy. Using available data, the connecting phases of 

the models have been tested to determine the effects of silvicultural treatments (or no treatment) on long-term stand response. The models are 

coded in FORTRAN 77 and are available on mainframe and IBM compatible 

microcomputers with a minimum of 256 K. 

ODC. 181.65, 228.5, 228.82 

Keywords: Growth model, Northern hardwoods, even-aged 

*U. S. GOVERNMENT PRINTING OFFICE: 198'7/748-076/60001 
Headquarters of the Northeastern Forest Experiment Station are in Broomall, Pa. 

Field laboratories are maintained at: 

Amherst, Massachusetts, in cooperation with the University of Massachusetts. 

Berea, Kentucky, in cooperation with Berea College. 

Burlington, Vermont, in cooperation with the University of Vermont. 

Delaware, Ohio. 

Durham, New Hampshire, in cooperation with the University of New Hampshire. 

Hamden, Connecticut, in cooperation with Yale University. 

Morgantown, West Virginia, in cooperation with West Virginia University, 

Morgantown. 

Orono, Maine, in cooperation with the University of Maine, Orono. 

Parsons, West Virginia. 

Princeton, West Virginia. 

Syracuse, New York, in cooperation with the State University of New York 

College of Environmental Sciences and Forestry at Syracuse University, 

Syracuse. 

University Park, Pennsylvania, in cooperation with the Pennsylvania State 

University. 

Warren, Pennsylvania. 

Persons of any race, color, national origin, sex, age, religion, or with any handicapping condition are welcome to use and enjoy all facilities, programs, and services 

of the USDA. Discrimination in any form is strictly against agency policy, and 

should be reported to the Secretary of Agriculture, Washington, DC 20250.