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United States
Department of
.
Agnculture
Forest Service
Pacific Northwest
Forest and Range
Experiment Station
General Technical
Report
PNW-128
May 1981
DOUGLAS AL
AN fv\AGUI
RE
A New Stand
Simulator for Coast
Douglas-fir: DFSIM
User's Guide
Robert 0. Curtis, Gary W. Clendenen, and Donald J DeMars
..
This file was created by scanning the printed publication.
corrected; however, some mistakes may remain.
Misscans identified by the software have been
Authors
ROBERT 0. CURTIS and GARY W. CLENDENEN are
mensurationists at the Forestry Sciences Laboratory,
Pacific Northwest Forest and Range Experiment Station,
3625 93rd Ave. S.W., Olympia, Washington 98502.
DONALD J. DEMARS is forester at the Pacific Northwest
Forest and Range Experiment Station, 809 N.E. 6th Ave.,·
Portland, Oregon 97232.
DOUGLAS ALAN MA
GUIRE Abstract
C u rtis, Robert 0., Gary W. Clendenen, and Donald J. DeMars.
1 98 1 . A n ew stand s i m u l ator for coast Douglas-fi r: D FSIM user's guide. USDA
For. Serv. Gen. Tech. Rep. PNW-1 28, 79 p. Pacific Northwest Forest and
Range Experiment Station, Portland, Oregon.
DFSIM (Doug las-fi r S i m u l ator) is a new managed stand si mulation p rogram for
'
coast Doug las-fi r (Pseudotsuga menziesii ( M i rb.) Franco var. menziesii). It was
developed from remeasured p l ot data contributed by many organ izations in the
Pacific N orthwest. D FSIM i s based o n more extensive data and i s considerably
more flexible than previous whole-stand s i m u l ators for the species. It produces
yield tables for managed stands w h i ch i nclude estimates of effects of i n itial
spacing, precommercial and com mercial t h i n n i ng, and n itrogen ferti l i zation.
Top i cs d i scussed i nclude basic data, simulator construction and operation,
l i m itati ons of the prog ram , and potential for further deve l opment. The program
i s avai lable from the authors o n req uest. A subsequent publication w i l l present
DFSIM yield tables for a n u m ber of management regi m es.
Keywords: Simulation, yield tables, g rowth models, fert i l ization (forest), thi n n i ng
effects, computer programs/program m ing, Doug l as-fi r, Pseudotsuga menziesii.
DOUGLAS AlAN
MAGUIR
Contents
1
2
2
3
3
3
4
4
5
16
17
17
18
20
21
24
25
25
27
27
28
28
30
42
56
59
64
64
65
65
66
72
73
73
73
74
75
78
Introduction
The Data
Sources, Assembly, and Editing
Treatment of Understory
Height Estimates
Top Height and S ite Index
Plot Summaries
Screen i ng and Combining Growth Periods
Data D istribution
Regression Analyses
The Simulator
Juve n i le Stand Development
Main Stand Development
Simulator Performance
Limitations
Relation of DFSIM to DFIT
Future Development
Application
Conclusion
Metric Equivalents
Literature Cited
Appendix 1. Program Operating Instructions
D FSIM Options
Control Card Formats
Messages Printed During Execution
Appendix 2. Description of Program Segments
Appendix 3. Driving Functions
Height and Height I ncrement Equations
Volume-Basal Area Ratio Equation {VG RAT)
Juvenile Stand Equations
Main Stand Equations
Defau lt Commercial Thinning Regime
Appendix 4. Notes on Testing DFSIM Using Real Data
Distinction Between Juveni l e and Main Stand Procedures
Stands Less Than 5.55-l nch D.B.H .
Stands 5.55-lnch D. B. H . and Larger
Appendix 5. Yield Table Format
Glossary
E
Introduction
I n 1 974, the Pacific N orthwest Forest and Range Experiment Station and
Weyerhaeuser Com pany agreed to combine their data with that of other
interested organizations, in a j oint effort to develop new and more broadl y
. based yiel d estimates for managed stands of coast Dougl as-fir (Pseudotsuga
menziesii ( Mirb.) Franco var. menziesii). The objective was a system which
wou l d describe development of even-aged Doug las-fir stands for a range of
initial stand conditions and treatment regimes, and which cou l d be modified to
incorporate improved information in the future.
Thirteen organizations contributed the data which form the basis for the new
stand sim u l ator D FSI M1 (Dou g las-fir Sim u l ator). This is probably the largest
agg regation of remeas ured research p lot data for the species. The predecessor
of D FS I M was D F IT (Bruce, DeMars, and Reukema 1 977; Reukema and Bruce
1 977). The new simu l ator is a whole-stand model (Munro 1 974), similar to D FIT
in general nature and intended application. The principal differences are (1) a
m uch stronger base in data from treated stands, and (2) an internal structure
and available options which we believe are more flexible and have g reater
potential for future modification and extension.
DFSIM does have its defects and limitations, which may be corrected i n the
future. Major improvement witt probably req uire u pdating and extension of the
data base and development of improved estimates of component rel ationships.
We believe the present version of D FSI M has had s ufficient development and
testing to j ustify its u se in timber management.
In this report we wil l provide an understanding of the nature and operation of
D FSIM, and sufficiently detailed information to al low inte l ligent use of the
program and of tables generated by it. The first part of the report is a general
discussion of data used as the basis for the sim u l ator, methods of analysis,
structure and operation of the program, limitations and prospective uses, and
related background information. This is fol l owed by a more detailed presenta·
tion of the mechanics of operating the program, prog ram options, certain
prog ram components, and a sample yie l d tabie.
A companion publication wil l present DFSIM yiel d tables for a series of
management regimes.
1We acknowledge the contributions of James D. Arney and
Rodney Meade of Weyerhaeuser Company, who measured
plots and assembled and edited much of the data; and of
Donald L Reu kema of the Pacific Nort hwest Forest and
Range Experiment Station, who provided helpful advice and
review during analyses.
The Data
Sources, Assembly, and
Editing
We canvassed interested organizations and co mpiled a list of data like ly to be
useful. We sought remeasured research plots, primarily those fro m thinning
and fertilization experiments. We did not use inventory pl ots becavse of
expected difficulties with smal l plot sizes, truncated diameter measurem ents,
inadequate sam pling of heights and ages, and similar characteristics comm on
in inventory plots not specifical ly designed for use in yield tabl e construction.
The thirteen organizations which contributed data that appeared suitable for
our purposes were:
British Columbia Forest Service
Bureau of Land M anagement
Canadian Forestry Service
Crown Ze l l erbach Corporation
International Paper Company
MacMil lan-Bioedel ltd.
Oregon Department of Forestry
Oregon State University
Pacific Northwest Forest and Range
Experiment Station
Roseburg Lum ber Com pany
University of Washington
(includes coo perators in the Regional
Forest Nutrifion Research Program)
Washington De partment of Natural Resources
Weyerhaeuser Com pany
Despite initial screening, the data we received were extremely variable in
standards of m easurement and l acked a consistent and com patibl e format and
coding system. Particularly serious and widespread problems were inconsistent
and inadequate sam p ling and measurem ent of heights and ages, and unreliable
or missing information on stand characteristics prior to initial thinning.
Some p lots were revisited during 1 975 to check data and obtain missing
information.
A standard tree record format and coding system was developed.2 Data were
checked for omissions and inconsistencies and corrections made where
feasib le. A l l data were converted to the standard format and coding system.
Asse m bly, editing, and conversion of data to a common system proved to be a
massive task, requiring several e m p loyee-years of work by the Experiment
Station and Weyerhaeuser Com pany.
2Arney, James D. and Robert 0. Curtis. 1977. Code legend for
standardized permanent plot records. In Standards of measure
and data sharing: A Report of the Committee on Standards of
Measure and Data Sharing (COSMADS) of the Western Stand
Management Committee of the Western Forestry and
Conservation Association, Append. A, p. 1-18. D. R. Reimer,
Chairman. West. For. and Conserv. Assoc., Portland, Oreg.
Dec. 1977.
2
Treatment of Understory
Douglas-fir is relativel y intolerant of shade, a nd stands often develop an
u nderstory of small, younger stems of cedar, hem lock, and true firs. These
smal l stems have little effect on volume growth or harvestable volume, but their
presence strongly affects calcu lations involving number of trees and average
diameter. We atte m pted to excl ude these s mal l stems when they were clearly
of a different age cl ass from the main stand.
We calcu lated plot means and s.tandard deviatio ns of diameters for Douglas-fir
and coded as "understory" any stem of an associated species which on its first
appearance in the record was smal ler than the plot mean d iameter of Doug las­
fir at that time, less 2112 standard deviatio ns. Such u nderstory stems were
excl uded from all s ubsequent computations.
Height Estimates
Weaknesses and incon sistencies in heigh t sam pling and measurement were
wides pread and obviously critical to the plan ned analyses.
Where reasonable sam ples were availabl e for given dates, we fitted regressions
of the form
I n (height - 4.5)
=
a
+
b (dbh)c
in which a and b were coefficients estimated for each measurement date. A
sin g l e overall estimate of c was used for all meas urements on any one plot to
provide consistency among curves for s uccessive measurements.
We also fitted a height:d.b. h.-age regression to all measurements for each plot,
in which the a and b coefficients were exp ressed as functions of age (Cu rtis
1 967). This "pooled" regression was u sed to estimate heights in cases where
the height sam ple was lacking or g rossl y inadequate for a partic u l ar date, or
where the curve for a partic u lar date appeared inconsistent with those for other
ages on the same plot.
These relationships and the Bru ce-DeMars (1 974) vol u m e equatio n were used to
assig n an estimated height and vo lume to each tree for each date of
measurement.
Top Height and Site
Index
As the basic measure of stand height and the basis for site index, we adopted
a top height (H40) defined as mean height of the "n" largest trees on the plot
(by d.b.h.) , w here
n
=
40.0
•
(plot area in acres)
with restriction n
2:
4.
Site index (S) values were assigned to p lots using H40, corresponding p lot age
b.h., and King's (1 966) site index curves. A lthough H40 is not identical with the
stand fraction used by King, differences are u s ually s mal l. If s ucce ssive
measureme nts bracketed age 50 b.h., we estimated site index by linear
interpol ation; otherwise, we used the estim ate for the measurement age
nearest 50 b.h. If the stand had been fertilized p rior to age 50 b.h., we
substituted the mean of the estim ates for the associated control plots.
3
Plot Summaries
I ndividual tree records with assigned heights and vol umes, p lot values of H40
and site i ndex, and i nformation from the p lot i ndex file were u sed as i n put to a
plot summary program. This program gave us (1) stand statistics at each
meas u rement date for trees over 1.55-inch, 5.55-inch, and 7.55-inch d.b. h . , (2)
merchantab le vol u mes to various size l i mits, and (3) correspo nding val ues for
periodi c mortal ity, i n g rowth, and cut.
Screening and
Combining Growth
Periods
At this stage, some p lots and i ndividua l measurements with i n p l ots were
rejected. These incl uded:
1 . Plots less than SO-percent Douglas-fir by basal area.
2. Excessively smal l p lots. Pl ots were ranked by size relative to average
d i ameter and the smal lest were d ro pped. M i n i m u m acceptable relative size was
necessari ly a com promise between the analyst's concept of desirable size and
the realities of avai lable data. Rejects incl uded most 1/20-acre plots, and some
1 /10-acre plots i n stands of l arge average d i ameter.
3. Fert i l i zed p l ots of marg inal s ize lacking buffers between treatments.
4. Plots with obvious catastrophic morta l ity.
5. Plots with more t han one age class in the mai n stand.
6. Plot s with m i ssing or obviously i n correct val ues, which prevented calculat i n g
a fu l l set o f stand statistics. (Add it ional deletions were made a t l ater stages,
when previously u n detected errors or widely aberrant val ues were
encountered.)
The ori ginal measurements were made at intervals varyi ng from 1 to 10 or more
years. We attem pted to combine these i nto growth periods of more nearly
com parable length.
We used King's (1 966) height-age equations to calculate years req u i red for 1 0
feet of height g rowth at each i n itial age. Where possible, successive g rowth
periods were combi ned to approximate this interval, s u bject to three
restrictions:
1. N o period could overlap a t h i n n i ng or fert i lizati on date.
2. No period could be less than 2.6 years.
3. No period could have basal area mortal ity per year exceed i n g five perce nt of
the l ive basal area.
Any period or combi nation of periods not m eeting these req u i re ments was
deleted.
/
After screening and com bining, there was sti l l considerable variation i n period
l engths, whether measured in years or height i ncrement.
4
Data Distribution After these operations (and subsequent occas ional deletions), we had avai l able
for anal yses 2,654 g rowth periods from 1 ,434 p lots on 203 i nstal l at ions.
Overa l l d i stribution of data is shown i n tables 1 -3 and figures 1 -9. When a l l
plot s are considered, there i s a reasonabl y good d i stribution across sites and
ages. The d i stributi o n is m u ch less sati sfactory, however, when the data are
subd i vided by stand ori g i n and treatment c lass, and when one remembers that
m u ltiple p l ots in a single instal l ation are not real ly i n dependent observations.
In particu l ar, there were l ittle or no data for p l antations older than about 40
years, for any stan ds over 80 years, for stands w ith repeated fert i l i zation or long
periods of observation fo l lowing fert i lization, or for older, t h i nned stands with a
h istory of low i nitial den sity or early stocking control.
TABLE 1 - Number of growth periods used in DFSIM analysis, by stand origin
and treatment
Treatment
No CT2 or fert i lization
CT, no fert i l ization
No CT, ferti l ized
CT and fert i li zed
All treat ments
Planted stand
No PCT1 PCT
N atural stand
No PCT PCT
Total
1 67
13
88
12
31 0
126
1 05
93
484
445
486
1 28
1 00
68
29
0
1 ,061
652
708'
233
280
634
1 ,543
1 97
2,654
1PCT (pre-commercial thi nning) is any thi nning made when the average diameter of a stand is less
than 5.55 inches.
2cT (commercial thinning) is any thinning made when the average diameter of a stand is 5.55 inches
or l arger.
5
TAB L E 2- N u mber of plots used in DFSIM analyses, by stand origin and
treatment
Treatment
No CP or fertil izati o n
CT, no fert i l izat ion
No CT, fert i l ized
Planted stand
No PCT1 PCT
68
6
CT and fert i l i zed
33
6
A l l t reatments
113
N atural stand
No PCT PCT
94
291
89
11
208
424
51
245
Total
485
67
32
37
17
0
990
86
1 ,434
340
485
124
1PCT (pre-commercial thi n n ing) is any thinning made when the average diameter of the stand is less
than 5.55 Inches.
2CT (commercial t hi n n i ng ) is any thi n n i n g made when the average diameter of a stand is 5.55 i nches
or larger.
TAB LE 3- N u mber of installations in DFSIM analyses represented by each
stand origin and treatment1
Treat ment
N o CP or fertili zat ion
CT, no fertilization
N o CT, fert i l ized
CT and fertil ized
Planted stand
No PCP PCT
26
4
7
3
18
11
4
2
N atural stand
PCT
N o PCT
1 50
44
120
14
22
5
7
0
1There were a total of 203 installations. Most contained multiple plots representing di fferent
t reatments.
2PCT (pre-commercial t hinning) is any thi n ning made when the average diameter of the stand is less
than 5.55 inches.
:JeT (commercial thinning) is any thi n n ing made when the average diameter of a stand is 5.55 inches
or larger.
6
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Fig ure 1.-Distribution of growth periods by site index and
age b.h., all data.
7
200.00
180.00
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Figure 2.-Distribution of growth periods by s i te index and
age b.h., u ntreated natural stands.
8
70.00
80.00
90.00
100.00
200.00
180.00
160.00
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20.00
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Figure 3.-Distribu t ion of growth periods by site i n dex an d
age b.h., u n t reated plantations.
9
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Figure 4.-Distri bution of growth periods by site index an d
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stands.
·
10
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100.00
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Fig ure 5. - Distribution of g rowth periods by s i te index and
age b.h., thinned (precommercial or commercial) plantations.
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140.00
I:
a:i 0 120.00
In
G)
Ol
<
G)
rn 100.00
Ill
Ill
)(
G)
'0
r::
G)
....
80.00
•2
(j)
60.00
40.00
20.00
0
0
10.00
20.00
30.00
40.00
50.00
60.00
Total Age
Figure 6.-Distribution of growth periods by site i ndex and
age b.h., fert i l i zed, unthi n ned, natural stands.
12
70.00
80.00
90.00
100.00
200.00
180.00
160.00
140.00
9 8 8 9
66 54 54
J:
aj
0
It)
G)
01
<(
G)
120.00
II) 100.00
Cll
m
x
G)
"D
c
80.00
4
!
(j)
9
9
60.00
40.00
20.00
0
0
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
100.00
Total Age
Fi gure 7.-Distribution of growth periods by site i ndex and
age b.h., ferti l i zed, u nt h inned plantations.
13
200.00
180.00
160.00
36 36 36
140.00
4 4 3
J:
H22Uf
22 22
2
9 f f 9 8 9823 4f
2
m
0 120.00
10
Q)
Ol
<(
Q)
Ill 100.00
Ill
m
)(
Q)
"0
c:
f
fH2Hf
f
f
2
33
80.00
Q)
....
ij)
60.00
40.00
20.00
0
0
10.00
20.00
30.00
40.00
50.00
60.00
Total Age
Figure B.-Distribution of growth periods by site index and
age b.h., ferti lized and thinned natural stands.
14
70.00
80.00
90.00
100.00
200.00
180.00
160.00
4 4
140.00
99 99 99*99*
59 69 o9
I:
ai
0
U)
(I)
01
<(
(I)
fl)
ca
lXI
x
(I)
"D
c
120.00
100.00
80.00
5
s
co
60.00
40.00
20.00
0
0
10.00
20.00
30.00
40.00
50.00
60.00
Total Age
Figure 9. - D i stribution of growth periods by site index and
age b.h., fertilized and t h i nned p l antations.
70.00
80.00
90.00 100.00
b. Plan tat ions. The user must supply the n u mber (N 0.0) of al l successfu l ly establ i shed stems.5 The program then assumes no fu rther i ngrowth and an arbitrary, very l ow mortality u n t i l . either the stand reaches a di ameter of 5.55 i nches or N 00
exceeds the estimated n u m ber of stems over 1.55 i nches for the u ntreated,
n at u ral stand of the same s i te and age (a con d i t ion l i kely to occur only i n
p l antations with extens ive nat u ra l fil l -i n). I f the l atter occurs, the natura l
stand esti mate i s substit uted.
c. Precommercial ly t h i n ned stands, nat u ral or planted.
The nu mber of stems (N 00) left after precommercial t h i n n i ng and age at
precom mercial thi n n i ng are s pecified by the user. The p rogram then assu mes
no i ngrowth and an arbitrary, very low mortal ity u n t i l the stand reaches
5.55-i nch d.b.h.
3. Quad rat ic mean d i ameter (D1.6).
Quadratic mean d .b.h. of stems ove r 1.55 i nches is calculated for each
successi ve year, using function DIAMJ with H40, N 1 6, and specificat ions for
_
precommercial t h i n n i n g and fert i l ization.
4. Mortal i ty. Any mortality occurring d uring juven i l e stand development is excl uded from est imates of cumulative mortal ity given i n later program summaries. Main Stand D.evelopment
1. St and projection.
After stand di ameter reaches 5.55 i n ches, stand projection proceeds as fol lows:
.
-
a. I ncrement i n H 40 (dH 40) is esti mated by fu nct ion HTG ROW, and
s uccessive H 40s are est i m ated by add i ng successive d H 40s to attained H 40.
b. G ross i ncrements in basal area and vol ume are predi cted by fu nctions
BAINCR and VINCR. These gross i ncrements are subdi vi ded i n to correspond­
ing net i ncrement and mortal ity using functions BAN ET and VN ET. If needed,
i ncrements are adjusted to keep vol u m e/basal area ratios co nsistent w ith
function VGRAT.
c. N et i n crement i n quad rat ic mean d iameter (D) is est i mated by fu nction
D I N CR.
d. If needed, the three net i ncrement est imates and associated mortal i ty
estimates are adjusted to mai ntain co nsis tency among estimates. Live stand
stat istics are advanced by 1-year growth periods by s u m mati o n of estimated
i n crements.
e. N u mber of mortal ity trees i s calcu lated as the difference i n n u m bers of
l ive trees calculated from successive l ive stan d diameters and basal areas.
Diameter of mortality trees is calculated from the n u m ber of th ese t rees and
their basal area. Cumu l at ive mortality is the sum of mortal ity i ncrements
since the stand reache'd a d iameter of 5.55 i nches.
5For very small diameters this introduces a bias, since
function DIAMJ was derived using N1 rather than N00. This
6
becomes negligible for D1 larger than about 4 inches.
6
_
18
Stand p rojections are made by summ i n g esti m ated a n nual i ncrements, as
out l i ned above. The fu nctions for vo lume i nc rement, basal area i ncrement, and
di ameter i nc rement were derived as reg ressions using stand stat i stics at the
mid point of the measurement period as p redictors (X.).
Th i s was done beca use
I
of the variable lengths of actual meas u rement periods i n the data. Since val ues
of the X; avai lable fo r use i n stand p rojectio n s are those at the beg i n n i ng of t he
1 -year projection pe riod rather than the m i d poi nt, est imates made using i n itial
val ues are biased by an amount which depends o n curvature of yield fu nctions
at that poi nt. This bias i s contro l l ed by a p roced u re which calculates
approxi mations to the m i d po i nt val ues of the X.I and then uses these to
calcu late the final estimates of i ncrements.
2. Fert i l ization. The functions for height , g ross vol ume i ncrement, g ross basal area in crement, and n et stand diameter i n c rement i nclude a term wh ich i nc reases g rowth rate for a l i m ited period fo l low ing app l ication of n it rogen fert i l i zer (s ubrout ine XFERT). 3. Commercial t h i n n i ng. The user can s pecify t i m i ng, type, and severity of t h i n n i ng by several options as d iscussed in the section on program operation (append ix 1 ). If n ot otherwise s pecified, t h i n n i ng fol lows a reg ime i ncorporated i n the program (appendix 3), which we t h i n k is reasonable but not n ecessari ly optimum. The u ser can mod i fy this by specifying residual basal areas, diD ratios to be u sed (diD = (q uad rat i c mean d.b.h. of cut)l(quad ratic mean d.b.h. of stan d before cut)), m i n i mu m basal area (in stems over 5.55 i nches) at which the first t h i n n i ng can be made, and m i n i m u m acceptable average d iameter of cut trees. When a commercial th i n n i ng is made from above (diD ratio for all trees over
1.55 i nches i s greater than 1 .0), H40 is red uced by an amount which depends
on the amount cut.
The functions i nc l ud e terms which modify estimates fol lowi n g t h i n n i n g . These
involve one or more of the variables t h i nned versus u n th i n ned, height
i n c rement si nce the most recent th i n n i ng, ratio of H40 to l ive stand D1 .6, and
relative density.6
Because m u ch of the data lacks rel iable i n formation on stand statistics p rior to
the i n it i al t h i n ning or crown developm ent, we were u nable to use expressions
i nvolving p reth i n n i ng stand stat i stics, n u m be r and size of stems cut, or c rown
deve lopment as pred ictors of th i n n i ng res ponse.
6Relative density is expressed as the variable RD "" GI{D'�>),
where G is basal area in stems over 1.55-inch d.b.h., and D is
the corresponding quadratic mean diameter. RD is directly
proportional to the ratio of observed basal area to basal area
of a "normal" stand of the same average diameter. {Derivation
given in: Curtis, Robert 0. A simple index of stand density for
Douglas-fir. Manuscript in preparation.)
19
4. Sum mary tables.
A summary show i ng stat i stics for l ive stand, cut stand, re sid ual stand, and
cumu lative val ues for cut and mortality for stems over 1.55-i nch d . b.h. i s
p roduced for each t h i nn ing date and final harvest. Intermed iate sum maries are
optional and can be requested at any specified age (appendix 1).
Optional summary tables are provided for me rchantabl e volu mes in cubic feet
of stems over 5.55-inch d . b.h., and in cubic feet and board feet for stems over
7.55-inch d . b. h . These valu e s are derived from the correspondi n g values in the
basic output tab le (stems over 1.55- i nch d.b.h.) by using the merchantable
vol ume rati os (Su broutines VOLCO N, M E RCHV and M ERCHT) given by
W i l l iamson and Curt i s (1980).
Note that cut totals for t h i n ne d stands do not i nclude potentially salvable
mortal ity.
Simulator
Performance
How wel l d oes DFS I M represent reality? U nfortunately, we cannot p rovide an
expl icit answer.
Ideal ly, a simulator shou ld be tested agai nst a sam ple of data wh ich i s
independent of that u sed i n its construction and representative of the range of
possi b l e conditions and treatments for which the simu lator might be u sed.
Although a large n u m ber of plot measurements were avai l able, they came from
a m uch smal ler n u m ber of i nstal l atio ns, and plots within one i n stal lation are
certainly not independent. We coul d not draw a truly i ndependent sample from
the data w ithout seriously i m pairing the data base avai lable for construct i ng
. the simulator. Th erefore, we chose to use all ava ilable data for the original
analyses.
A second difficulty was the heterogeneous nature of the d ata. There was wide
variation i n l ength of observation period, i n itial age, num ber of serial observa­
tions per plot, number of pl ots per i n stal lation, and d i stribution of treatments
by age and site. We cou l d see no computationally feasible way i n which a
com parison over a l l data of pred icted with observed val ues for each of the
stat istics of i nterest cou l d be reduced to a simp le, meani ngfu l, and read i l y
interpretable set o f stat istics.
We therefore chose a l i mi ted number of instal lations, judged "best" by l ength
of record and apparent rel iabi l ity of measurements, to com pare w it h simul ator
pred ictions. Each s i m ulation began with observed plot statist ics. Each time a
thi n n i ng was made on a real plot, the s i m u lated stand was thinned (when
possible) to the same resi d ual basal area and number of stems. G rowth trends
i n net and gross vol u m e and basal area; d i ameter of l ive trees; and numbe r,
basal area, and average d i ameter of mortal ity were com pared graph ical ly and by
means of rat ios of the form r:: (estimated increment)/i:: (observed i ncrement). A
partial summary is given i n tabl e 4.
20
Con c l usions drawn from suc_h a partial comparison are necessari l y i ncom p l ete
and s u bjective.
Certain i nstall ations showed consistent deviations from predicted trends. Some
deviations c learly res u lted from differences in height g rowth pattern. Some may
have arisen from errors in estimating stand age and site i ndex in very you ng
stands. Some probably res u l ted. from d ifferences i n early stand h i story, site
characteristics, or other attributes associated with physical location and not
adequately ex pressed by the variab les used.
I nitial comparisons appeared to show a tendency to overestimate mortal ity i n
you ng, th inned stands. There was also some tendency t o u nderestimate growth
in young stands on good sites which had received very early, repeated
t h i n n ings and had been maintained at low densities. This categ ory is
represented by the LOGS studies (Wi l liamson and Staebler 1 971 ) and a few
s i m i l ar i nstallations. There were no low-s ite stan d s with s i m il ar treatments
which had yet attained sizes al l owing com parison with those on better sites.
These instal lations had been highly selected for stand u niformity and good
c rown development, had received caref u l ly control led thinning, and had not
ex hibited the growth depression or "th i n n i ng shock" sometimes observed on
poor si tes. Stand descri ptors i n our equations m ay not satisfactorily distingu ish
these i n itial conditions from those associated with l esser response.
We made some adjustments to the mortal ity computations, and to the
i nc rement fu nctions for you ng, low density (RD less than 40), thin ned stands.
Wit h i n the l i m itations of our present data, we do not see a c l ear need for
f u rther modification. We think estimat.es are a good reg ional average, even
though i n d ividual i nstal lations may d iffer considerably.
Limitations
DFSIM users should be aware of some u ncertain ti es and l i mitat ions, which
arise mainly from l i m i tations of the basi.c data. These are not pec u l iar to
D FS I M ; s i m i lar q ua l i fi cations apply equal ly to most other stand simulators and
yield estimates.
A f u n damental l i m itation in any attem pt to estimate development of intensively
managed stands over an entire rotation is the simple fact that there are n o
stand s n o w i n existence, avai lable for sam p l ing, w h i c h have developed to a n
advanced age under t h e type of management which seems l i kely i n the future.
Older stands had no reg u lation of competition in early l i fe , and therefore
common ly have restricted crown development and l i m ited responsiveness to
treat ment.
·
Some of our "th inned" stands represented treatments which many foresters
wou ld not consider reasonable thinnings. We had l ittle data for repeated
commercial t h i n n i ngs in plantations or stands which had early density control.
Comparison with the l ittle data avai l able from the LOGS studies and s i m i lar
con ditions s ugg ests that potential benefits of systematic carefu l thinnings,
beg u n early, i n-stands which have not experienced severe competition, may be
greater than indicated by our estimates.
21
'·
TABLE 4-Summary of comparisons of DFSIM estimates with observed gross
volume increment, gross basal area increment, and net stand diameter
increment
Ey estl!:y obs 1
Site class
I
Installation
Age span number
(total age)
805
36-52
806
41-52
Treatment
3
class
Number
of plots
dVgross
Nat
Th
12
1.07
1.11
1.06
Nat
NT
3
0.88
0.86
1.00
Th
9
0.95
0.97
1.20
F
3
1.00
0.98
0.90
Th+ F
9
0.94
0.88
1.03
NT
3
0.84
0.81
0.91
Th
5
0.94
0.85
0.96
F
3
1.13
1.11
1.13
1.13
Origin
2
4
dGgross
5
dD6
7(145)
808
17-26
p
10
1.21
1.12
NT
1
1.12
0.90
Th
1
1.10
0.90
1.09
1.00
0.95
1.04
Th+ F
827
829
II
52-75
24-37
Nat Nat NT
Th
18
0.89
0.85
0.93
1.10
1.14
1.56
200
27·32
p
NT
1
Th
13
302
19-26
p
NT
3
Th
(125) 319
320
25-47
37-49
p
Nat
1.21
1.22
1.11
(0.83)
(0.79)
1.16
24
1.08
1.04
1.03
NT
1
1.42
1.60
1.52
Th
2
1.24
1.40
1.13
NT
1
0.99
1.01
1.10
T
2
1.01
1.00
1.09
(0.87)
(0.75)
1.12
554
18-25
p
NT
3
Th
24
600
21-31
Nat
NT
3
Th
601
43-64
Nat
NT
650
18-29
p
Th
809
826
20-30
16-27
Nat
p
1.07
1.05
1.08
(0.62)
(0.47)
0.94
24
0.76
0.71
0.75
2
0.85
0.83
0.75
Th
11
0.94
0.84
0.78
NT
2
1.15
1.10
1.04
6
1.08
1.10
1.09
NT
3
0.90
0.93
1.02
Th
24
0.92
0.92
0.94
NT
4
0.96
0.90
0.82
Th
4
0.97
F
0.93
0.97
4
1.10
0.97
0.94
11
1.24
1.17
1.11
Th+ F
22
8
1.15
TABLE 4-Summary of comparisons of DFSIM estimates with observed gross
volume Increment, gross basal area increment, and net stand d i ameter
increment, continued
r. y est/r.y obs 1
Observed plot statistics Site class
Installation
Age span
number
(total age)
251
I ll 35-50
Treatment
3
class
2
Origin
Nat
( 1 05) 308
40-58
Nat
310
29-34
Nat
317
328
329
IV-V
18-62
22-62
48-69
Nat
Nat
Nat
Number
of plots
dVgross
4
dGgross
5
dD6
NT
7
1.22
1.22
Th
20
1.06
1.07
1.16
NT
12
1.05
1.03
0.89
Th
25
0.96
NT
3
Th
1 .25
1 .03
0.96
( 1 .02)
(0.89)
2.15
24
0.97
0.90
0.90
NT
1
0,91
0.78
0.90
Th
2
1.21
1.21
1 .18
NT
1
1 .1 0
1 .02
1 .06
Th
2
1.15
1 .05
1.1 1
0.97
NT
2
1.12
1 .04
Th
2
1 .06
1.04
1 .14
Th
2
0.92
0.92
0.95
782
19-27
Nat
Th+F
4
1 .08
1 .08
1 .07
825
52-80
Nat
NT
3
0.87
0.87
0.94
Th
4
0.79
0.82
0.93
306
"23·48
p
NT
17
1.10
1 .14
1.13
307
60·97
Nat
NT
2
1 .03
1 .08
1.15
Th
4
1 .35
1.23
1.28
NT
3
1.19
1 .25
1 .00
F
9
0.96
1.07
0.86
(85·65)
322 37-48
p
1Estimated increment/observed increment.
2Nat
natural; P :::: planted.
3NT :::: no treatment; Th
thi nned; F
=
fertil ized; Th+ F
t h inned and fert i l ized.
4Gross volume increment. Parentheses indicate a ratio of net values, used because plots were less
than 5.6- inch quadratic mean d . b.h. and estimates therefore omitted mortal ity.
5Gross basal area increment. Parentheses indicate a rat io of net values, used because plots were
less than 5.6-inch quadratic mean d.b.h.
6Net stand diameter increment.
7Height i n feet at age 50 b. h.
23
Because of data l i m itat ions, we have assu med that res ponse to late t h i n n i ngs
i n ol der stands is representative of stands of s i m i lar age u nd er a reg ular
t h i n n i ng regime (probably u ntrue). We have been unable to utilize stand co ndition
prior to i n itial t h i n n i n g as a predictor of response. We have assumed that height
i n cre ment is n ot affected by juveni l e stand density or early stocki ng control. For
these reasons, also, our estimates of treatment response may be low.
Relations h i ps of mortality to stand attributes are weak, and estimates g iven by
the mortal ity functions are unrel iable. S i nce these est i mates have a m ajor
i n fluence in determ i n i ng the u pper l i m it s of estimated stand densities and
vol umes in u n treated stands, w e have adjusted the mortality-density
rel ationshi ps to cause these estimates to stab i l ize at a density corresponding
to the mean of the older u ntreated stands. This is somewhat hig her than the·
"normal" of McArd le et at. (1961), but considerably l ower t han maximum
densities attai ned by some i n d ividual p lots. This as sumpti on of a fixed u p per
density l i m it, appl icable to al l locations, is probably biolog ically i ncorrect (K ing
1970) but appears a n ecessary simpl ificat ion.
The basic data contained few p lantations with less t han 300 i n itially
establis hed stems per acre, few stands with early precommerc i al t h i n n i n g to
less than 300 stems per acre, few stands kn own to have had low i n itial
stoc king or strongly c l u mped stem d i stributions, and few stands treated with
several appl ications of fert i l izer. Predictions for cond i tions outside these l i m i t s
are qu estionable extrapolations.
Relation of DFSIM
to DFIT
DFS I M d iffers from the earl ier program DFIT (Bruce, DeMars, and Reukema
1977) i n data base, i nternal structu re, and options available. DFIT was
developed from a more restricted data base and rel ied heavily o n theoretical
rel ationships. D FSI M , with a more extensive though not ent i rely adequate data
base, re l i es more on fitt i n g empirica l l y derived fu nctions to t h e data.
Because of d i fferences i n data, structure, and model i n g approaches, i t i s
i nevitable that n u merical est imates g iven b y t h e two simulators w i l l differ.
Neither simu lator has had sufficient ext e n s ive or d irectly com parable test i n g to
indicate t h at one is "better" than the ot her. To us, the most stri k i ng po i nt i s
not that esti mates d i ffer i n some respects but that two completely different
analyses using d ifferent data have prod u ce d esti mates which are remarkably
s i m i l ar.7 Th is tends to g i ve confidence in both.
Compared to DFIT, the pri n c i pal advantages of DFSI M are a broader data base,
greater flex i b i l ity to represent a w ider range of stand conditions and
t reatments, and greater potential for extension and mod i fi cat i on.
7Personal communication from Donald L . Reukema.
24
Future Development
Data u sed i n our analyses are from 1 974 or earlier. Additional data on fert i l izer
response and the development of young stands with early density control are
acc u m u lati ng and should soon provide the basis for imp rovi ng estimates.
Although al l components cou ld certainly be i m p roved, changes in many of
them wou l d have l ittle effect on overal l estimates. The reall y critical
relationshi p s are few:
1 . H eight i ncrement function. Effects o n height i ncre ment of stand origin, i n itial density, early density control, and fert i lizer treat ment need further i nvestigation. 2. Gross volume inc rement, g ross basal area i ncrement, and net d iameter i ncrement functions.
These need better data o n thin n i ng response, especial ly for low residual
densities. Present fu nction s ap pear excessively complicated, and si mpler
eq uations may be poss ible. The fertil izer response function may not correctly
represent trends of response over t i me and possible i nteractions with other
stand treatment and i n itial conditions. It d oes not consider possible differences
associ ated with form of n itrogen and method and time of application.
3. (Net i ncrement)/(gross i ncrement) rat io functions. These mortal ity estimates are imprecise and poorly defined, and the present equations l i kely confound age and density effe cts. 4. J uveni l e stand d iameter function. Representation of the effects of precom mercial thinning and fertil ization could p robably be i m p roved. Two additional featu res woul d be d esirable: the abil ity to generate diameter
d istributions correspon d i ng to p red icted stand statistics and estimates of the
d iameters of the largest 40 stems per acre.
Application
DFSI M is a "stand averag e" model derived from small research plots. It
represents the devel opment of relatively homogeneous, even-aged stands of one
'
pri ncipal species and is not app l i cable to other types of stands. We regard it
pri marily as a means of sum marizing results of nu merous small thi n n i ng and
fertil ization trials. It was not designed as a means of projecting i nventory data. I t
can, however, be u sed t o estimate probable future development of existing
stands, providing these are within the range of the data used and some judg ment
is used in application.
We be lieve the present version of DFSIM has had sufficient development and
testing to justify its use· in management. It can provide:
1 . Estimates of average stand development u nder alternative management
regimes.
25
2. G uides for stand management, i ncluding desirable stocki ng and seq uence and
t i m i ng of thi n n i ngs associated with i nitial number of trees planted or left after
precommercial thinning.
3. Est i m ates of long-term prod uction potential of managed stands.
D FSIM users should recal l the l i m itations of the basic data; estimates for
conditions which are clearly outside the range of the data should be viewed
skeptically. Some specific cautions:
1. The data give no basis for esti mates for stands over 100 years of age.
Estimates for stands 80-100 years old are at the margin of the data and should be
regarded as plausible extrapolations.
2. Estimates for stands planted to less than 300 stems per acre or with early
precommercial thi n n i ng to less than 300 stems per acre, are outside the range of
data.
3. Estimates for stands having frequently repeated fert i l i zation or fertil i zed with
more than 400 pounds of n itrogen per acre are extrapolations. Repeated thi n n i ng
and fertil ization i n combi nation w i l l soon produce stands outside the range of
the data. The program provides for one precommerc ial thi nning and one
fertilizat ion during j uvenile stand development (stand diameter u nder 5.55
i nches). Thi s number should not be exceeded.
4. When using simu lat ions beg i n n i n g w ith observed stand characteristics:
a. Do not beg i n simulations w ith observed i n itial numbers and diameters of
natural, u nthi nned stands at top heights of less than 30-35 feet. If they are
begu n earl ier, large errors w i l l be i ntroduced by the un known i ngrowth
component.
·
b. Simu lations begun with observed n u m ber and diameter in very young
plantations or precommercially thin ned stands are sensitive to errors and
i nconsistencies i n i nitial diameter and u nusual heightfdiameter rat ios. In very
you ng stands, small absolute errors i n start i ng d iameters or in the correspond­
i ng DFSIM regression esti mates represent large percentage errors; they w i l l be
carried forward in the simulation process. For plantations or precom mercially
thi n ned stands less than about 30-feet top height, it i s preferable to beg i n
sim ulat ions w ith observed number o f stems (al l stems, regardless o f d iameter)
and accept the esti mates of i n itial diameter generated by the program, even
though these may differ somewhat from the observed initial values. Otherwise,
s ubstantial errors may be introduced through the biases (see footnote 5) and
i nconsistencies associated with d iameter measurement for smal l trees and the
extrapolation of diameter and number of trees functions to very you ng stands.
c. Starting numbers and d iameters are l i kely to produce unsatisfactory results
if they (1) are obtained from excessively smal l plots (smal l tree samples), or (2)
include un derstory stems of associated species, or (3) are based on measure·
ment to diameter l i mi ts different from those specified, or (4) are otherwise
in consistent w ith the basi c data used in D FS I M .
26
d. The j uveni l e stand "approach to normal" trends i n DFSIM are j u dgment
relationships, which behave reasonably for stands that are fairly uniform and
somewhat above or below the "normal" nu mber of trees. Simulations for very
dense or very open, natural u ntreated stands or stands w ith strongly clumped
distributions are very uncerta,i n extrapolations.
The yield table for a "natural untreated stand," prod uced by D FSIM when i n it ial
cond itions are not spec ified by the user, corresponds to a tradi tional normal
yield table. It represents the development of stands which were in itially well·
stocked and which have had rio substant i al non-suppression mortality. It is a
convenient reference standard for compari ng development u nder alternative
regi mes, but otherwise has on ly very l i m ited application.
This natural untreated stand or " normal " table represents an average of the
u ntreated control plots in our data. The majority of these control plots were
smal l and subjectively chosen for a degree of uniformity, stocki ng, and freedom
from i nj ury which occur only on selected smal l areas w ithi n w i l d stands.
Vol umes and basal areas shown are therefore higher and d iameters smaller than
for many w i l d stands. And, because severely damaged plots were excluded and
many plots were observed for only relatively short periods, after i n itial selection,
they have not in most cases had the g roupw ise i rregu lar m ortal ity and damage
which i n wild stands l ead to stand i rregu larities and openi ngs, a process which
is m uch red uced u nder any consistent thi n n i ng regi me.
"Normal" stands are an occasional rather than a usual result of no management.
Comparisons of esti mates for managed stands with this "natural , u ntreated
stand" table should not be i nterpreted as measures of the potential gain
from management.
Conclusion
Development of a s i m u l ator such as DFSIM i s an evo l utionary process. Thi s
f i rst version should b e regarded as a framework for i n corporating i mproved
rel at ionsh i ps as they are devel oped, .and integrating the resu lts of many
i ndividual studies i nto reg ional esti mates of potential yield and response to
treatment.
We anticipate con t i nued m odif i cation and evol ution.
Metric Equivalents
1 i n ch (in)
1 foot (ft)
=
2.54 centimeters
0.3048 meter
1 sq uare foot (ft2) = 0.09290 square meter
1 square foot per acre (ft 2/acre) = 0.2296 square m eter per hectare
1 cubic foot per acre (ft3/per acre) = 0.06997 cubic meter per hectare
=
27
Literature Cited
Bruce, David, and Donald J. DeMars. 1 974. Volume equations for second-growth Douglas-f ir. USDA For. Serv. Res. Note PNW-239, 5 p. Pacific Northwest For. and Range Exp. Stn., Portland,
Oreg.
·
Bruce, David, Donald J. DeMars, and Donald L. Reukema. 1977. Douglas-f i r managed yield s i m u l ator- DFIT u ser's guide. USDA For. Serv. Gen. Tech. Rep. PNW-57, 26 p. Pac. N orthwest For. and Range Exp. Stn., Portland, Oreg. C u rtis, Robert 0.
1967. Height-diameter and height-diameter-age equations for second-growth
Dou glas-f i r. For. Sc i. 1 3(4):365-375.
King, J ames E.
1966. Site i nd ex c u rves for Douglas-fir in the Pac ific N orth west.
Weyerhae u se r For. Pap. 8, 49 p. Weyerhaeu ser For. Res. Cent., Centralia,
Wash.
King, James E.
1 970. Princi ples of g rowi ng stock classification for even-aged stands and an
application to nat u ral Doug las-f i r forests. Ph. D. thesis. U n iv. Wash., Seatt le.
90 p .
M cArd le , Richard E., Walter H. Meyer, and Donald Bruce. 1 961. The yield of Douglas-f i r in the Pacific Northwest. U .S. Dep. Ag ric. Tech. BulL 201 , 72 p. Washi n gton, D.C. M u n ro, Donald D.
1 974. Forest g rowth models-a prog nosis. In G rowth model s for tree and
stand s i m u l ation. Joran Fries, ed. Proc. I U F RO Work. Party S4.01 -4 , 1 973, p. 7-21. l nternatl. U n ion For. Res. O rgan.
Reukema, Donald L., and David Bruce. 1 977. Effects of t h i n n i n g on yield of Do uglas-fir: Concepts and some esti mates obtained by simulation. USDA For. Serv. Gen. Tech. Rep. PNW-58, 36 p. Pac. Northwest For. and Range Exp. Stn., Portland, Oreg. Will iamson, Richard L., and Robert 0. Curt i s. 1 980. Converting total cubic vol umes of second-growth Doug l as-fir stands to merchantable vol u mes. USDA For. Serv. Res. N ote PN W-353, 1 4 p. Pac. N orthwest For. and Range Exp. Stn., Portland, Oreg. W i l l iamson, Ric hard L., and George R. Staebler. 1 971 . Cooperative l evels-of-grow i ng stock study in Dou g l as-f i r. Report N o. 1 - Descri ption of study and ex i st ing study areas. USDA For. Serv. Res. Pap. PNW- 1 11, 1 2 p. Pac. N orthwest For. and Range Exp. Stn., Port l and, Oreg. Appendix 1 .
Program Operating
Instructions
28
DFSIM i s written i n FORTRAN IV and is operational on the CDC CYBER 170-750 computer at the U n i versity of Washi ngton Com p uter Center in Seattle, Washi ngton. The program can be easily i nstal led on the U N IVAC 1 1 08, the I B M 360/370 series, a n d s i m i lar computers w i t h mi nor mod ifications. On t h e CDC CYBER 1 70-750 computer, DFSIM requ i res 42,300 (octal) words of memory and takes approxi mately 0.25 seconds of execution time per yield table. Execution t i me w i l l vary depending o n the number of years for the s i m ulation and the types of yield tables prod uced. DFS I M reads i n put data f rom log ical unit 5 and . writes output tables on log ical unit 6. A general ized flow chart of DFS I M i s presented i n f i g ure 1 0. A typical simulation set u p w i t h three stand sim u lations is i l l ustrated i n figure 11 . An example of a yield table is i l lustrated in f i g u re 1 2. Figure 1 0. -Generalized flowchart of D FSI M .
Compute
inHial
simulation
condHions
and print
yield table
heading.
(HEADER)
COmpute
appropriate heights for existing stand , D > 5.55 inch
.
(HTCAL)
No
(FRSTCT)
Grow stand
to first
commercial
thinning.
Grow stand
to harvest
time
without
commercial
lllinning
�.-.;..;.;..;;;;.;;;::.;_....J (NDTHIN)
Yes
•
Final
harvest
cut
29
EOF
End of file card
ENO
Optional
Control Cards
Title Card
Optional Control Cards Master Control Cant Title Card
Optional Control Cards Title Card
Figure 1 1 .- DFSI M control card setup for t h ree simulations.
The m i n imum successful output from DFSIM is a yield tabl e for all trees
1.6-inch d.b.h. and larger. The i n put conditions are l i sted at the beg i nn i ng of the
yield table.
DFSIM Options
At f i rst g l ance, D FS I M can seem rather complex. Th i s section provide s an
overview of the basic opt ions and how they fit together. No atterr)Pt is made to
cover all options and combi nations.
DFS I M has many options: two for stand type, four for juvenile stand h istory, 30
for com mercial t h i n n i n g , two for fi nal harvest t i m i ng, two for fe rt i l ization, one
for observed stand height/age relationship and eight for output tables.
30
EXAtfi..E
PAGE 1
D F S I ·"
VERSION 1 . 0
D F S I " DEFAULT THitfUNJ OOTPUT WITH fERCHANTABI..E V(J.ll£ YIELDS
t'IINAf£D YIELD TABLE
FOO OOUGLAS-FIR
1 . 6 INCI£S PLUS
SITE INDEX
=
125. (50 YEARS IIU
STAND ORIGIN -- NATt.IRAL. STAND WILL BE PRECOittERClALLY THINNED AT AGE
1 1 . TO
300 . TREES PER ACRE. n£ SCHEOOLED AGE AT 1l£ HARVEST CUT IS SO. Tl£ OOTPUT TABLE WILL HAVE REPOOT AGES OTI£R THAN CUTTING AGES. THE AVERAGE DIAPIETER CF ALL CliT TREES AT CCMRCIAL THINNING$ I'IUST BE AT LEAST 8.00 INOES. THE BASAL AREA CUT AT EACH COiftRCIAL THIN'4ING I'IUST BE
AT LEAST 20. SOOARE FEET PER ACRE.
.
THE BASAL AREA PER ACRE OF All TREES 5. 6. INCHES PLUS tiUST BE AT LEAST 1 00 . 0 SQUARE FEET BEFOOE Tl£ FIRST COI'II'£RCI AL THINNIMJ CAN (ICCU1 . TOT BH
AGE AGE
YRS YRS
LOREY
HT40 HT
FEET FEET
BASAL TREES
DBH MEA/A PER
ltDI SQ FT
ACRE
CVTS
PER
CAl
ACRE
CVTS
300 .
300 .
300 .
300 .
300 .
300 .
300 .
300 .
300.
26.
o.
2.
52.
27.
4.
96.
160.
44.
64.
7.
11.
11
4
14.4
o.o
1 .67
4. 6
12
5
1 7. 4
1 1 .8
2. 1 5
7.6.
13
14
15
6
7
8
20. 4
23. 5
16. 4
20. 3
2.68
3. 21
11.7
16. 9
26. 6
23.8
3 . 74
22. 9
16
17
9
10
29. 8 27. 1
33.0 30.3
4.26
4 . 77
29.8
37.2
18
11
36. 1
33. 4
5 . 26
45 2
19 12
39 . 2 36.3
YEARlY ttOOTALITY
20 1 3
42. 3 39. 3
5.72
3.99
53.5
1
6.21
62. 9
VEARlY JUlRTALITY
4.21
6.66
1
72.3
21
14
45. 4
42. 2
VEMI.Y ttOOTALITY
4. 38
7.09
4 . 39
7.48
4.39
7.85
4 . 39
8. 19
4 . 39
55.5
YEARlY ttmTALITY
62. 7 57. 9
27 20
48.4 45. 0
22 15
VEMLY ttOOTALITY
23
16.
51 .4
47. 8
YEARLY MORTALITY
54.3 50.4
24 17
VEARlY ttOOTALI TY
57.2 53. 0
25 1 8
YEARLY MORTALITY
26.
19
60.0
•
•
•
1
1 . 6.+
1 . 6.+
246.
86.
16.
355.
489.
646.
109.
134.
22.
29.
5.6+
7.6 +
158.
36.
181 .
44.
•
299 .
1 043.
216.
52.
52.
37.
17.
1.
1200 .
237.
61 .
61 .
46.
26.
255 .
70.
70.
56.
37.
270.
79.
78.
65.
48.
283.
87.
87.
74.
59.
294.
96..
95.
82.
6.9.
1
1
•
299.
1
•
298.
90. 9
298.
1
99. 8
1
297.
1
tltfAI CV411
827.
1.
81.7
.1
•
fi'IAI CVTSt
t£T l1mS NET HHNETHH
1.
•
1.
1535.
1.
1805.
1.
2008.
•
1.
108.5
.1
297.
2382.
1.
2.
8. 51
1 17.0
296.
2682.
299 .
103.
103.
91 .
79.
4.42
8 . 82
1
125.2
I.
3.
2990.
308.
111.
111.
98.
88.
•
•
1
295.
Figure 1 2. - Sample yield table for total stand, stand over
5.55-inch d.b.h., and stand over 7.55- inch d.b.h.
31
D F S I ft VERSI
1.0
PA(i; 2
EXAtiPLE D F S I H I:EFAlU THI.,.ING OOTPUT WITH I'ERCHANTABLE VOI..U1'1E YIELDS
I'IANAGEII YIELD TABLE
FOR lnRAS-FIR
1. 6 INO£S PLUS
SITE INr£X
TOT BH
AGE AGE
YRS YRS
LOREY
HT
FEET FEET
HT40
YEARlY
TALITY
28 21
65. 5 60.3
YEARLY I'IORTALITY
29
22
YEARlY
30
30
23
23
IEFOOE
CUT
RESIDUfi..
4 . 61
2 .
1
CYTS CAI II'IAI CVTSI III'IAI CV4H
PER ta GROSS NET 11Ht£TIHI
ACRE CVTS 1 . 6+ 1 . 6+ 5.6+ 7 . 6+
•
4.
9. 12
133. 2
294.
3305.
4.79
9. 41
2
141 . 0
2.
6.
292.
3627.
TALITY
4 . 97
.3
2.
9.
70. 7
64. 9
9. 70
148 . 5
289.
70. 7
64. 9
9.70
9. 14
148 . 5
35. 5
289.
78.
932. 9.90
1 13. 1
212.
3020 . 35. 5
. 78.
1.2
11.
932.
29.
68. 1
70. 7
62. 6
65. 4
Al..I TY
•
•
316.
1 19.
1 18.
106
•
97.
322.
126.
125.
1 13.
105.
3952.
325.
133.
132.
120.
1 1 3.
3952.
325.
133.
132.
120.
1 13.
335.
139.
138.
126.
120.
334.
145.
144.
133.
127.
5.42
.1
o.
2.
10.27
1 21 . 5
21 1 .
3355 .
5. 54
.1
o.
2.
10. 61
5 . 75
129. 4
.1
211.
3690.
1.
3.
10. 93
5. 95
137. 0
.1
210.
1.
4024.
4.
335.
151.
150.
139.
134
74. 8
1 1 . 24
144. 2
209.
4360.
336.
157.
156.
144.
140.
.1
1 51 . 2
1.
77. 0
6. 1 5
1 1 . 52
209.
5.
4697.
336.
162.
161 .
150.
146.
6.35
.2
1.
6.
1 1 . 80
6.54
157. 9
.2
208.
5034.
7.
337.
1 67.
166.
155.
1 51 .
12. 06
164.3
5371 .
337.
172.
170.
159.
156.
6 . 72
12. 32
.3
170. 5
1.
9.
206.
5708.
337.
176.
175.
164.
160.
6 . 91
.3
1.
11.
12. 57
. 7 . 09
176. 5
.4
205.
6044.
336.
181.
179.
168.
165.
1.
13.
12. 82
182. 3
204.
6379.
335.
185.
183.
172.
169.
IEFORE
94. 2 87. 5 12. 82
CUT
10. 84
RESI DUAL 94 . 2 ss. o 13. 76
182. 3
204. 6379.
335.
185.
183.
172.
169.
45.6
136. 7
71 .
132.
31
24
73. 3
67. 8
YEARlY HOOTALI TV
32
25
75. 8
70.2
YEARlY HOOTALITY
33 26
78. 3
72. 5
YEARlY lllUALITY
34
27
YEARlY
35 28
YEARLY
36
29
80.7
Al..ITY
83. 1
Al.ITY
85. 4
79. 2
YEARLY HORTALITY
37
30
87. 7
81 . 3
YBlRI..Y HOOTAI..I TY
38
31
89.9
83.4
YEARlY rgTALI TY
39
32
92. 1
85 . 5
YEARlY HOOTALITY
40
33
40
33 94. 2
87. 5
Figure 1 2.-contin ued
32
125. (50 YEARS BIH
BASAl TREES
DBH MEA/A PER
INCH SQ FT ACRE
SIJt CUTS
SIJt rgTAI.. ITY
YEARLY
=
1.
207.
1643.
4736.
.
•
EXAI'IPLE
D F S I l't
PAC£ 3
VERSICW 1 . 0
D F S I " IEFAtl.T 1Hitf4ING OUTPUT WilH t£RCHANTABLE VQ..ll£ YIELDS
IWWED YIElD TABLE
FOO I:lWVIS-FIR
1 . 6 INCI£S PLUS
SITE INDEX
·
TOT
BH
AC£ AGE
YRS YRS
LOOEY
HT
HT40
FEET FEET
81. 1
·
TALITY
41 34
YEARLY
42 35
96. 3 90. 0
TALITY
98. 4 92.0
YEARLY
43 36
YEARLY
44
37
YEARLY
45 38
YEARLY
125. (50 YEARS DIU
3. 0
149
19.
•
7.84
.1
. . o.
14.09
143. 1
132.
8. 01
14.40
.1
149.2
o.
8.30
.1
100.4 94. 0
TALITY
14. 70
8.52
155. 0
.1
132.
102. 4
95 . 9
14. 98
160. 7
131.
TALITY
104.3 97. 8
8.73
15. 25
1
166. 2
131.
8. 95
.2
TALITY
ALITY
CVTS CAt · fi'IAI CYTSf fftfAI CY4n
PER t£T lJmS NET fHft£THH
ACRE CYTS 1 . 6+ 1 . 6+ 5.6+ 7.6+
BASAL TREES
DBH AREA/A PER
ACRE
ItDf 5Q FT
Slit CUTS Slit
TALITY YEARLY
=
•
.
2575.
90.
3
•
320.
188.
186.
175.
173.
318.
192.
189.
179.
176.
5690.
4.
316.
195.
192.
182.
179.
6004.
s.
314.
197.
195.
184.
182.
o.
313.
200.
198.
187.
184.
o.
6.
131. '6629.
7.
o.
312.
203.
200.
190.
187.
310.
205.
202.
192.
189.
309.
207.
205.
194.
192.
210
•
207.
196.
194.
132.
().
o.
5055.
3
· .
5373.
4.
6317.
46 39
YEARLY
106. 2 99.6
Tftl..ITY .
15. 52
9. 16
171 . 6
40
108. 1 101. 4
15. n
176. 8
130.
6939.
YEARLY
48 41
TALITY
109. 9 1 03. 2
9.37
16.03
.2
181 . 9
o.
9.
130.
7248.
9.58
.2
o.
10.
49 42 1 1 1 . 7 105. 0
YEARLY tmTALITY
16.27
9.78
186. 8
3
129.
1.
7555. . 3(}7
50 43 1 13. 5 106. 7
16. 52
191 . 6
129.
7861 .
306.
212.
209.
198.
196.
9.99
1.
128.
13. 8165. 304.
214.
21 1 .
200.
198.
47
YEARLY
YEARLY
51 44
TAl. lTV
TALITY
1 15. 2 108.4
.2
•
•
11.
16.76
.3
196 . 4
YEARLY ttOOTALITY
10. 20
.4
1.
52 45
YEARLY
116.9 1 10 . 0
ALI TV
16. 99
10.41
20 1 . 0
.4
128.
1.
8467.
17.
302.
216.
212.
202.
200. 53 46
300.
218.
214.
203.
201 .
297.
220.
216.
205.
203.
297.
220.
216.
205.
203. 15. 1 18.6 1 1 1 . 7
17.23
205. 5
127.
8767.
YEARLY
54 47
ALITY
120 . 2 1 13.3
10.62
17.46
.4
209. 9
1.
126.
19.
9064.
BEFOOE
120. 2 1 13. 3
17. 46
209. 9
fl:SIDUAL 120. 2 1 13. 7
41.5
168. 3
126.
38.
9064.
14. 19
18. 68
54 47 CUT i
'
.
Slit CUTS
SUit
TALITY
88.
1900.
7164.
122. 6
187.
4475.
6. 1
25.
217.
'
Figure 12. -cont i n ued
33
EXAMPLE
D F S I H
D F S I M
PAGE 4
VERSI
1.0
DEFAI..JLT THINNING OOTPUT WITH I'ERCHAHTABI..E V(LUME YIELDS
·
HANAGED YIELD TABLE
FOR IX.UJLAS-FIR
1 . 6 INCHES PLUS
SITE INDEX
=
125. <50 VEMS BH l
BASAL TREES
TOT BH
AGE AGE
HT40
YRS VRS
FEET FEET
INCH
YEARLY P'KJRTALITY
55 48 121 . 9 1 15. 4
CAl IP'IAI CVTSI
NET GROSS NET
CVTS 1 . 6+ 1 . 6+
Ht'¥U CV4H
fHfNETHI*
5 . 6+
7.6+
7469.
304.
221 .
217.
206.
204.
88 .
5.
n69.
301 .
223.
219.
208.
206.
o.
6.
183. 4
88.
224.
220.
209.
207.
o.
8066.
7.
297.
.2
188. 2
88.
8361 .
294.
225.
22 1 .
210.
208.
o
8.
8652.
9.
292.
227.
222.
212.
210
PER
CVTS
PER
SQ FT
ACRE
ACRE
1 3 . 85
1 8 . 98
.1
1 73. 5
o.
4.
88.
YEARLY fiJRTALITY
56 49 123. 4 1 17. 0
14. 12
19.27
.1
1 78 . 5
o.
VEARLY IOUALITY
14.39
.1
57 50
YEARLY
125. 0 1 18. 5
TALITY
1 9 . 54
14.66
126. 5 120. 1
19. 81
YEARLY
TIUTY
59 52 128.0 121 . 6
YEARlY I'DmV ITY
1 4 . 92
20.07
15. 18
2
1 92. 9
60 53 129.5 123. 0 20. 32
YEARLY IOUALITY
15. 43
61 54 131 . 0 124 . 5 20 . 57
1 97 . 4
.2
201 . 9
88.
YEARLY P'llRTAl.ITY
62 55 132.4 125. 9
15. 69
20.81
.2
206. 3
o.
87.
YEARLY
15. 94
.3
o.
58
51
LOREY
HT
...
TALITY
DBH AREA/A
•
.2
•
88 .
0.
8941.
10.
289.
228.
224.
213.
21 1 .
o.
87.
9228.
287.
229.
225.
214.
212.
11. 9513. 285.
13.
230.
226.
215.
213. 63 56
YEARLY
133.8 127. 3
TALITY
21 . 05 210. 5
16. 1 9
.3
87.
0.
9796.
14.
283.
231 .
227.
216.
214.
64 'ST
135. 2 128. 7
21 . 29
214 . 8
87. 10076.
280.
232.
227.
216.
215.
YEARLY
65 58
TALITY
136.6 130. 1
16. 44
21 . 52
.3
218. 9
278.
233.
228.
217.
215.
16.68
.4
1 37 . 9 131 . 4
TAl. lTV
21 . 74
16. 93
86. 1 0630.
o.
19.
276.
234.
229.
218.
216.
139. 2 132. 7
21 . 97
222. 9
.4
226. 9
86. 10903.
274.
235.
230.
219.
217.
TALITY
1 40 . 5 134.0
17. 18
22. 1 9
.4
230. 9
271 .
236.
230.
219.
217.
¥EARLY tllRTAl.ITY
66
59
VEARLY
67 60
YEARLY
68 61
VEARLY
TALITY
63
•
5
15.
87. 10354.
o.
17.
o.
21 .
86. 1 1 175.
o
•
22.
86. 1 1443.
o.
24.
85. 1 1709.
269.
236.
231 .
220.
218.
143. 1 136.6
234. 7
5
22. 63 238. 5
266.
237.
231 .
220.
219.
143. 1 136. 6
22 . 63
238. 5
85. 1 1709.
266.
237.
231 .
220.
219.
69 62 141 . 8 135. 3
YEARLY I'K'JRTALITY
70
17.43
o.
22. 41
17.67
•
70 63
BEFORE
CUT
RESIOOAL 143. 1 1 36.8
SIJ1 CUTS
SIJ1 tllRTALITY
F i g ure 1 2. -cont i n ued
34
18.82
38 . 5
23.67 200. 0
20.
65.
2025.
9684.
161 . 1
10. 4
207.
28.
6500.
422.
EXAMPLE
D F S I If
D F S I ·If VERSION 1 . 0
· PAGE 5
JHAULT THitf.IING OUTPUT WITH ftERCHANTABLE IJOLUI£ Ylfl.DS
MANAG£0 Ylfl.D TABLE
FOR OCWLAS-F IR
1. 6 INCHES PLUS
SITE INIEX
TOT
BH
AGE AGE
YRS YRS
HT40
FEET
LOREY
HT
FEET
=
125. !SO YEARS ao
PASAI.. TREES
DIIH AREA/A PER
ACRE
INCH SQ FT
CVTS
CAl
ft!AI CVTSt
fftfAI CV4n
PER t£T GROSS NET fHINETnn
ArnE CVTS 1 . 6+ 1 . 6+ 5.6+ 7.6+
YEARLY I'IORTALITY
71 64 144 . 3 138. 2
23. 95
1
204 . 5
65.
7
9967.
283.
238.
232.
221 .
219.
YEARLY MORTALITY
72 65 1 45 . 5 1 39 . 4
19. 06
24. 22
2
208. 9
9
o.
65. 10244.
277.
239.
233.
YEARLY I'IORTALITY
220.
273.
239.
233.
222.
221 .
270.
240.
234.
223.
221.
VEARlV tllRTALITY
75 68 149. 1 143. 1
19.36
.2
24. 49 213. 3
19.65
2
24. 75 217.5
.2
19. 94
25 . 01 221 . 7
222.
267.
240.
234.
223.
222.
YEARLY lmTALITY
20. 23
.3
76 69 150. 2 144. 3
YEARLY I'IORTALITY
25. 26
20 . 51
225.8
.3
264.
241 .
234.
224.
222.
151 . 4 145 . 5 25. 51
·
73 66 146. 7 140 . 7
YEARLY MORTALITY
74 67 147 . 9 141 . 9
18. 76
•
•
•
o.
•
•
0.
10.
65. 10517.
o.
11
65. 10787.
•
0.
12.
65. 1 1054.
o.
13.
65. 1 1318.
14.
o.
229.8
65. 1 1 580.
261 .
241 .
235.
224.
222.
YEARLY tllRTALITY
78 71 152. 5 1 46 . 6
20:80
25 . 76
.3
233. 8
0.
15.
65. 11839.
259.
242.
21 . 00
.3
235.
224.
YEARlY tmTALITY
223.
17.
79 72 153. 6 147. 7
YEARLY tllRTAI.. lTV
26. 00
21 . 37
237 . 7
.3
256.
242.
235.
224.
223.
1 54.7 148 . 8 26. 23
241 . 5
64. 12349.
254.
242.
236.
225.
223.
154. 7 1 48 . 8
241 . 5
64. 12349.
254.
242.
236.
225.
223.
402. 6
271 . 18849.
549.
29.
n 70
80
73
o.
64. 12095.
o.
18.
00 73
HARVEST
Slft CUTS
sutt I'IORTALITY
26. 23
12. 9
Figure 1 2.-cont i n u ed
35
EXIIfRE
D F S I I1
YERSIM 1 . 0
PAGE 6
D F S I 11 DEFIU.T THIPMI"' OOTPUT WITH I'ERCHIWTABLE IIOU.tE YIELDS
fiANA(E) YIELD TABLE
oo.o.AS-FI R
F
5. 6 INCf£S PLUS
SITE INDEX
=
125. (50 YEARS BHl
TOTAL.
CUBIC FEET
BASAL AREA TREES
PER ACRE
PER CUBIC FEET PER ACRE
ACRE PER ACRE 4-It«:H T(F
INC1£S SQ. FT.
DBH
TOTAl rf£
30.
BEFOOE
CUT
RESIIXIAL.
10. 3
9.4
10.7
stt1 CUTS
sttl tml'Al.ITY
TOTAl AGE
1 2. 9
11.0
RESIIXIAL.
13. 8
stt1 CUTS
sttl IU«Al.ITY
35.2
74.
916.
10.
835.
182.0
45. 5
136. 5
200.
6364.
69.
6042. 1530.
131 .
1635.
4729.
80. 7
143.
2552.
2765.
4512.
2364.
47.
17. 5
14. 2
18. 7
RESIOOAL
sttl CUTS
Stlt tmTALITY
209. 9
41 . 5
168. 3
126.
9064.
8702.
38.
88 .
1900.
7164.
1814
6887.
122. 2
181 .
4452.
4178.
•
156.
70.
IEFOOE
22. 6
238. 5
85.
1 1 709.
CUT
RESIOOAL
18. 8
23.7
38. 5
200. 0
20.
65.
2025.
9684.
1 1241 .
1944.
9296.
160.7
201.
Mn.
6123.
SU1'1 CUTS
Figure 1 2.-continued
36
3881 .
916.
2965.
54.
BEFORE
CUT
TOTAL AGE
249.
74.
176.
40. BEFORE
CUT
TOTAL rf£
3600.
835.
145. 0
35. 2
109.8
.
EXA!tli D F S I "
PAGE 7
D F S I " YERSI
1.0
IEFAllT THitfut«J OOTPUT WITH tEROWflABLE VOUJE VIB.DS
PIAtWD YIELD TABLE
FM OOB..AS-F IR
5. 6 It«:t£S Pl.US
SITE INIEX
=
125. {50 YEARS an
TOTAL
CUBIC FEET
BASAL AREA TREES
PER ACRE
PER CUBIC FEET PER ACRE
INCt£S SQ. FT.
ACRE PER ACRE 4-It«:H T<P
DBH
362.
Slti i'KRTALITY
TOTAL Af£
80. HARVEST
26. 2
StJ1 CUTS
SLtl roiTAL ITY
241 .5
64.
12349. 1 1855.
402. 3
265.
18826. 17978.
488.
Figure 12.-continued
37
EXAMPLE D F S I "
PAGE 8
D F S I 11
VERSitJ4 1 . 0
DEFAllT THI ING MPUT WITH tfERCHANTABlE VCMJJ£ YIELDS
MANAGED YIELD TABLE
FOO OO.WS-FIR
7.6 INO£S PLUS
SITE INDEX
TOTAl AGE
BASAL
AREA TREES
PER ACRE PER
DBH
INCI£S SQ. FT. ACRE
CVTS
CV4
CV6
IV6
SV6
11.0
10. 1
11.3
CUT
RESIWAI..
Sltl CUTS
Sltl PmTAI.. ITY
13.2
11.5
R£SIWAI..
14. 0
Sltl CUTS
Sltl l'llRTAI.. I TY
202.
3525.
3384.
2973.
819.
2707.
762.
2622.
637.
2336.
1 5723.
3402.
12321.
1 1829.
56.
146.
31 . 0
Sb.
819.
3.
762.
637.
3402.
2502.
178. 9
43. 7
135. 2
188.
60.
127.
6268.
1574.
4693.
5987.
1486.
5593.
33292.
1347.
791 1 .
4501 .
4246.
25380.
2718 1 .
6155.
21025.
74. 7
1 16.
2393.
2248.
1 984.
1 1314.
8657.
4n2 1 . 2502.
9327.
18.
54. BEFOOE
17. 5
9064.
8702.
8498.
54796.
14. 2
209 . 9
41 : 5
126.
CUT
38.
1900.
1814.
1758.
1 1 125.
9309.
RESIWAI..
18. 7
168. 3
88.
7164.
68S7.
6740.
43671 .
38412. 1 16.2
154.
4293.
4062.
3742.
22439.
17966. Sltl CUTS
Sltl l'llRTAI.. I TY
TOTAl AGE
84.
70.
BEFORE
22.6
238. 5
85. 1 1 709. 1 1241 .
1 1 128.
756bb.
68609.
CUT
R£SIWAI..
18.8
23. 7
38.5
200.0
20.
65.
2025.
9684.
1944. . · 1925.
9296.
9203.
12953.
62713.
56829.
154. 7
1 74.
6318.
6007.
35392.
29746.
stJI CUTS
Figure 1 2.-continued
38
133. 3
31.0
1 02 . 3
40.
BEFOOE
CUT
TOTAl AGE
125. C50 YEARS BH>
30.
BEFOOE
TOTAl AGE
=
561J7.
1 1780.
D F S I Jll
EXAMPLE
PAGE
YERSICW 1 . 0
9
D F S I Jll DEFAllT THINNING OUTPUT WITH PERCHANTABI..E VOUJE YiaDS
tW4AGED YiaD TABLE
FOR 11001AS-fiR
7. 6 INCI£S PLUS
SITE INDEX
=
125. (50 YEARS BtU
BASAL
AREA TREES
DllH PER ACRE PER
INl£5 SQ. FT. ACRE
CVTS
299.
stJf I'KIRTAL ITY
TOTAL AGE
CV4
CV6
IV6
SV6
241 . 5
64. 12349. 1 1 855.
1 1737.
81822.
75523.
396. 2
238. 18667 . 1 7862.
00.
HARVEST
26. 2
stJf CUTS
stJf I'KIRTALITY
1 7403. 1 1 7214. 105270.
416.
Figure 1 2 . - continued
Stand Type Options-The stand type option is selected with the variable EXIST
[0, 6]8 on the Master Control Card. Most simu lations w i l l be for the reg ional
"average" stand for the site and stand history. To simulate the regional
"average" stand, the variable EXIST [0, 6] i s left blank or coded a zero. The
second type i s the existing stand. To s i m ulate an existing stand, the variable
EXIST [0, 6] is coded 1 and card type 1 is also used. All remai n i n g options apply
to both the reg ional "average" stand and an existing stand.
Juvenile Stand Hi story Options-The four j uveni l e stand h istory options are
(1 ) natu ral ori g i n or seeded stands without precommercial thi n n i ng , (2) n atural
ori g i n or seeded stands with precommercial thi n n i ng, (3) planted stands without
p recom mercial thi n n i ng, and (4) planted stands with precomm erc ial th inning.
The p lanted stand h i story opti o n is selected by coding the vari able IORG
[0, 2] as 1 . Precom m ercial t h i n n i ng i s sel ected by cod i ng the variable PCT
[0, 3] w ith the total stand age at the t i m e of precommercial thinn i ng . The
variable TAST [0, 4] serves a dual purpose: If the stand is planted and
precom mercial thinning is not selected, then TAST [0, 4] is coded with the
n u m ber of establ ished seed l ings per acre; if the stand, either natural or planted,
i s precom mercially thi n ned, then TAST [0, 4] is coded with the n um be r of
resi d ual trees per ac re after t h i n n i ng. O n ly one precommercial thinning can be
done. The remai n i ng opt ions apply to a l l juvenile stand histories.
j
1
8The notation [0, 6] means the sixth variable on the Master
Control Card; the notation [1, 3] means the third variable on
card type 1, etc. Card types and variables are discussed i n the
next section, "Control Card Formats."
39
No Commercial Thi n n i ng Option-If a simu l ation i s w ithout commerc ial
thi n n i ng, the variable I UT [0, 7] i s coded a 1. Thi s cod i n g w i l l suppress all
commercial thi n n i ng, even i f commercial thi n n i ng has been sel ected by opt ions
to be di scussed l ater. If a natural stand without precommerci al thi n n i ng i s
bei n g s i m u l ated w ithout commercial thi n n i ng, the resu lt w i l l b e a "normal "
y i e l d table. Thi s "normal" y i e l d table represents the average o f the untreated
plots in our data set and should not be i nterpreted as the "average" w i l d stand.
Compari sons between this "n ormal" stand and treated stands do not represent
the pote ntial gains from management.
Commercial Thinning Timing Options.- There are four opt ions for t i m i ng
commerc ial thi n n i n g . Two spec ify i ntervals i n years and in feet of hei ght
growth, and two specify stand ages and hei ghts. Only one t i m i ng option can be
sel ected for each s i m u l ation. I f no t i m i ng options are sel ected, D FSIM does a
defau lt thi n n i ng . If a thi n n i ng i nterval i n years is wanted, then the variable Tl
[0, 10] is coded with the m i n i m um number of years between com merc i al
thi n n i n gs.9 If a thi n n i ng i nterval in feet of height growth i s wanted, then the
variable DH [0, 14] i s coded with the m i n i mum n u m ber of feet of height growth
between thi n n i ngs. If thi n n i ngs are wanted at specific ages or heights then the
variable CTAS [0, 12] or SCTHT [0, 16] is coded a 1, and card type 2 or card
type 3 is u sed to specify those ages or heights.
Type of Commercial Thinning Options.-Three opt ions are ava i lable for
contro l l i ng the type of com mercial thi n n i ng to be done and res u l t i ng attri butes
of the residual stand. The options are (1) specified rat ios of average diam eter of
cut trees to average d i ameter of l ive trees before thi n n i n g (diD), (2) speci fied
resi dual basal areas (G R ES D), and (3) speci fi ed residual n u m bers of trees
(TAR ESD). Any one or two of these opt ions can be u sed w ith any of the other
options discussed el sewhere. Or none need be u sed. If all three options are
specified, then G RESD and TARESD w i l l be used and diD w i l l be i g nored by
DFSI M .
I f speci fi ed diD i s wanted, then the variable I D R [0, 18] i s coded as 1 or 2 . I f
coded a s 1, then the fol lowi ng restriction o n diD w i l l b e i mposed b y DFSIM:
0.80
:5
diD
:5
1.15
If 2 i s coded, DFSIM w i l l not i m pose the above rest riction and the user m ust be
especi al ly careful about speci fying reasonable diD. If I D R [0, 18] i s coded as
1 or 2, then card type 4 i s used to specify the diD.
·
I f specif ied G R ESD is wanted, then the variable IGS [0, 19] is coded as 1 and
card type 5 is u sed to specify the G RESD.
If specif i ed TARESD is wanted, the n the variable LTREE [0, 20] is coded as 1
and card type 6 i s u sed to specify the TAR ESD.
9-Jhe variables FlY [0, 1 1 ] and F I H [0, 1 5] are used if the i nterval
from the last commercial thinning to the final harvest cut is
d ifferent from that spec i f i ed by Tl [0, 1 0] and DH [0, 1 4]
respectively.
40
G i ven the stand attributes before t h i n n i n g , then any two of the three options­
diD, GRESD, and TARESD -defi nes the val ue of t h e t h i rd . I f only diD or
TA RESD i s speci f ied, t hen GRESD is defi ned by DFSIM u s i ng the default
equation g i ven i n appendix 3. I f only G R ESD i s sp ecified, then diD is defi ned by
D FS I M using the default equat ion gi ven in appe nd i x 3. If none of the opt io ns
diD, GR ESD, or TARESD are selected, then both the default equations above
wi l l be used by DFSI M .
Number of Commercial Thinnings Option.- The n u mber o f commercial
t h i n n i ngs can be control led in several ways. First, t h e maxim um number of
comm erc ial t h i n n i n g s can be spec ified on the Master Contro l Card by cod ing
the vari able N CT [0, 8] with t he num ber of t h i n n ings wanted. The n u m ber of
t h i n n i ngs is automat ical ly i m p l ied by the n u m ber of entries on card type 2 or 3
if one of them is u sed . If N CT [0, 8] is coded zero or left blan k, or the n u mber of
t h i n n i ngs i s not i m pl ied by card type 2 or 3, then DFSIM sets a default
max i m u m of 15, the max i m u m al lowabl e.
Final Harvest Cut Timing Options.- The stand age at the f i nal harvest cut i s
usually cod ed i n vari able AHARA [0, 13] o n t h e Master Con trol Card. T h e t i m e
o f f i nal harvest can be specified b y stand height by cod i n g the variable
HTH ARV [0, 17] with the stand height at the t i m e of t h e f i nal harvest cut. I f
A H AR A [0, 13] o r HTH ARV [0, 17] i s not coded and card type 2 o r 3 i s u sed,
then the last entry on card type 2 or 3 determ i nes when the fi nal harvest cut i s
made.
If the age at fi rst com mercial t h i n n i n g has bee n coded (a) in the variable FCT
[0, 9] and (b) N CT [0, 8] and Tl [0, 10] or DH [0, 14] have been coded and (c)
A H AR A [0, 13] or HTH ARV [0, 17] has not been coded and (d) card type 2 or 3
has not been used, then the t i m i ng of the f i nal harvest cut i s determ i ned by the
fo l l ow i ng form ula dependi ng u pon whether Tl [0, 10] or D H [0, 14] was
speci fied:
1. Tl [0, 10] only spec ified: AH ARA
( N CT
+
2. Tl [0, 10] and FlY [0, 11] speci fied: AHARA
1) (TI)
=
+
FCT
(NCT) (TI )
+
FCT
+
FlY
3. D H [0, 14] on ly spec ified: HTHARV = ( N CT + 1) (DH) + H FCT; where
H FCT = stand height at first comm ercial t h i n n i ng i m p l i ed by FCT [0, 9]
4. D H [0, 14] and F I H [0, 15] spec ified: HTHARV
=
(N CT) (DH)
+
H FCT
+
FIH.
I f DFS I M can not determ i ne a t i m e for the fi nal harvest cut from the
specifications, then i t sets a default value of 100 years.
41
Fertilizer Options.- There are two options for speci fying the t i m i n g of n itrogen
fert i l izer. If the variable FERTCT (0, 24] is coded as 1 or 2, the fert i l izer i s
appl i ed only at ti mes o f com mercial thi n n i ngs. I f the variable FERTAS [0, 25] is
coded as 1 or 2, then fert i l izer is appl i ed at ages speci f i ed by the user. Both
opt ions req u i re the u ser to specify the pou nds of n itrogen per acre appl i ed at
each fert i l ization on card type 7. If FERTCT [0, 24] has been coded and fert i l izer
i s not to be app l i ed at a speci fi c com mercial thi nni ng, then the n u m ber of
pounds of n itrogen coded on card type 7 for that thi n n i ng . wou l d be zero. I f
FERTAS [0, 25] i s coded, then the ages when fertil izer i s applied must a l s o be
speci f ied on card type 7. D F S I M can hand l e only one fert i lization pri or to the
stand reachi ng 5.55- i nch d. b.h.
Observed Height/Age Trend Option.- DFSIM uses the height/age trend
developed by Bruce (see footnote 4) and presented i n Appendix 3. If another
trend is wanted, then the variable lOBS [0, 5] is coded as 1 , 2, 3, 4, or 5 and
card type 9 is used to speci fy the wanted height/age trend.
Output Options.- DFS I M al ways produces a yield table for trees 1 .55-i nch d. b.h.
and l arger. If yield tables are wanted for the stand components 5.55-i nch and/or
7.55- i n ch d . b.h. and l arger, the variable I MV [0, 26] is coded as 1, 2, or 3
depe n d i n g upon which add it ional yi eld tables are wanted.
DFSIM always produces stand statist i cs at the t ime of commercial cutt ings for
trees 1 .55-i nch d.b.h. and larger. If stand stat i stics are wanted at other t i m es for
trees 1 .55-i nch d.b.h. and l arger, then the vari able N RA [0, 27] is coded as
1 , 2, 3, 4, or 5. I f N RA [0, 27] is coded as 1 , 2, 3, or 4, then card type 8 is used to
speci fy the ages when stand statistics are to be printed. If N RA [0, 27] is coded
5, then stand statistics w i l l be printed for every year of the s i m u lation and card
type 8 i s not u sed.
Control Card Formats
42
The spec ificat ions for one D F S I M s i m ul ation are presented to the computer
through a spec i al deck of cards (or card i m ages) cal led a contro l deck. Each
card i n the control deck contains spec ific i n formation about the s i m u l at i on and
is arran ged i n a defin ite format. Several s i m u l ations can be ru n consecutively
by stacki ng control pecks. Control decks are not separated by end-of-record or
end-of-file cards. The last card for any job, whether for one s i m u l ation or a set
of consecut ive s i m ulation s, m u st be a card w ith E N D i n col u m n s 1-3. The END
card s ignals D F S I M that all control decks have been processed and control i s
retu rned t o the computer system .
Each type of control card i s d escribed i n this section. The descri ption i ncl u des
the format, the i nformation it m ust contai n, and, where appropriate, the purpose
and use of the i nformation. This section may be used both as a detailed l i st of
i nstructions for cod i n g the s i m ul ation spec ifications, and as an outline to
fol low so the specifi cations are complete. Control cards are d i sc ussed in the
order they m ust appear in the control deck. N ot all control cards are necessary
for each sim u lation, but those used must be i n their proper positions w i t h i n the
contro l deck. The variable KRD, card type, and the conti nuation code, when
appropriate, are i n c l u ded o n each optional card type for the user's conven ience
in ordering the contro l deck. Fol l owing the Title Card and the M aster Control
Card, all opt ional control cards in the deck are placed in ascendi n g order by
card type and conti n u ation codes. The Title Card and the M aster Control Card
m u st be i n all control decks. The use of addit ional control cards depends o n
specifications made on t h e M aster Control Card.
Title Card.- The f i rst card i n each DFSI M control deck is the Tit l e Card. It m ust
be present even if l eft blank. The Title Card carries a title suppl ied by the
user which i s pri nted at the top of each page of the yield table. Up to 80
characters can be u sed. The title shou l d be centered on the card for proper
posit ioning on the pri nted yield tab le.
Variable Name
Format
Colu m n s
Contain
!TITLE
20A4
1 -80
AAA . . . A Up to l30 al phameric characters,
g iving a descri ptive title for the
simu l ation. The word END
cannot appear in the f i rst three
col umns because this word is
reserved for the l ast card of a
job and signals DFSIM that al l
control decks have been
processed.
Explanation
Master Control Card.- The second card i n each D FSIM deck is the M aster
Control Card. T h i s card speci fies the s i m ul ation. Opt ions sel ected determine
wh ich, i f any, add itional control cards are needed i n the deck for the
s i m u l ation. There are four types of parameters on the M aster Control Card:
stand, cutting (t h i n n i n g and harvesti n g), fert i lization, and output. Stand
parameters establ i sh i n itial condit ions. Cutt i ng parameters determ ine t i m i ng
and type of cutting to be done. Fertil ization parameters determ ine t i m i n g and
quantity of n it rogen fert i l izer appl i ed. Output parameters determi n e types of
yield t ables and amounts of i n formation to produce .
.
4 .
43
· sTAN D PARAMETERS
Variable Name
Format
Columns
Contain
Explanation
Sl
. F3.0
1 -3
xxx o
Site i ndex (based on breast
height at age 50).
Blank
1X
4
b1 1
Blank.
IORG
11
5 .
0 or b ·
1
Nat u ral or seeded stan d.
Plantation.
Blank
1X
6
b
Blank.
PCT
F2.0
7-8
XX,
Total stand age at time of
p recommercial thinning, i f
stand i s to b e precommercially
th i nned.
Blank
1X
9
b
Bl.ank.
TAST
F4.0
1 0-1 3
xxxx,.
N u m ber of trees per acre after
precommercial thinning or
n umbe r of established seed­
l i ngs i n a p l antation @!!_ trees
regardl ess of d iam eter).
Blank
1X
14
b
Blank.
l OBS
11
15
0 or b
N o observed heights cards are
i n contro l deck. Bruce's (see
footnote 4) height c urves are
u sed.
Bruce's h e i g ht cu rves are n ot to
be u sed. Height/age relationship
to be s peci fied on one card
type 9.
1
Blank
1X
16
2
Bruce's height curves are not to
be u sed. H eight/age re lationship
to be specified o n two card type
9's.
6
Bruce's h e i g ht curves not to be
u sed. Heig ht/age rel ationship
s pecified o n six card type 9's.
b
Blank.
10rhe notation XXX. , in the contain column means three
numeric characters with implied decimal point at the end.
XX,XX means four numeric characters with implied decimal
point in the middle. This notation is used throughout the
remaining discussions.
11The notation b in the contain column means blank.
44
STAN 0 PARAMETERS-Continued
Variable Name
Format
Columns
Contain
Explanation
EXIST
11
17
0 or b
An "average" stand is to be
s i m u l ated.
An existing stand is to be
simulated beg i n n i ng at a userspecified total stand ag e,
quad rati c mean diameter, basal
area, and n u mber of trees. For
stand s with q uadratic mean
d iameter in the range of 1.6· to
5.6-in c h d.b.h., it is only
necessary to know the n umber
of stems and age. One card
type 1 is i ncl uded in control
deck.
1
'I '\1.
Blank
1X
18
b
Blank.
C UTTING PA RAMETERS
Variable Name
Format
Columns
Contain
Explanation
I UT
11
19
0 or b
Commercial thinni n g to be
d one.
No commercial t h i n n i ng to be
done, even though co mmercial
thinni ng is specified on other
options. Th i s prod uces a
" normal " y ield table if a nat u ral
"average," untreated stand i s
simulated.
1
·'
Blank
1X
20
b
B lan k.
N CT
12
21-22
1 f12
Max i m u m number of
com mercial thinnings. If left
blank or coded zero, and if the
n u m ber of commercial t h i n­
n ings has not been i m p l ied on
card types 2 or 3, a defau lt
maxi mum of 15 commerci al
thinni ng s i s assi g ned .
Blank 1X
23
b
Blank.
FCT F2.0
24-25
XX
Blank 1X
26
b
A
Earli est possible total stand age
for a commercial t h i n n i ng .
B lank.
12-rhe notation I I i n the contain column means a two-digit
i nteger field.
45
CUTIIN G PARAMETERS-Continued
Variable Name
Format
Columns
Contain Explanation
Tl
F2.0
27-28
XX M i n i m um n u m be r of years
between commerc i al thi n n i ngs.
Blank
1X
29
b
Blank.
FlY
F2.0
30-31
XX B lank
1X
32
b
Blank.
CTAS
11
33
0 or b
Com mercial t h i n n i n g ages are
not to be specified. No card
type 2 i n control deck.
Commercial t h i n n i n g ages
specified on card type 2.
'
N um be r of years from last
. commerc ial thi nn i n g to final
harvest cut, i f different from Tl
above.
'
1
Blank
1X
34
b
AHARA
F3.0
35-37
XXX
Blank
1X
38
b
DH
F2.0
39-40
XX
Blank
1X
41
b
FIH
F2.0
42-43
XX N um ber of feet of stand top
height g rowth from last
commerc i al th i n ni n g to final
harvest cut, if different from D H
above.
Blank
1X
44
b
Blank.
SCTHT
11
45
0 or b
Commercial thi n n i n g heights
are not to be specifi ed. No card
type 3 i n control deck.
Com mercial thi n n i ng stand top
heights to be specified on card
type 3.
Blank.
.
Blank.
M in i m um number of feet of
stand top height g rowth
between commercial t h i n n i ngs.
A
Blank.
A
1
46
Total stand age at time of final
harvest cut.
Blank
1X
46
b
HTHARV
F3.0
47-49
XXX
B l ank
1X
50
b
Blan k. A
Stand top height at time of final _
harvest cut.
B l ank.
CUTTING PARAMETERS - Continued
Variable Name
Format
Columns
Contain
Explanation
IDR
11
51
0 or b
Ratios of d i ameter of cut trees
to d i ameter live stand; before
t h i n n i n g (d/D) are not be
specified. No card type 4 i n
c ontrol deck.
d/D to be specified on card type
4.
d/D to be s pec ified on card type
4. d/D can exceed l i m its of 0.80
:::;; d/D :::;; 1 . 1 5.
1
l
'!I'
2
Blank
1X
52
b
Blank.
IGS
11
53
0 or b
Basal area residuals are not t o
b e spec ified f o r each com­
mercial th i n n i ng . No card type 5
i n contro l deck.
Basal area resi d uals are to be
s pecified for each commercial
t h i n n i n g on card type 5.
1
Blank
1X
54
b
B lank.
LTREE
11
55
0 or b Residual n u m ber of trees i s not
to be s pecified for each com­
m ercial th i n n i ng . No card type 6
i n control deck.
Residual n u m ber of trees for
each com mercial thi n n i ng to be
speci f i ed on card type 6.
1
Blank
1X
56
b
Blank.
DUM
F3.1
57-59
XX X
M in i m u m q uadratic mean
d i ameter of trees removed i n
commercial thi n n i ngs. If this
field i s l eft blank o r coded zero,
a defaul t val ue of 8.0 i nches i s
assigned.
Blank
1X
60
b
B l ank.
GCLIM
F2 0
61 -62
XX
.
A
M in i m u m basal area to be
removed for com m erc ial
thinni ng. If l eft blank or coded
zero, a default val ue of 20.0 is
assigned.
47
CUTTING PARAM ETERS-Continued
Variable Name
Format
Columns
Contain Explanation
Blank
1X
63
b
B lank.
GUM
F3.0
64-66
XXX "
M i n i m u m basal area needed i n
l ive trees 5.6-i nch d.b.h. and
larger before first commerc i al
th i n n i ng can be done. I f left
blank or coded zero, a defau lt
val ue of 1 00.0 i s assigned.
Variable Name
Format
Columns
Contain
Explanation
Blank
1X
67
b
B l ank.
F ERTCT
11
68
0 or b Stand not to be fert i l ized at t i me
of com mercial thi n n i ngs.
Stand to be fert i l ized at time of
commercial th i n n i ngs. N umber
of pounds of ni trogen applied at
each commercial t h i n n i n g to be
specified on one card type 7.
Stand to be fertil ized at t i me of
commercial t h i n n i ngs. N u m ber
of pounds of n itrogen appl ied at
each commerc i al t h i n n i ng to be
specified em two card type 7's.
FERTI LIZATION PARAMETERS
1
2
Blank
F ERTAS
X
11
69
b
B lank.
70
0 or b Stand not to be fert i l ized at
spec ified stand ages.
Stand to be fert i l i zed at
specified stand ages. Ages and
n umber of pounds of n i trogen
for each appl i cation to be
s pecified on one card type 7.
Stand to be fert i l ized at
specified stand ages. Ages and
n u m ber of pounds of n itroge n
for each application to be
specified on two card type 7's.
1
2
Blank
48
1X
71
b
B l ank.
OUTPUT PARAM ETERS
Variable Name
Format
Col umns
Contain
Explanation
IMV
11
72
0 or b
Prin t yield tabl e for 1 .6-inch
d.b.h. and l arge r stand
component only.
Print yield tab l es for 1 .6-inch
d.b.h., and 5.6-i nch d.b.h., and
7.6-inch d.b.h. and larger stand
components.
Pri nt yield tabl e s for both
1 .6-i nch d.b.h. and 5.6-inch
d.b.h. and larger stand
components.
1
"'
2
3
Print yield tables for 1 .6-i nch
d.b.h. and 7.6-i nch d.b.h. and
larger stand components.
Blank
1X
73
b
B lank.
N RA
11
74
0 or b
Stand stat i stics to be printed
only at times of cutting. N o
card type 8 ' s t o b e incl uded i n
control deck.
Stand statistics to be pri nted at
spec ified report ages, p l u s at
times of cutting. Report ages to
be specifi ed o n one card type 8.
Stand statistics to be p ri nted at
specified report ages, p l us at
times of cutting. Report ages to
be specif ied on card type 8's.
1
2
4
5
Blank
..
..
6X
75-80
b
Stand stat i st ics to be printed at
s pecified ages p l us at t imes of
cutting. Report ages to be
s pecified on four card type 8's.
Stand statistics to be printed
for every year of t he s i m ul ation.
N o card type 8's to be i n c l uded
in control deck.
B lank.
Existing Stand Card (Card Type 1).-The Exist i ng Stand Card i s used to begi n a
s i m ul ation at a specific total stand age for an exist i ng stand. It i s u sed only i f
stand parameter EXIST [0, 6] o n the M aster Control Card, colu m n 1 7, i s coded 1 .
I t establ i shes i n itial exist i n g stand conditions.
49
There are two primary ways to use the Exist i ng Stand Card. First, if (a) the
n u m ber of stems is known at the desi red i n itial age, and (b) basal area or
quadrat ic mean stand diameter are u n known , are i m p recisely estimated, or
un usual i n relation to the age/height relationsh ip, or (c) if stand top height i s
l e s s than 3 0 feet, t h e n only t h e a g e a n d n u m ber o f stems i s coded. Second, if
(a) the quadratic mean stand d iameter and/or basal area i s known and i s not
un usual in re lation to the age/height relationship, and (b) stand top height is
g reater than 30 feet, then age and any two of the three variables SOIA [1 , 2],
S BA [1 , 3], and STA [1 , 4] can be coded.
If o n l y age and n u m be r of trees are spec ified, then q uadrat ic mean stand
di ameter is determ i ned using the equation presented i n appendix 3 for In D.
Th i s use of the Exist i ng Stand Card shou ld not be made when the stand top
. height exceeds approxi m ately 80 feet.
Variable Name
Format
Columns
Contain
Explanation
SAGE
F3.0
1 -3
XXX
Total stand age at beg i n n i n g of
s i m ul ation.
Blank
1X
4
b
S OIA
F4.2
5-8
XX XX Quadratic mean stand di ameter
at beg i n n i n g of simul ation for
trees 1 .6-i nch d.b.h. and larger.1 3
Blank
1X
9
b
B l ank.
SBA
F4.1
1 0- 1 3
xxx.x Basal area per acre at beg i n n ing
of simul ation for trees 1 .6-i nch
d.b.h. and larger.
Blank
1X
14
b
Blank.
STA
F5.0
1 5-1 9
XXX XX
Blank
59X
20-78
b· . . b
B l an k.
KRD
11
79
1
Card type.
I CO NT
11
80
0
Not a cont i nuation card.
B l ank.
'
13AII trees, regardless of d.b.h., for planted and pre·
commercially thinned stands.
50
'
A
N um ber of trees per acre at
beg i n n i ng of s i m u l ation for
trees 1 .6-inch d.b.h. and larger.
2).- The Speci f ied
'
Com me rcial Thi n n i n g Age Card is used w hen t tie cutt i ng parameter CTAS [0, 1 2]
on the M aster Control Card, col u m n 33, is coded 1 . It is used whenever
commercial th i n n i ngs are wanted at specific stand ages. If harvest ag e (A HARA
[0, 1 3]) was not speci fi ed on the Master Control Card, col u m ns 35-37, then the
harvest age m ust be the last age spec ified on card type 2. Up to 15 commercial
t h i n n ing ages can be speci fied.
Specified Commercial Thinning Age Card (Card Type
Variable Name
Format
Columns
Contain
Explanation
Blank
2X
1 -2
bb
B l ank.
AGET(1 )
F3.0
3-5
XXX
Total stand age for the first
com mercial t h i n n i ng.
Blank
2X
6-7
bb
Blank.
AG ET(2)
F3.0
8-1 0
XXX
AG ET(3-1 5)
1 3(2X,F3.0) 1 1 -75
Total stand age for the second
commercial thi n n i ng .
A
bbXXX
A
Total stand ages for the next 1 3
com mercial cutti ngs, i f any.
Blan k
3X
76-78 .
bbb
Blan k.
KRD
11
79
2
Card type.
ICONT
11
80
0
N ot a contin uation card.
3).-The Specified
Com me rcial Thi n n i n g Height Card is used when the cutt i ng parameter SCTHT
[0, 1 6] on the Master Cont ro l Card, col u m n 45, is coded 1 . It is used whenever
com mercial thi n n i ng s are wanted at spec ific stand top heights. If h arvest age
(A HARA [0, 1 3]) or harvest height (HTHARV [0,1 7]) is not specified on the M aster
Control Card, col umns 35-37 and 47-49 respectively, then the harvest height
m ust be the last height specified on card type 3. U p to 1 5 commercial t h i n n i ng
heig hts can be specified.
Specified Commercial Thinning Height Card (Card Type
Variable Name
Format
Columns
Contain
Explanation
Blank
2X
1 -2
bb
Blan k.
HY40(1 )
F3.0
3-5
XXX
B l an k
2X
6-7
bb
B l ank.
H Y40(2)
F3.0
8-1 0
XXX
Stand to p heig ht for the second
commercial thinning.
H Y40(3-1 5)
1 3(2X, F3.0) 1 1 -75
Stand top height for the f i rst
commercial thinning.
A
bbXXX
A
Stand top heights for the next
1 3 com merc ial cutti ngs, if any.
Blank
3X
76-78
bbb
B l ank.
KRD
11
79
3
Card Type.
I CO NT
11
80
0
N ot a conti n uation card .
51
diD Ratio Card (Card Type 4).- The d/0 Ratio Card is used when the cutting
parameter lOR [0, 1 8] on the M aster Control Card, col u m n 51, is coded 1 or 2. It
i s u sed whenever the ratios of cut d i ameters to l ive stand d i ameters before
thi n n i ng are to be speci fi ed. Ratios g reater than 1 .0 i mply t h i n n i n g from above;
ratios less than 1 .0 i m pl y thi n n i n g from below. This option req u i res a rat i o to be
specified for each commercial thinning. U p to 1 5 ratios can be specified.
Variable Name
Format
Columns
Contain
Explanation
Blank
2X
1 ·2
bb
Blank.
DR(1 )
F3.2
3-5
x.xx
d/0 for f i rst commercial
t h i n n i ng.
Blank
2X
6·7
bb
B lank.
D R(2)
F3.2
8-1 0
x.xx
d/0 for second commercial
t h i n n i ng .
bbX"XX
Blank
3X
76-78
bbb
d/0 for the next 1 3 commercial
thi n n i ngs, if any.
B lank.
KRD
11
79
4
Card type. ICO NT
11
80
0
N ot a continuation card. D R(3·1 5)
1 3(2X,F3.2) 1 1 -75
Residual Basal Area Card (Card Type 5).- The Residual Basal Area Card is u sed
when the cutting parameter IGS [0, 1 9] on the M aster Control Card, col u m n 53,
is coded 1 . It i s used whenever the default lower thi n n i ng l i m it is not wanted.
This option requ i res a residual basal area to be specified for each com m ercial
t h i n n i ng. U p to 15 residual basal areas can be specified.
Variable Name
Format
Columns
Contain Explanation
Blank
2X
1 -2
bb Blank.
G RESD(1)
F3.0
3·5
XXX,.,
Res i d ual basal area for f i rst
com merc ial t h i n n i ng .
Blank
2X
6·7
bb Blank.
G R ESD(2)
F3.0
8-1 0
XXX. Resi d ual basal area for second
com merc i al thi n n i n g .
G RESD(3-1 5)
52
1 3(2X,F3.0) 1 1 -75
bbXXX,., Residual basal areas for the
next 13 comme rcial thi n n ings,
i f any.
Blank
3X
76-78
bbb B l ank.
KRD
11
79
5
Card type.
I CO N T
11
80
0
Not a cont i nuation card.
Residual N u m ber of Trees Card (Card Type 6). - The Residual N u m ber of Trees
Card is u sed when the cutti ng parameter LTR E E [0,20] on the Master Control
Card, col u m n 55, is coded 1. Thi s option req u i res a residual number of trees to
be specified for each commercial thinning. Up to 1 5 residual number of trees
can be specified.
Variable Name
Format
Columns
Contain
Explanation
Blank
1X
1
b
Blank.
TAR ES D( 1 )
F4.0
2-5
xxxx" Residual number of trees for
first comm ercial thinning.
Blank
1X
6
b
Blank.
TARESD(2)
F4.0
7-1 0
XXXX A Residual number of trees for
second com mercial thi n n i ng.
TARESD(3- 1 5) 1 3(1X, F4.0) 1 1 -75
bXXXX A Residual numbe r of trees for
the next 13 com mercial
th i n n i ng s, i f any.
Blank
3X
76-78
bbb
Blan k.
KRD
11
79
6
Card type.
I CO NT
11
80
0
N ot a continuation card.
Fertilization Card (Card Type
7).-The Fertil ization Card is used i f the fertil izer
parameter FERTCT [0,24] or FERTAS [0,25] on the Master Control Card, columns
68 and 70 respectively, i s coded 1 or 2. If FERTCT i s coded 1 or 2, the stand
ages can be left blank. If FERTAS is coded 1 or 2, the total stand age m ust be
specified for each n itrogen fert i l izer app l i cation. These cards are used
whenever n itrogen fert i l izer is to be appl i ed. If FERTCT is coded 1 or 2, the
q uantity of n itrogen applied m ust be specified for each commercial thi nning
with zero pounds a val id code. Up to n i ne fert i lizer applicat ions can be
spec ified on the first card type 7. If more than n i ne fert i l izer app l i cations are to
be spec ified , then a second (continuation) card type 7 is needed. U p to 1 5
nitrogen fertilizer appli cations can be specified.
Variable Name
Format
Columns
Contain Explanation
Blank
1X
1
b
Blank.
AG EF( 1 )
F3.0
2-4
XXX" Total stand age fo r fi rst
nitrogen fertil izer application.
Blank
1X
5
b
Blank.
PN IT( 1 )
F3.0
6-8
XXX A Quantity of nitrogen fert i l izer, in
pounds per acre, for first
appl ication.
Blank
1X
9
b
Blan k.
AG EF(2)
f3.0
1 0- 1 2
XXX " Total stand age for second
n itrogen fertil izer appl ication.
53
Variable Name
Format
Columns
Contain
Explanation
(Contin ued)
Blank
1X
13
b
Blank.
P N IT(2)
F3.0
1 4- 1 6
XXX,
Quant ity of nitrogen fertil izer, i n
pounds per acre, for second
application.
bXXX,
Total stand age and q uantity of
n i t rogen fertil izer, in pounds per
acre, for seven additional
appl ications.
((AGET(I),
P N IT(I)),
I = 3-9)
1 4(1 X, F3.0) 1 7 73
Blank
6X
74-78
bbbbbb
Blank.
KRD
11
79
7
Card type.
I CO NT
11
80
0
N ot a cont i nuation card.
If FERTCT or FERTAS is coded 2, then a cont i nuation card is used to specify
the rema i n i n g n it roge n fert i l izer appl i cat ions (maximum of six) using the above
format, except ICONT is coded 1 .
Report Ages Card (Card Type 8).- The Report Ages Card is used i f the output
parameter N RA [0, 27] on the M aster Contro l Card, col u m n 74, is coded 1 -4.
This card is u sed if stand stat i st ics are to be pri nted at ages other than cutt i ng
ages i n the yield tabl e for 1 .6-i nch d. b.h. Each report age wanted m u st be
s peci f i ed i n ascending order. U p to 1 9 re port ages can be specified on each
of four cards. The n u m ber of cards depends u pon the total n u m ber of report
ages to be specified. The format of all four cards is exactly the same. If N RA
;::: ·5, no Report Ages Cards are used, but the program w i l l print stand stat istics
for every year of the s i m ul ation.
Variable Name
Format
Columns
Contain
Explanation
Blank
1X
1
b
B lank.
RAN(1)
F3.0
2-4
XXX,..
Total stand age when f i rst set
of stand statistics is to be
pri nted.
B l an k
1X
5
b
Blank.
RAN(2)
F3.0
6-8
XXX,..
Total stand age when second
set of stand stati stics is to be
pri nted.
bXXX,..
Total stand ages when the t h i rd
through the n i n eteenth set of
. stand statist ics i s to be printed.
RAN(3-1 9)
54
1 7(1 X, F3.0) 9-76
Blank
2X
77-78
bb
B lank.
KRD
11
79
8
Card type.
I CO NT
11
80
0
N ot a con t i nuation card.
I f N RA i s coded 2-4, then the additional report ages are specified on co ntinuation cards using the above format, except I CONT i s coded 1 , 2, or 3 dependi ng u pon whether the continuation card i s the fi rst, second, or third continuation card. Observed Heights Card (Card Type 9).-The Observed Heights Card is used i f
the stand parameter l OBS [0,5] o n the M aster Control Card, col u m n 1 5, i s coded
· 1 -6. Observed heights are u sed if height g rowth trends for a stand d iffer
s i g n i f i cantly from the height g rowth trends developed by Bruce (see
footnote 4). Up to 30 height observat ions can be s pecifi ed using this option,
al lowing the u ser a great amou nt of flex i b i l ity in def i n i n g an alternative
heig ht/age c u rve. A l i near rel ations h i p is assu med between height observations.
For each observation age, two heig hts are called for: the height before thinn ing,
i f any, and the height after thinning, i f any. I f both heights are the same, only
the f i rst height need be coded for that observation age. It is not necessary to
s pecify heights for each t h i n ni ng unless the height changes as a result of
t h i n n i ng ; however, if a height observation does not coincide with thinnings
havi ng d/D g reater t han 1 .0, D FSIM w i l l red u ce the height as defi ned by
function CTHTC d i scussed in appendix 2, but i ncrements impl ied by the
specified observed height t rend w i l l be mainta ined.
Each of the six Observed Height Cards have the same format. The number of cards u sed depends u pon the nu mber of height observations. Variable Name
Format
Columns
Contain Explanation
Blank
1X
1
b
B lank.
O BSAG E(1 )
F3.0
2-4
XXX . Total stand age at f i rst
observation of stand top height.
Blank
1X
5
b
Blank.
OBSHTS( 1 , 1 )
F4.1
6-9
xxx.x Stand top height before thin­
n in g , i f thinning done at this age, at first observation. Blan k
1X
10
b
Blank.
O BSHTS(2, 1 )
F4.1
1 1 -1 4
xxx.x Stand top height after t h i n n i ng,
if th i n n i ng done at this age, at
first observation. If same as
col u m n s 6-9, this field can be
l eft blan k.
Blank
1X
15
b
Blank.
O BSAG E(2)
F3.0
1 6- 1 8
XXX. Total stand age at second
observation of stand top height.
Blank
1X
19
b
Blank.
OBSHTS(1 ,2)
F4.1
20-23
xxx.x Stand top height before t h i n­
n i ng , if thinning done at this age, at second observation. Blank
1X
24
b
Blank.
55
Variable Name
Format
Columns
Contain . Explanation
(Cont i nued)
OBSHTS(2,2) .
((OBSAGE(I),
O BSHTS(1 ,1),
OBSHTS(2,1)),
I = · 3-5)
Blank
. . KRD
ICONT
F4.1
25-28
3(1 X, F3.0, 29·70
1 X, F4. 1 ,
J X, F4. 1 )
XXX AX
Stand top height after t h i n n i ng,
if thinning done at this age, at
second observation. If same as
columns 20-23, this field can be
l eft blan k.
bXXX" .
Total stand ages and stand top
. . heights before and after thin·
bXXX"X ning, if thinni ng done at these
ages, for the third through the
bXXX..;X fifth observations.
ax
71 -78
bb . . . bb Blank.
11
79
9
Card type.
11
80
0
Not a continuat ion card.
If lOBS is coded 2·6, then tlie additional height/age poi nts are spec ified on
continuation cards using the above format; except ICONT i s coded 1 ·5
depend i ng on whether the cont i nuation card is the f i rst, second, . . . fith
cont i n uation card.
·
Messages Printed
During Execution
·
During execution, DFSIM may print several messages other than simu lation
i n put cond itions and stand stati sti cs. These messages appear when p roblems
. are e ncountered in p rocessing the control deck or when t h i n n i ng specifi cations
cannot be met. These messages are explai ned below.
1 . A M I N I M U M OF TWO OBSERVATION P ERIODS REQUI R E D FOR USER·
SPECI FIED HEIGHTS. CORR ECT A N D RERUN.
The stand parameter lOBS [0, 5] on the Master Control Card, column 1 5, was
coded 1 or larger and only one height/age point was found on card type 9. This
error w i l l stop the processi n g of any succeed i ng simul ations.
2. A MAXI M U M OF 30 OBS ERVATIO N PERIODS IS A LLOWED FOR USER·
S P ECIFIED H EI GHTS. CORR ECT A N D R ERUN.
The stand parameter lOBS [0, 5] on the M aster Control Card, column 1 5, was ·
coded g reater than 6 and exceeds d i mensioned space fpr OBSAG E and
O BSHTS. Th i s error w i l l stop the processing of any succeeding simul ations.
3. WAR N I N G - RESI D UAL TREES AFTER PRECO M M ERCIAL T H I N N ING AT
AG E XX. EXCEEDS EXISTI N G TREES . NO PRECOM M ERCIAL TH I N N I N G
WAS DON E.
Informative message. Nu mbe r of trees i s not changed, stand is t reated as
.
unthinned, and simulat ion conti n ues. .
56
4. T H E STA N D DOES N OT M E ET TH E DIAMET ER A N D BASAL AREA LI M ITS
AT AG E XXXX. T H E FI RST COMM ERCIAL TH I N N I N G WI LL BE MADE AT
AGE XXXX.
I n formative message. Stand does not meet the l i mit specified or impl ied by
D U M [0, 21] and/or G U M [0, 23] on the M aster Control Card, col u m n s 57-59 and
64-66, respectively, for the m i n i m u m q uadrati c mean diameter or basal area i n
trees 5.6-inch d.b.h. a n d larger for the first specified commercial thinn i ng. The
f irst commerc ial t h i n n i n g is postponed, and s i m u lation contin ues.
5. TH E STA N D DOES N OT M E ET T H E M IN I M U M TH I N N I N G LI M IT AT XXX
FEET. T H E FI RST COM M ERCIAL TH I N N I N G WI LL BE DON E AT XXX FEET.
I nformative message. Stand does not meet the m i n i m u m basal area cut
specified or i m p l ied by GCLIM [0, 22] on the M aster Control Card, col um n s
61 -62, for t h e first s pecified commercial t h i n ni n g. T h e fi rst commercial thi n n i ng
is postponed, and s i m u lation continues.
6. T H E STA N D DOES NOT M E ET TH E M I N I M U M T H I N N I N G LI M IT AT XXX
YEARS. T H E F I RST COM M E RCIAL T H I N N I NG WI LL BE DON E AT XXX
YEARS.
Informative message. Stand does n ot meet the m i n i m u m basal area cut
s pecified or i m pl ied by GCLIM [0, 22] on the Master Control Card, colu m ns
6 1 -62, for the fi rst specified com mercial t h i n n i ng . The fi rst comm e rcial thi n n i ng
i s postponed, and s i m ul ati on cont i n ues.
7. T H E USER-SU PPLI E D VALU E OF X.XX FOR (DCUT/DBEFORE) EXCEEDS
T H E ACC EPTABLE LI M IT OF X.XX.
I n fo rmative message. A d/0 was specified which exceeds the fo llowing l i mits
and lOR [0, 1 8] specified o n the M aster Control Card, col u m n 51 , was coded 1 :
d/0 rati o
d/0 rati o
d/0 rati o
>
>
>
1 .1 5
1 .0 and stand diameter
1 0.0
1 .0 and stand height > 1 00.0
T h i n n i n g is done, but at the max i m u m d/0 i nd icated above, and simulation
cont inues.
8. THE USER-SU PPLIED VALU E O F .XX FOR (DCUT/DBEFORE) WAS LESS
THAN TH E ACCE PTABLE LI M IT O F 0.80.
I nformative message. A d/0 was specified less than 0.80 and l O R [0, 1 8]
s pecified on the Master Control Card, col u m n 51 , was coded 1 . T h i n ning is
done with a d/0 of 0.80, and s i m ul ation contin ues.
9. THE LAST COMM ERCIAL TH I N N I NG N OT DON E AT XXX. YEARS, BECAUSE
T H E HARVEST CUT IS SCH EDU LED IN LESS THAN 5 YEARS OR LESS
THAN TH E FINAL TH I N N I NG I NTERVAL.
57
I nformative message. Thinning is not done, and simulation continues to the
harvest cut.
1 0. TH E FI RST COM M ERCIAL TH I N N I N G NOT DONE AT XXX. YEARS,
BECAUSE TH E N EXT TH I N N I NG IS SCH EDULED IN LESS THAN 5 YEARS
OR LESS THAN THE SPEC I FIED TH I N N I N G INTERVAL IN YEARS.
I n formative message. F i rst commercial th i n n i ng is postponed, and s i m ulation
conti n ues.
1 1 . TH E LAST C.O M M ERCIAL T H I N N I N G N OT DON E AT XXX. F EET, B ECAUSE
TH E HARVEST CUT IS SCH EDU LED IN LESS THAN 1 0 FEET OF H EIGHT
G ROWTH OR LESS THAN FINAL T H I N N I N G H EIGHT I NTERVAL
Informative message. Th i n n i ng is not done, and simu lation continues.
1 2. T H E FI RST COM M E RCIAL TH I N N I N G N OT DON E AT XXX. FEET, B ECAUSE
T H E N EXT TH I N N I N G IS SCH EDU LED IN LESS THAN 10 FEET OF H EI G HT
G ROWTH OR LESS THAN TH E SPECI F I E D TH I N N I N G INTERVAL I N YEARS.
I nformative message. F i rst commercial t h i n n i n g is postponed, and simulation
contin ues.
13. WARN ING -STA N D STATISTICS B EYO N D 1 00 Y EARS ARE G ROSS
EXTRAPOLATIONS OF MODEL.
I n formative message. User sho u l d be extremely cautious about i nterpretations
beyond 1 00 years, because esti mates are outside the range of the basic data.
Esti mates in the range of 80·100 years are at the marg i n of the data and can be
regarded as p lausible extrapolations, but estimates beyond 1 00 years should be
regarded as q uestionable extrapo lati ons.
1 4. WAR N I N G -STA N D STATISTICS BEYO N D XXX.X FEET OR SITE I N D EX
XXX. ARE G ROSS EXTRAPOLATIONS O F MODEL.
' i
Informative message. XXX.X feet i s expected height at 1 00 years for the i nd icated
site i ndex. Above cautions apply.
1 5. WAR N I N G - EXISTING STA N D D IA M ETER AT B EG I N N I N G OF SI M U LATION
IS TH R EE (3) O R MORE STANDARD ERRORS FROM REGIONAL AV ERAG E.
I nformative message. The relationsh i p between diameter, height, and n umber of
trees i s out of balance for an existing juven i l e stand, resulting i n possible
u n realistic growth trends, especially for the juveni l e stand. Recommend
beg i n n i ng with only stand age and number of trees on existing stand card (card
type 1 ).
1 6. WA R N I N G - EXISTI N G STA N D H EIG HT OVER DIAMETER RATIO OF XX.XX
AT BEG I N N ING OF SI M U LATI ON IS 3 OR MORE STANDARD ERRORS
FROM REGIONAL AVERAG E.
58
I nformative message. The d i amater/height rel ationship for an existing stand
with diameter g reater than 5.55- i nch d.b.h. is out of balance, resulting i n
possible unreal istic g rowth trends. Check i n put statist i cs on existing stand
card (card type 1) for possible errors.
1 7. WARN I N G - EXISTING NATURAL STA N D I N ITIAL N U M BER OF TREES
EXCEEDS + OR - 50 PERCENT O F "NORMAL. " QU ESTIONABLE EXTRAPOLATIO N O F M O D EL. I nformative message. The n u m ber of stems/height relationship is out of
bal ance for an exist i n g j uven i l e stand, resulting i n possible unreal i stic g rowth
trends.
1 8. WARN ING -STA N DS PLANTED OR PRECOM M E RCIALLY TH I N N E D TO
LESS THAN 300 STEM S PER ACR E ARE QU ESTIONABLE
EXTRAPOLATIONS OF MODEL.
I nformative message. Stands of 300 stems per acre are at the marg i n of the
basi c data, and stands with fewer stems can result in unreal istic g rowth trends.
I nterpretations of results shoul d be done with caution.
1 9. STA N DS PLANTED OR PRECO M M ERCIALLY TH I N N ED TO LESS THAN 1 00
STEMS PER ACRE CA N N OT BE S I M U LATED. YI ELD TABLE N OT
PRODUCED.
Stands with less than 1 00 stems per acre after planting o r precommercial
thi n n i ng are well outside data, and u n real istic g rowth trends usually occur. This
yield table w i l l not be produced, but ot her yield tables, if any, w i l l be produced.
20. WAR N I N G - FREQUENT REPEATED FERTI LIZATIONS ARE G ROSS EXTRAPOLATI O N S OF M O DEL. I nformative message. Four or more fert i l izations have been spec ified . Possible
u n reali stic g rowth trends may result.
21 . WAR N I N G-USER SPECI F I ED RESI DUAL N U M BER OF TREES AN D/OR RESI DUAL BASAL AREA RESULTS I N Q U ESTIONABLE (DCUT/DBEFORE) OF XX.XX. Informative message. N u m ber of trees and basal area cut are out of balance,
resulting in unreal i st i c removals.
Appendix 2.
Description of
Program Segments
We have not incl uded a FORTRAN l i sti n g of the DFSIM program in this paper,
because of its length. The various subrouti nes and functions are l i sted in the
order i n which they appear i n the program, with brief statements of the
operations performed by each.
PROGRAM DFSIM
This is the contro l l i n g p rogram of the simulator. It cal ls the fol lowing
subrouti nes: REA D I N , H EADER, HTCAL, JUVGRO, FRSTCT, COMTH N ,
NOT H I N , HARVST, VOLCO N.
59
S U B RO UTI N E R EA D I N
Reads control cards for simu l ation. Cal l ed b y D FSIM. Cal l s B HAG E.
SUBROUT I N E H EADER
Com p utes conditions i m pl i ed by contro l deck and pri nts h ead i ngs for yield
tables for stand over 1 .55-i nch d.b.h. Cal l ed by D FSIM, J UVGRO, T H I N
G ROWT H , COMTH N , HARVST. Cal l s BHAGE, H EIG HT.
S U B ROUTIN E X FERT
Cal c u l ates the val u e of the variable expressi ng fertil izer effects i n the increment fu nctions in HTG ROW, V I N CA, BAI N CR, DI NCR. Cal l ed by J UVG RO, G ROWTH, and HTCAL. Call s TOAG E. SU B ROUT I N E J UVGRO G rows all j uveni l e stands from start of s i m u l ation to a stand d i ameter of
5.55-i nch d . b.h. A l l ow s for one preconi mercial thi n n i ng and one fert i l izat ion
w h e n speci f i ed . Cal l ed by D FS I M . Cal l s A DJ N U M, A G EJUV, B H AG E, D I A M J ,
H EADER, H EIGHT, HTG ROW, HTLOR, SORG, T H N , TOAG E, TREN U M , VG RAT,
and X F E RT.
SU BROUT I N E G ROWTH
G rows all stands 5.55·inch d.b.h. and l arger by 1 -year g rowth periods. Pri nts
intermediate stand s u mmaries for each year specified. Cal led from F RSTCT,
N OT H I N , and COMT H N . Cal l s BAI N C R, BAN ET, D I N C R, GADJ, H EADER,
HTG ROW, HTLOR, M ERCHV, TOAG E, VADJ, VG RAT, VI NCA, V N ET, and
XFERT.
S U B ROUTI N E TH I N
Carries out commercial t h i n n i n g accord i ng t o specifications. Cal led by
COMTH N . Cal ls CTHTC, DCODB, G LTL, H EADER, M ERCHT, and VG RAT.
SU B ROUTI N E F RSTCT
Grows the stand from 5.55-inch d.b.h. to f i rst commercial thinning, when
s pecifications call for com mercial th i n n i n g . Call ed by D FSIM. Cal l s BAPA56,
BHAGE, G LTL, G ROWTH , SORG, T H N , and TOAG E.
SUBROUTI N E N OT H I N
G rows t h e stand from 5.55-i nch d.b.h. to f i n al harvest cut, when s pecifications
call for n o commercial th i n n i ng . Cal l ed by D FSIM. Call s G ROWT H , HTLO R,
M ERCHV, SORG, T H N , and TOAG E .
SU B ROUTI N E COMTHN
Grows the stand from f i rst comm ercial t h i n n i ng to fi nal harvest cut, and writes
60
a yield table for t h i n n i ng. Cal led by DFS I M . Cal l s G LTL, G ROWTH, H EADER,
HTLOR, M ERCHV, SORG , TH I N , THN, and TOAG E.
S U B ROUTI N E H ARVST
Writes the yield table for f inal harvest for the stand over 1 .55-i nch d.b.h. Cal led
by DFSI M . Cal l s H EADER, HTLOR, M ERCHV, and TOAG E.
SUBROUTI N E HTCAL
Cal culates various heights associated with exist i n g stand val ue s supplied by
the user, when program i s e ntered with observed val ues for an existing stand
over 5.55-inch d.b.h. Cal led by D FSI M. Cal ls BHAGE, H EIGHT, HTGROW,
SORG, THN, VGRAT, and XFERT.
SUBROUTI N E M ERCHV
Cal c u l ates average d iameter, basal area, and cubic-foot vol ume (total and to a
4-i nch top) of l ive trees for the stand over 5.55-inch d.b.h. and for the stand over
7.55-inch d.b.h. Called by G ROWTH, N OTH I N , COMTH N , H ARVST. Cal l s
BAPA56, BA76, CVTS56, CVTS76, CV456, CV476, DIAM56, a n d DIAM76.
SUBROUTI N E M E RC HT
Calcul ates average d i ameter, basal area, and cubic-foot vol u m e (total and to a
4-i nch top) of trees removed duri ng comme rcial t h i n ni n g, for trees over
5.55-i nch d.b.h., and for trees over 7.55-inch d . b.h. Called by TH I N . Call s BAC56,
BAC76, CVC456, CVC476, CV656, CVC76, DCUT56, and DCUT76.
SUBROUTI N E VOLCON
Produces summary tables for trees over 5.55-inch d . b.h. and for trees over
7.55-inch d.b.h., when these options are cal led for. Cal led by D FS I M . Cal l s
CVC676, CVM56, CVM 76, CVS676, CV676, SV676, TOAG E, VIC676, and V1676.
F U N CTION SORG
Defi nes a variable i n d i cati n g stand ori g i n . SORG has value 0.0 if the stand is of
nat u ral o rig in. If the stand i s planted, SORG has value 1 .0 u p to a height of 60
feet. After the stand reaches 60 feet, SORG decays l i n early to 0.0 over the
i nterval of 60-1 00 feet, and is 0.0 thereafter. Cal led by JUVGRO, FRSTCT,
N OTHI N , COMTH N, and HTCAL.
F U N CTION THN
Defines a variable i n dicat i ng t h i n n i ng. THN has val ue 0.0 in an unthi nned stand.
It takes the val ue 1 .0 when the stand i s t h i n ned. After 40 feet of height g rowth
s i nce the most recent t h i n n i ng , THN beg i n s to decay l i nearly, becoming 0.0
after 80 feet of height g rowth s i n ce t h i n n i ng . Cal l ed by J UVGRO, F RSTCT,
N OTHIN, COMTH N, and HTCAL.
61
FUNCTION H EIG HT
Cal c u l ates height (H40) from given age b.h. and site i ndex, using Bruce's
equation (see footnote 4). Cal led by H EA D ER, JU VGRO, and HTCAL. (Option
provides an estimated H 40 by i nterpolation between specified known heights.)
F U N CTION HTG ROW
Derived from function H EIG HT. Calculates annual i ncrement in H 40, g iven site
i ndex, age b.h., and fertil izer treatment. Cal l ed by J U VG RO, GROWTH , and
HTCAL.
F U N CTION HTLOR
Calc ulates Lorey's height (height of tree of mean vol u m e) using an algebraic
rearrangement of the B ruce-DeM ars (1 974) volume eq uation. Cal l ed by JUVGRO,
G ROWTH , NOTH I N , COMTH N , and H ARVST.
F U N CTION B HAG E
Converts total age to corresponding age at breast height, g iven site i ndex.
Cal l ed by R EADI N , J UVG RO, FRSTCT, H EADER, and HTCAL.
F U N CTION TOAGE
Converts age b.h. to correspondi ng total -age, g iven site i ndex. Cal led by
XFERT, J UVGRO, G ROWTH, FRSTCT, NOTH I N , COMT H N , HARVST, and
VOLCON .
F UN CTION AGEJUV
Cal culates age b.h. corresponding to a spec ified H 40 and site i ndex. Used to
determ ine start i ng point for j uveni l e stand computat ions. Cal l ed by J UVGRO.
F U N CTION DIAMJ
Est imates quadrat ic mean diameter of the juve n i l e stand, g iven hei ght, number
of stems, thi nned versus not thi nned, height at thinning, numbe r of pou nds of
nitrogen appl ied , and height at fertil ization. Cal l ed by J UVGRO.
FUNCTION TREN U M
Est i mates " normal " number of stems a s a function o f height, based o n data
from u ntreated control plots. Used for j uve n i le stand only. Cal l ed by J UVGRO.
FU NCTION ADJ N U M
Esti mates n um be r of trees 1 year hence, g iven present n u m ber and height,
height 1 year hence, "normal" numbe r, and "normal" n u m ber 1 year hence.
Used i n proj ections of j uveni l e stand when a known number of stems at a g iven
age is used as the starting poi nt for p rojection of a non-normal, untreated,
natu ral stand. Cal l ed by J UVGRO.
62
FUNCTION V I NCA
Esti mates g ross vol ume i ncrement in ft3/acre per year, from attributes of the
l ive stand and h i story of treatment. Cal led by G ROWTH.
FU N CTION V N ET
.j,..
.l
l
i
!
Est i mates net vol u m e i ncrement i n ft3/acre per year, g iven annual gross vol ume
i ncrement, current attributes of the live stand, and h i story of treatment. Call ed
by G ROWT H .
FUNCTION BAI NCR
Esti mates annual basal area gross i ncre ment in ft2/acre per year, g iven
att ributes of the l ive stand and h i story of treat m ent. Cal l ed by G ROWTH.
FUNCTION BAN ET
Est i m ates net basal area i ncrement i n ft2/acre per year, g iven ann ual g ross
basal area i ncrement, current attributes of the l ive stand, and h istory of
treatment. Cal l ed by G ROWTH .
FU N CTION DINCR
Esti mates a n n ual net i ncrement of stand d iameter, g iven current attributes of
the l ive stand and h i story of treatment. Cal led by G ROWTH.
FU N CTION VG RAT
Esti m ates vol u m e/basal area rat i o of l ive stand from attributes of l ive stand and
stand h istory. Used to calculate vol ume from predicted basal area in s u brou t i ne
JUVGRO, and to convert vol ume to basal area and vice versa i n s ubroutine
G R OWTH and T H I N . Cal led by JUVGRO, G ROWTH, THI N , and HTCAL.
FUNCTION VADJ
Adjusts vol um for consistency with vol u m e/basal area rati o estimated by
FU NCTIO N VG RAT. Called by G ROWT H .
FU NCTIO N GADJ
Adjusts basal area for consistency with vol u m e/basal area rat i o est i mated by
FU N CTION VG RAT. Called by G ROWTH.
FUNCTION DCOD B
Calculates defaul t d/D f o r com merc ial t h i n n i n g , g iven d i ameter o f l ive stand,
orig i n , and thi n n ing h i story. Commercial t h i n n i ng s u se this d/D rati o u nless
user specifies or i mp l ies a different one. Cal led by TH I N .
63
FU NCTIO N CTHTC
Reduces stand height to al low for the effect of removing top height trees i n
thi n n i ng , g iven statist ics for l ive stand and cut stand. Used o n l y if diD i s
g reater than 1 .0. Cal l ed by T H I N .
FU NCTION G LTL
Calculates lower l i m it of allowable basal area after t h i n n i ng, g iven diameter and
site i ndex. Limit i s overriden if user specifies a different residual basal area.
Cal l ed by T H I N , FRSTCT, and COMT H N .
FU NCTI O N DIAM56, . . . FU N CTION CVM76
This i s a g roup of 24 functions of the general form
Ymerch/ytotal
=
f(stan d variables)
used to convert stat istics f.or a l l trees over 1 .55-inch d.b.h. and total cubic
vol ume (CVTS) to corresponding statistics for trees over 5.55-i nch d.b.h., for
trees over 7.55-inch d.b.h., and merchantable volumes, by means of the
eq uations g iven in W i l l iamson and Curtis (1 980).
Appendix 3.
Driving Functions
We make no attempt to present i n this report al l the equat ions used i n D FSIM.
We will, however, di scuss the princi pal d riving funct ions used i n D FS I M version
1 .0, and some related topics.
These specific equation forms and coefficients are not fi nal or essent ial to
D FS I M . Most could and some p robabl y w i l l be replaced i n the future by other
equations perfo rm i ng the same functions.
Sym bols used are defi ned in the G lossary.
Height and Height
Increment Equations
Bruce's (see footnote 4) height and height i nc rement equations, w h ich provide
estim ates of top height (H40) and top height an nual i n c rement (dH 40), are basic
driving equations in the projection routi nes for bot.h juveni l e and main stands.
The seem i ng complexity of these equations results from a translation of axes
which places the ori g i n of tlie curves at total age zero, although the equations
are entered with age b.h.
Height equation (H EIGHT)14.-
H 40
=
[S] exp(bi(A
where b2
and b
3
=
=
+
1 3.25 - S/20)ba - (63.25 - S/20)ba)];
l n[4.5/S]/[(1 3.25 - S/20) ba - (63.25 - S/20)ba),
- 0.477762 - 0.894427 (S/1 00)
+
0.793548 (S/1 00)2 - 0. 1 7 1 666 (S/1 00)3•
14Names i n parentheses refer to the DFSIM function or
subroutine containing the equation.
64
Height increment equation (HTGROW) - This eq u ation, obtai ned by
d ifferencing the height equation using D.A = 1 , i s:
d H40
I
;
C.
where F
Volume-Basal Area Ratio
Equation (VGRAT)
.
. I
.
---···· .
1-,---
· ····· t '
[S] exp[ - b (63.25 - S/20)b3] [exp(b (A + 1 4.25 - S/20)
2
2
- exp(b (A+·· f3.25---- .. SJ2d)b3 ) exp [0.54989(F)];
2
=
...
___
·
" ·· ·· -··· ·· · · ··
)
.... ·· ········· · ··--i
fert i l izer response variable15, defi ned in a later section.
=
Vol ume-basal area ratios are esti mated by the regression:
l n(V/G)
=
0.42332 + 0.3731 9 ( I n H40) - 0.24306 (In 0)2 + 0.26034 (I n H40) (In D)
- 0.00028026 (A) (I n H40) + 0.00034474 (RD) + 0.022759 (PORT);
w h ere the variable PORT assu mes val ue 1 .0 for p l anted or thin ned stands, and
0.0 for other stan ds.
R21n(VIG)
=
S EE,n(VIG)
0.995
=
0.038 1 , or approximately
±
4 percent for the u ntransformed
variable V/G.
5.55-i nch d.b.h.) to
This eq u ation is u sed in projections of j uveni l e stands (D
calcu l ate vofumes from estimates of number of stems and basal area. It is u sed
i n the projections of mai n stands (D > 5.55-i nch d .b.h.) as one of the
const ra ints on estimates of vol ume and basal area i nc rements, and in com pu­
tation of resi d ual vol u m e after t h i n n i ng.
Juvenile Stand Equations
The basic d riving eq u ations for juve n i l e stand g rowth are (1 ) the height and
height increment fu nctions given previously, (2) a numbe r of trees function
applying to wel l-stocked natural untreated stan ds, and (3) a stand average
d iameter f unct ion applying to all stands.
Number of trees equation (TRENOM). - This eq u ation provides an estimate of
the n u m ber of trees per acre in wel l-stocked, natural, untreated stands, as a
function of top h e i g ht . It was derived as a reg ression fitted to values for
unt reated plots of natural ori g i n (control plot s in thinning and fertilizer stud ies).
l n(N)
=
45.8267 - 5.29786 (In H 40) - 70.8701 (In H40) - 1 ;
where
S EE1n(N)
=
0.41 56; or, approximately, - 34 to + 51 percent for the variable N .
15The form o f F , and hence the associated coefficient, differs
slightly from that used in Bruce's (see footnote 4) analysis.
65
There was also a significant trend with site i ndex, but it appeared u n reasonable
i n magn itude and may possi b l y be associated with occurence of stagnated
stands on poor sites. We chose to base t h i s esti mate on top height alone.
Quadratic mean diameter, juvenile stands (DIAMJ).-Quadratic mean diameter
(stems over 1 .55-inch d.b.h.) is estimated by the fol lowing equation, fit to values
for those stands with H40 under 1 00 feet and not more than one prior thinning
or fert i l ization. The equation applies to both natural and planted stands.
In D
- 7.4044
=
+
4.0036 (In H40) - 4.1 8 1 5 (In H 40)/N - 0.30037 (In H 40)2
- . 1 1 268 (In N)(ln H 40)
+
0.44634 I n N/(ln H40)
.31 679 T - 0.0096588 (T)(In N)(ln H 40)
+
+
+
0.0099793 l n2(H40 - HT)
0.1 9352 FAT;
where
T
1 .0 if thi nned, otherwise zero
=
HT
=
0.0 if unthinned; otherwise HT
l n2(H40 - HT)
FAT
=
=
H40 at time of thinning
0.0 if H40 - HT is less than 1 .0
=
fert i lizer response variable for j uvenile stand diameter
=
I n [#N (v e- ·11 312
+
1 .0]/(H F + 1 )
i n which
#N
v
=
=
HF
A2 n
1 D
=
SEE, no
number of pounds of nitrogen app l i ed per acre
elapsed increment i n H40 s ince fertil ization
=
H40 at time of fert i lization
0 .969
=
0.0863, or approximately
±
9 percent for the untransformed
variable D.
Main Stand Equations
The basic driving equations in projections of the mai n stand consist of ( 1 ) the
height and height increment equations g iven previously, (2) gross i ncrement
equations for volume and basal area and a net increment equation for average
diameter of the stand, and (3) equations estimating the ratio of net to gross
i ncrement in vol ume and basal area.
Increment functions.- The dependent variable, before transformation, was
periodic annual i ncrement:
y
=
(periodic increment)/(years in period).
Corresponding values of the i ndependent variables (X1) used were those at the period midpoints, calculated as the means of endpoint values. 66
Increment functions were fit as weighted logarithmic regressions in which the
dependent variable was Y = w l ny, where w is a weighti ng factor defined
previously (see footnote 3). The usual regression measures of fit apply to the
weig hted transformed variable and are not readily interpretable. Here, we express
fit by two measures:
t
l
R2w lny
=
Rei EY
Rei
Ey
=
fraction of the total sum of squares for the weighted transformed
variable accounted for by regression.
relative error of y = approximate relative standard error of estimate
for the untransformed variable y, obtained by dividing the regression
standard e rror of estimate by the mean weighting factor, and then
express ing values corresponding to ± 1 SEE on logarithmic scales as
correspond ing percentages of untransformed . means, i .e.,
i n percent
=
100 exp [( ± SEEw 10)/W];
wh ere w i s mean weighting factor (see footnote 3).
We chose logarithmic equations because of the expected multipl icative nature of
relationships, the fact that estimates could not logical ly assume negative values,
and the cost and computational d i fficulties of fitting equ ivalent equations in non­
l i near form.
·
We expected Y to be predictable as some combination of transformations of the
basic variables (1 ) height, (2) height i ncrement rate, (3) age, (4) diameter,
(5) basal area, (6) an expression representing fertil izer effect, and (7) an ex pres­
sion representing effect of thinning, if any, over and above the effect of the other
variables. Where feasible, we used height, height i ncrement, and age rather than
site i ndex, to simpl ify expression of fertil izer effect on height growth and to
al low su bs.t itution of different height and height i ncrement functions without
altering other relationships in the simulator.
·
We started with s i m p le forms such as: In y
=
a .+ b I n S
+
c InA
+
dA
+
Since InS can be approxi mated as
In y
=
a
+
b l n(H40)
+
c I nA
+
dA
e In RD. +
b1 l n(H40)
+
e A - v•
+
+
c1 A - '12, then d I n RD. Fit was considerably improved by i ntroducing i nteractions, other transformations, and dH40. This led to more compli cated form s, alth ough some
of the com plexity may simply reflect peculiarities of an unbalanced data set.
Because of correlations among basic variables, there are a number of
com bi nations of variables which g ive regressions with ap proximately equ ivalent
statistical fit. We derived several forms of each increment function, which gave
very s i m i lar estimates.
67
Among approximately equivalent forms, we chose those which appeared best
behaved near the marg i n s of the data. After trial s in the simulator, we made
some further changes in variables and transformations which had l ittle effect
on standard errors but e l i m inated certain marg inal anomalies that were
q uantitat ively smal l but logical l y unacceptable.
G ross volume increment rate (VI NCR).l n(dV/yr)
=
- 0.291 1 9 - 0.0036761 x, + 1 .0840 X4
j/7
-
o. 72916 X6 + 3.2253 X7
1 .9337 X10 + 0.44557\X14 + 0.75 1 34 X1 5;
\
. ·"·· where
R2w lny
Rei E
0.91
=
- 1 2 to + 1 4 percent
=
Y
and
the X, are defi ned below.
G ross basal area increment rate (BAI NCR).l n(dG/yr)
=
0.79737 + 1 .26 1 2 X2 + 2.2704 X5 - 1 .4 1 64 X1 1 + o.72673 . X,4 + 1 .4689 X, 5
1 8.729 X,8; -
where
.
R2w lny
0.81
=
Rei E Y
=
- 1 6 to + 20 percent
. Net diameter increment rate (DINCR).l n(d D/yr)
=
- 3.6383 - 3.9828 X3 + 1 .701 X8 + 0.21 584 X9 + 0.25949 X1 2 - o.o074227 X,3 + 0.86855 X,4 + 0.99647 X, 5 + 2.8978 X,6 + 3.6 1 83 X17; where R2w lny
Rei E
68
Y
=
=
0.78
- 12 to + 28 percent.
Def i n ition of variables i n above equations (see G lossary for def i n ition o f
symbols):
X3
=
1 /A
X4
=
I n H40
X5
=
(d H40
*
5
5
R D)0·2 /A0·
X6
=
(d H40
*
RD
X7
=
(dH 40/A)0·25
X8
=
I n d H40/A'12
Xg
=
I n (H 40/D)
•
*
H40)0·25/A0·5
(RD)0·20
X10
=
ln(H40/D)IInRD
X11
=
(1/A'12)(1 nH40) l n(H 40/D)/InRD
X12
=
1 .0 if planted or precommercially thinned, otherwise 0.0
x13
=
x1 2
X14
=
}n2[#N(x e - x18)3
*
RD
+
1 .0]/S
=
nitrogen fertil izer response variable, discussed
in the fol lowing section
where
x
8
elapsed years since fert i l izer app l i cation
=
=
X1 5
4.7 1 88 - 0.01 667($)
[1 /AY2][1/p][(H40/0)(1 /d H40)z
=
a thinning response variable, discussed later, i n which
z
p
=
=
height increment elapsed s i nce thinn ing, and
1 .0 i f RD
X16
=
In 0/RD
X17
=
In D/A112
=
1 /(RD)2
. 1a
e - !H401D)(11dH40lzjliRD
=
<
51 .0, otherwise (RD - 41 )/ 1 0
69
; \
Fertilizer effect variable (XFERn.- The four increment functions (hei g ht, gross
vol u me, gross basal area, and net di.ameter i ncrement) all contai n a variable
expressi n g the effect of n itrogen fertil ization. On the logarithmic scale used i n
fitting, this is a single add itive term of the form:
where
#N
x
=
=
n u m ber of pounds of n itrogen app l ied per acre, most recent ap plication,
years elapsed s i nce appl ication
B = 4.71 88 - 0.01 667 (S).
On untransformed scales, this becomes a multipl ier of the form ebF, where
b is a coefficient estimated from the data. This g ives a response starti n g from
zero, i ncreasi ng to a max i m u m at a t i me si nce applicat ion ranging from 2 years
on site 1 45 to 3.5 years on site 65, and then gradually dec l i n i ng to zero at a rate
which varies with site i ndex. Response is greater on low sites than on high
sites and i ncreases at a decreas i ng rate with i ncreased n itrogen dosage.
Location of the max i m u m response is controlled by "B," and the shape of the
response curve and rate of decay are control led jointly by B and the exponent,
here "3." Our data were i nadequate to clearly define either location of the
max i m u m or duration of response, and the val ues used here-though
consistent with our data and other avai lable information-will probably need
modification i n the future.
Expression of thinning effect in increment equations.-Since we lacked
i n formation on c rown devel opment or on stand characteristics before i n itial
thinning, we could not examine the possible effects of i n itial stand cond itions
on response to thinning except as these conditions may be reflected i n stand
statistics after thinning.
Di fferences i n current stand density, whether due to thinning or other causes,
enter the eq uations through the variable RD, but they are also associated with
various ratios such as height/diameter. No single coeffi cient i n th ese eq uations
can be speci fical ly identified as the estimated effect of stand density, or of
thinning .
X1 5
assumes non-zero val ues only for thi n ned stands. It can perhaps be
interpreted as an expression of that part of th i n n i ng response not satisfactori ly
represented by measures of density of the res idual stand. At l east this and
other similar expressions were consi stently significant over and above the best
com bi nation of variables without such a term.
X 15
70
iRo;
= (1 /A 'h ][1 /p](( H40/ D)(d H40)z e -(H40ID)(dH40)zr
where z =
elapsed i ncrement i n H40 s i nce th i n n i n g p
1 .0 i f R D
=
<
51 .0, otherw i se (RD - 4 1 )/1 0. The 1 /A v, and 1 /p com ponents were added after trials of i n i tially selected forms, to control anomalous behavior at the marg i ns of the ranges of age and density.
The effect of X15 i s to i ncrease growth rate of a th i n ned stand, relative to the
est i m ated g rowth rate of an unthi n ned stand of s i m i lar current attri butes, by an
amount which decreases with e lapsed height growth s i nce t h i n n i ng .
Mortality functions
Esti mates o f ratios o f net i ncrement to g ross i ncrem ent
were derived as weighted regressions. I n D FS I M , these ratios are used to
subdivide g ross i ncrement i nto net and mortality components, and other
associated val ues are derived from these.
.-
I n these data from smal l plots mortal ity was extremely variable and the regres·
sions derived, t hough "si g n ificant," account for only a smal l part of the total
variation. I n low density stands they are not m uch better than s i m pl e means.
Relationsh i ps are obviously weak and poorly defi ned, and D FS I M i ncludes a
series of constraints i ntended to mai ntai n con s i stency among estimates,
i nc l u d i n g derived values such as est i mated d i ameter of mortality.
Regressions derived were:
1. Vol u m e (VN ET):
a. For plots w ith R D
>
45,
y = dVnet/dVgross = 0.99787 - 0.0000069256(A)(R D)(H/D)
'
+ 0.001 052(T)(RD);
SEEY ""' 0. 1 7 ( = SEE of weighted regression/mean weighting factor).
b. For plots with RD :s; 45,
y
=
dVnet/dVgross
+
=
0.943 1 3
+
0.0026204(R D)
0.00001 1 1 58(A)(R D)(H/D)
0.0000431 99(T)(A)(RD) - 0.000 1 0773(T)(RD)(H/D);
with R2wy
=
0.09 SEEY ""' 0.09 71
2. Basal area (BAN ET):
a. For plots with R D > 45,
y
dGnetldGgross
=
=
0.87 1 2 6
+
0.0049359(A) - 0.00001 5861 (A)(RO)(H/D)
+
0.0021 756(RD) - 0.00001 5588(A)(RD)(H/0)
0.001 831 4(T)(R D); +
with R2w = 0.24 y
SEEy ""' 0.30 b. For plots with RD :S 45,
y
dGnetfdGgross
=
=
0.93609
0.000046458(T)(A)(RD); +
with R2w
SEs
Default Commercial
Thinning Regime
= 0. 1 1 y
""' 0. 1 4 Timing o f thinnings.-lf not otherwise spec ified by the user, the f i rst
. commercial thinning is made at the earliest age at which ( 1 ) basal area in trees
over 5.55-inch d.b.h, is at least 1 00 ft2/acre, and (2) it is possible to cut at least
20 ft2/acre i n trees with an average diameter of at least 9.0 inches i n natural,
previously unthinned stands, or 8.0 i nches in stands planted or precommer­
cially thi nned, and (3) RO (see footnote 6) is at least 47.5.
Subsequent thinnings are made when RD exceeds 50, except that ( 1 ) no
thinning is made if the stand i s within 10 feet in height or 5 years of scheduled
harvest, and (2) no thinning is made until i ncrement in RO since the last p rior
thinning exceeds 7.
Diameter of cut trees (DCODB). - I f not otherwise specified by the user,
d iameter of cut trees (d) i s defined by
d
=
8.0
+
0. 1 595 (0-6.0)1·5
with l i m its
0.80(0)
:S
d
:S
1 .00(0), if planted or p reviously thin ned,
d
:S
1 .05(0), if of natural ori g i n and not previously thi nned.
and
0.80
:S
Residual basal area (G LTL) -If not otherwise specified by the user, the l ower l i m i t of residual basal area is the greater of 72
(1 ) ov.[20.91
+
6.775(1n D)] or
(2) 011' [1 . 1 34
+
9.526(1 n A)];
with the restrict ions that resid ual basal area may not be less than 35(0'12), may
not be less than two-thirds of the prethinning basal area, and may not be less
than the residual basal area after the next prior comm ercial thinning, if any.
These are subjectively determ i n ed "best j udgment" relationships which
correspond to relative densi ties (AD's), ranging from 35 i n young stands of
smal l diameter to about 45 i n stands of large diameter or advanced age.
Appendix 4. Notes
on Testing DFSIM
U sing Real Data
The models in D FS I M were derived from reg ional data, and yield estimates
represent reg ional averages. The existi ng stand option was i nc l uded in D FS I M
primarily to allow testing on a s ubregional or instal l ation basis. Organ izations
having the necessary remeasured plot data and com puter facil i ties may wish to
ru n their own com parisons of D FSI M predictions with their data as a basis for
judging appl icabil i ty of D FS I M estimates to their lands and possible need for
modification for their use.
·
This section discusses methods of condu ct i ng plot com pari sons and points
out some p itfal l s i n their execution and i nterp retation.
Distinction Between
J uvenile and Main Stand
Procedures
DFSIM g rows stand s using two d i fferent growth procedures: (1 ) a j uven i l e stand
procedure when the stand is less than 5.55-i nch quad ratic mean diameter, and
(2) a main stand proced ure when the stand is 5.55 inches or larger. When
feasible, it i s desirable to test these two procedures separately because any
bias (particuarly if negative) introduced in the stand statistics by the juve n i l e
growth routine (J UVG RO) w i l l b e carried over i nto t h e m a i n stand routine and
may affect s ubsequent estimates.
Stands Less· Than
5.55·1nch D.B.H.
For a natural, previously unthinn ed stand, beg i n the simulation with the n u m ber
of stem s per acre greater than 1 .55-i nch d.b.h. at the beg i n n i n g total stand age.
For precommercially thinned or planted stands, beg i n the simu lation with the
n umber of resi dual trees or n umber of established trees r-egardless of d iameter;
this val ue can be approximated by the sum of the i nitial n umber l arger than
1 .55 inches p l u s the n u m ber of subsequent i ng rowth trees.
·
Research pl ots sometimes have multiple precom mercial thinni ngs. D FS I M
provides for o n l y o n e and cannot provide a f u l l y satisfactory representation of
the c u m u l ative effect of m u lti ple precommercial t h i n n ings. This situation can
be approximated, however, by beg i n n ing the s i m u l ation at the most recent
precommercial thinning by specifying the correspon d i ng n u mber of residual
trees and total stand age on the Existi ng Stand Card while specifyi ng the total .
stand age and residual number of trees at the earl iest precommercial thi n n i n g
on t h e Master Control Card.
One can simu late a p lanted stand which has a l so been precommercially
thinned . Remember t hat the number of trees speci fied or i m p l ied on the
Existing Stand Card controls the beg i n n i ng n u m ber of trees for the simu lation.
I f the simu lation i s to beg i n at the time of precommercial t h i n n ing, specify the
residual n u m ber of trees for the precommercial thinning on the Existi ng Stand
Card, spec i fy total stand age for the precommercial t h i n n i n g on both the
. Exist i ng Stand Card and Master Control Card, and s pecify the n u m be r of estab·
l i shed trees after planting on the Master Control Card.
73
If the s i m u lation is to begi n after a precommercial thinning, s pecify total age of
. existing stand and residual number of trees on the Exi st i n g Stand Card, and
specify total age of stand and residual n u m ber of trees for the precomm ercial
t h i n n i ng on the M aster Control Card. I n this case, OFSIM will pri nt the same
n u m ber of trees for both the pl antation and for the residual stand after
precommercial thi n n i ng. Planted n u m ber of trees is not u sed i n com putations
in this case because the s i m u l ation beg i n s with n umber of trees specified or
i m p l ied on the Existing Stand Card.
If s i m u l ation is to beg i n before a precomm ercial thinni ng, specify the n umber of
trees establ i shed by planting on the Exist i n g Stand Card, and specify total age
of stand and residual number of trees for the precom mercial th i n n i ng on the
Master Control Card.
We do not, however, recommend beg i nn i ng a p lot comparison s i m u l ation before a precommercial t h i n n i n g , because the only u ser contro l s over the t h i n n i ng are total age of stand and res i du al n u m ber of trees after th i n n i n g . Stands 5.55-lnch D. B.H.
and Larger
An additional option inc l uded i n OFSI M , pri mari l y f o r test u s e i n stands 5.55-inch d.b.h. and larger, is the option for observed stand top height . O bserved stand t o p heights can b e u sed i n cases where t h e trends i n height growth d iffer material ly from Bruce' s (see footnote 4) curves for the reg ional average. If observed stand top heig hts are u sed, a stand top height should be specified
before and after each commercial t h i n n i ng . If options for both observed stand
top heights and n itrogen ferti l ization are u sed, the ferti l izer effect w i l l not be
i n c l uded i n the height i ncrement except as i m p l ied by the observed stand top
heig hts. Fertil izer effects w i l l be i n cl uded in other statistics, in part, but may be
biased because other functions use height i ncrement as a predictor.
If the i nterval between t h i n n i n g s is too g reat for acceptable l i near approxi­
mation to the heig ht-growth curve, stand top heights should be s pecified at one
or more i n termediate ages.
When a commercial t h i n n i n g is s i m u lated, the thi n n ing can be contro l l ed by
specifying e ither (1 ) d/0 rati o and basal area c ut, or (2) residual basal area and
n u m ber of trees. We think the most reasonable and usef u l comparison with
observed development of actual stands is obtai ned by cutting back the
s i m u l ated stand to the observed residual basal area and n u m ber of trees at
each s uccessive thi n n i ng . Th i s also i m p l ies the same residual stand d i ameter
and has the effect of beg i n n i ng a n e w s i m u lation with each commercial
t h i n n i ng. Comparisons between the simu lated and real stand can then be made
in terms of sum mations of increments over successive t h i n n i n g i ntervals.
Whenever the options for residual n u m ber of trees and residual basal area are
used, the d/0 rati o option is inoperable; if diD rat io cards are in the control
deck, OFSIM i gnores them. Because of possi ble i mbalance between trees cut
and basal area cut, vol umes and d i am eters of trees cut may sometimes be
u n reasonable.
74
/
Appendix 5.
Yield Table Format
Development after t h i n n i ng in s i m u lated stands is i nfluenced by the rat io of
basal area cut to basal area before t h i n n i ng. If this ratio is less than 0. 1 5,
response from t h i n n i ng is reduced. Consequently, if more than 1 5 percent of
the basal area was removed from the actual stand and less than 1 5 perc ent was
removed from the s i m u l ated stand, the simu l ated stand can fal l beh i nd the real
stand in growth; and conversely. General ly, once t h i s process has beg un, it
te nds to become cumu lative, and the best solution is to start a new simu l ation
with each commercial t h i n n i ng.
Figure 1 2 shows the yield table produced by D FS I M for the following
speci ficat ions:
1 . Stand i s site i ndex 1 25 and of natural ori g i n .
2 . Stand is t o b e precom mercially t h i n ned a t age 1 1 t o 300 stem s p e r acre.
3. Commerc ial t h i n n i ng is to fol low the defau l t t h i n n i n g regi me, w h i c h spec ifies
that:
a. No commerc ial t h i n n i ng may be made unti l (1 ) average d iameter of cut
trees is at least 8.0 inc h es, w h i l e (2) basal area cut is at least 20 ft2/acre, and
(3) basal area of a l l trees 5.6-inch d.b. h . and larger is at l east 1 00 ft2/acre.
b. Commercial t h i n n i ngs are made whenever relative density (G/D '12 ) exceeds
50, subject to restrictions in (a).
c. d/D ratios and lower l i m its on resid ual basal areas fol low the d efau lt functions i n D FSI M. 4. Harvest cut i s to be at total age 80.
5. O ptional tables for trees 5.6-inch d.b.h. and larger and for trees 7.6-inch d.b.h.
and larger are to be prod uced.
6. I ntermediate statistics are to be pri nted for each year of the s i m u l ation.
Definition of the h ead i ngs are as fol l ows:
1 . Table for total stand (stems 1 .6-i nch d . b. h. and l arger).
TOT AGE=, YRS.-Age from seed .
BH AGE, YRS. -Years si nce attai n i n g a top height of 4.5 feet.
HT40, FEET. - M ean h e i g h t of the largest (by d i ameter) 40 ste m s per acre.
LOREY HT, FEET.- Height of the tree of mean vol ume.
DBH, I NC H . - Quad ratic mean d.b.h. ( = d.b.h. of tree of m ean basal area) of all
stems 1 .6 i nches and l arger.
75
BASAL A REA/A, sa FT. - Basal area in square feet per acre of all stems
1 .6-inch d.b.h. and l arger.
TREES PER ACRE. - N u m ber of stems per acre 1 .6-i n c h d . b.h. and larger.
CVTS PER ACRE.-Total vol u m e (CVTS) in ft3/acre of all stems 1 .6-i nch d.b.h.
and larger, i n c l ud i ng stu m p and tip.
CAl , N ET, CVTS.- N et current annual i ncrement in ft3/acre per year of total
vol u me of all stems 1 .6-i nc h d.b.h. and larger.
MAl CVTS, G ROSS, 1 .6 + -Gross mean annual i ncrement i n fetacre per year of
total vo l um e of al l stems 1 .6-i nch d.b.h. and larger. This is calcu l ated as
(total vol ume)
of l ive stand
cumulative vol ume of
commercial thinn i n gs
cumulative vol ume
of mortal ity
(total age)
N ote the omission of mortality t hat occurs before the stand attains an average
d i ameter of 5.55 i nches.
MAl CVTS, N ET, 1 .6 + -Net mean ann ual i ncrement i n fetacre per year of total
vol u me of all stems 1 .6 - inch d.b.h. and larger. This is cal culated as
total vol ume
of l ive stand
+
cumulative volume of
past commercial thinnings
(total age)
MAl CV4, N ET, 5.6 + - Net mean ann ual increment i n ft3/acre per year of vol ume to a 4.0-inch top d . i.b. (CV4) of al l stems 5.6-inch d.b.h. and larger. MAl CV4, N ET, 7.6 + - N et mean annual increment i n ft3/acre per year of vol um e to a 4.0-inch top d . i.b. (CV4) of al l stem s 7.6-inch d.b.h. and larger. Entries in the l i nes beg i n n i ng YEARLY M O RTA LITY g ive the stat istics for the trees which di ed i n the i ndicated 1 -year interval. The summary table for commercial thinn i n gs contai ns the fol l owing lines: B EFORE, the i nd icated statistics for the stand before t h i n n i ng. CUT, the i ndicated statistics for the trees removed in the c urrent thi nning. R ES IDUAL, the i n dicated statistics for the trees remai n i n g after the current t h i n n i ng. SUM CUTS, the cumulative totals of t he indicated statistics for all trees removed i n comm ercial t h i nn i ngs up to and i ncluding the current t h i nning. 76
SUM M O RTALITY, the cumulative totals for all trees which died after the year
i n which the stand attained a q uadratic mean diameter of 5.55-inch d.b.h.
At the time of fi nal harvest, the program p rints the fol lowing l ines:
HARVEST, stat istics for the stand in the year of f i n al harvest.
SUM CUTS, statistics for the sum of the harvest cut and al l prior commercial
t h i n n i ngs.
SUM MORTALITY, stati stics for the sum of all mortal ity which has occurred
si nce the stand attained a q uad rati c mean d i ameter of 5.55-inch d.b.h.
2. Tab le for stand 5.6-i nch d.b.h. and larger.
Col u m n headings correspond to those in the total stand table, except for the
add ition of CUBIC FEET PER ACRE, 4-I NCH TOP ( = CV4) and the fact that
statistics are for trees 5.55-inch d.b.h. and larger. Line head i ngs correspond to
those i n the summary table for the total stand.
3. Table for stand 7.6-i nch d.b.h. and larger. Co l u m n headings correspond to those in the table for total stand, except that the stat i stics are for trees 7.55-i nch d.b.h. and larger, and the fol lowing additional headi ngs appear: CVTS
=
total . volume i n fP/acre i ncluding stu m p and tip.
CV4
=
vol u me in ft3/acre to a 4-i nch top d.i .b., exclud i n g stump.
CV6
=
vol ume in te/acre to a 6-i nch top d.i .b., excluding stump.
IV6 = vol um e in board feet, international 1AI -inch rule, to a 6-inch top d.i.b.,
based on 1 6-foot log lengths.
SV6 = vol ume in board feet, Scribner ru le, to a 6-inch top d .i .b., based on
1 6-foot log l engths.
Line head i ng s correspond to t hose i n the summary table for the total stand.
77
G l ossary
A-Age b.h. (years s i nce attain i ng b.h.). Ar- Total
age (years from seed). b.h.-Breast height (4.5 feet height above g rou nd). CT -Com mercial thinning (any t h i n n i ng made when stand q uad ratic mean d.b.h. exceeds 5.55 i n ches).
CVTS-Cubic vol u m e i nc l ud i n g stump and t i p, expressed in ft3•
CV4- Cubic vo l u me to a 4-i nch top, exc l u d i n g stump, expressed in ft3•
CV6-Cubic volume to a 6·inch top, exc luding stump, ex p ressed in ft3•
d.b.h.-Diameter at breast height, expressed in i nches.
d - Q uadrati c m ean d.b.h. of cut trees.
diD - Ratio of q u ad ratic mean d.b.h. of cut t rees to that o f al l t rees before
cutting. D- 01 .6 (quadrat ic mean d.b.h. of all stems over 1 .55-i nch d .b.h.). 05.6-Quadratic mean d.b.h. of all stems over 5.55-inch d . b.h. 07.6-Quadratic mean d.b.h. of all stems over 7.55-i nch d.b.h . . dH40-A n nual i nc rement i n top height, ex p ressed i n ft/yr.
dV-Ann ual i n crement i n vol ume, expressed i n ft3/acre per yr.
dVnet- A nn ual i nc rement in net vo l u me, expressed in ft3/acre per yr.
dVgross -Annual i n c rement in g ross vol u me, e x p ressed in ft3/acre per yr.
dG-Ann ual i nc rement in basal area, expressed in ft2/acre per yr.
dGnet-Annual net i n crement in basal area, exp ressed in ft2/acre per yr.
dGgross-An n ual g ross i nc rement in basal area, e x p ressed in ft2/acre per yr.
dD- Ann ual i ncrement in stand quad ratic mean d iameter.
F - N i trogen fert i l izer response variabl e in i ncrement functions.
FRT - N it rogen fert i l izer res ponse variable i n j uven i l e diameter function.
G - Basal area, expressed i n ft2/ac re.
H40-Top height (mean height of 40 largest (by d.b.h.) stems p e r acre).
HF- H40 at time of fert i l izer appl ication.
IV6-Vol ume to a 6-inch top d . i.b. by 1f4 ·inch i nternational rule, expressed i n
board feet/acre. In-Nat u ral logarithm (logarithm to base e). 78
n - N umber of trees on p l ot, or a speci f i ed portion thereof.
N - N u m ber of trees per acre.
N0_0- N u m ber of estab l i shed t rees per acre, regardless of d i am eter.
N1 .6-N u mber of stems per acre over 1 .55- i n c h d.b.h.
Nu- N u m ber of stem s per acre over 5.55-inch d .b.h.
N7_6 - n u m be r of stem s per acre over 7.55-inch d. b.h.
#I N - Pounds of n it rogen per acre.
PCT- Precom mercial_ t h i n n i ng (any t h i n n i ng made when stand q u ad rat ic mean
d iameter i s l ess than 5.55 i nches).
PORT - A variab l e assum i ng a val u e of 1 .0 for p l an ted or t h i nn ed stands, 0.0 for others . RD-A measure o f relatively density, defi ned a s G/Dv'. S-S ite i ndex, base age 50 years b.h. SV6-Vo l u m e to 6-i nch top d.i. b. by Scri bner rule, 1 6-foot logs, expre ssed i n
board feet/acre.
R2 :-Coeff icient of d eterm i n ation of the variable y.
v
Rei EY - R elative error of t he u ntransformed variable y, expressed as the
percents correspondi ng to ± one SEE on logarithmic scales.
·
SEEY -Standard error of esti mate of the variabl e y.
T -A variabl e ass um i ng a val u e of 1 .0 for t h i n ned stand s, 0.0 for ot hers.
V/G- Ratio of vol u me to basal area
=
CVTS/G.
'
v-l ncrement i n H 40 si nce appl icat i o n of fert i lizer. w-Weighting factor i n regression. x- N u m ber of years si nce most recent fertil izer appl i cat ion. X1-ith i ndependent variable in reg ression. Y- Dependent variable in regression. z- l ncrement i n H 40 s i nce most recent thi n n i ng. <.. U.S.
GOVERNMENT PRINTING OFFICE: 1981 -798·4761237
79
I
I
I
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Curtis, Robert 0., Gary W. Clendenen, and Donald J. DeMars.
1981 . A new stand simulator for coast Douglas-fir: DFSIM user's gu ide. USDA
For. Serv. Gen. Tech. Rep. PNW-1 28, 79 p. Pacific Northwest Forest and Range
Experiment Station, Portland, Oregon.
DFSIM (Douglas-fir Simulator) is a new managed stand simulation program for coast
Douglas-f ir (Pseudotsuga menziesii (Mirb.) Franco var. menziesii). It was developed
from remeasured plot data contributed by many organ izat ions in the Pacific
No rthwest. DFSIM is based on more extensive data and is considerably more
flexible than previous whole-stand simu lators for the species. It produces yield
tables for managed stands which include estimates of effects of initial spacing,
precommercial and commercial thinning, and nitrogen fertilization. Topics discussed
include basic data, simulator construction and operation , l i m itations of the program,
and potential for further development. The program is avai lable from the authors on
request . A subsequent publication will present DFSIM yiel d tables for a number of
management regimes.
Keywords: Sim ulation, yield tables, growth models fert i l i zation (forest), thinning
effects, computer programs/programmin g, Dougla ·fir, Pseudotsuga menziesii.
The Forest Service of the U .S. Department of
Agriculture i s dedi cated to the pri nciple of m u ltiple
use management of the N ation's forest resources
for sustai ned yields of wood, water, forage, w i ld l ife ,
and recreation. Through forestry research,
cooperation with the States and p rivate forest
owners, and management of the N ati onal Forests
and National Grasslands, i t strives - as directed by
Congress - to provide increas i n g l y greater service
to a g row i ng Nation.
The U.S. Department of Ag ricu lture is an Equal
Opportunity Employer. Applicants for all Department
programs y.t i l l be g iven equal consideration w ithout
regard to age, race, color, sex, rel i gion, or national
ori g i n .