A New Stand Simulator for Coast Douglas-fir: DFSIM User's Guide

Transcription

1 f[.'!. 1% A '.s\. y.fi!j}; United States Department of. Agnculture Forest Service Pacific Northwest Forest and Range Experiment Station General Technical Report PNW-128 May 1981 A New Stand Simulator for Coast Douglas-fir: DFSIM User's Guide Robert 0. Curtis, Gary W. Clendenen, and Donald J DOUGLAS ALAN fv\guire.. DeMars

2 Authors ROBERT 0. CURTIS and GARY W. CLENDENEN are mensurationists at the Forestry Sciences Laboratory, Pacific Northwest Forest and Range Experiment Station, rd Ave. S.W., Olympia, Washington DONALD J. DEMARS is forester at the Pacific Northwest Forest and Range Experiment Station, 809 N.E. 6th Ave., Portland, Oregon

3 ' DOUGLAS ALAN MAGUIRE Abstract Curtis, Robert 0., Gary W. Clendenen, and Donald J. DeMars A new stand simulator for coast Douglas-fir: DFSIM user's guide. USDA For. Serv. Gen. Tech. Rep. PNW-128, 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-fir (Pseudotsuga menziesii (Mirb.) Franco var. menziesii). It was developed from remeasured plot data contributed by many organizations in the Pacific Northwest. DFSIM is based on more extensive data and is considerably more flexible than previous whole-stand simulators 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, limitations of the program, and potential for further development. The program is available from the authors on request. A subsequent publication will present DFSIM yield tables for a number of management regimes. Keywords: Simulation, yield tables, growth models, fertilization (forest), thinning effects, computer programs/programming, Douglas-fir, Pseudotsuga menziesii.

4 DOUGLAS AlAN MAGUIRE Contents 1 Introduction 2 The Data 2 Sources, Assembly, and Editing 3 Treatment of Understory 3 Height Estimates 3 Top Height and Site Index 4 Plot Summaries 4 Screening and Combining Growth Periods 5 Data Distribution 16 Regression Analyses 17 The Simulator 17 Juvenile Stand Development 18 Main Stand Development 20 Simulator Performance 21 Limitations 24 Relation of DFSIM to DFIT 25 Future Development 25 Application 27 Conclusion 27 Metric Equivalents 28 Literature Cited 28 Appendix 1. Program Operating Instructions 30 DFSIM Options 42 Control Card Formats 56 Messages Printed During Execution 59 Appendix 2. Description of Program Segments 64 Appendix 3. Driving Functions 64 Height and Height Increment Equations 65 Volume-Basal Area Ratio Equation {VGRAT) 65 Juvenile Stand Equations 66 Main Stand Equations 72 Default Commercial Thinning Regime 73 Appendix 4. Notes on Testing DFSIM Using Real Data 73 Distinction Between Juvenile and Main Stand Procedures 73 Stands Less Than 5.55-lnch D.B.H. 74 Stands 5.55-lnch D. B. H. and Larger 75 Appendix 5. Yield Table Format 78 Glossary

5 Introduction In 1974, the Pacific Northwest Forest and Range Experiment Station and Weyerhaeuser Company agreed to combine their data with that of other interested organizations, in a joint effort to develop new and more broadly. based yield estimates for managed stands of coast Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco var. menziesii). The objective was a system which would describe development of even-aged Douglas-fir stands for a range of initial stand conditions and treatment regimes, and which could be modified to incorporate improved information in the future. Thirteen organizations contributed the data which form the basis for the new stand simulator DFSI M1 (Douglas-fir Simulator). This is probably the largest aggregation of remeasured research plot data for the species. The predecessor of DFSIM was DFIT (Bruce, DeMars, and Reukema 1977; Reukema and Bruce 1977). The new simulator is a whole-stand model (Munro 1974), similar to DFIT in general nature and intended application. The principal differences are (1) a much stronger base in data from treated stands, and (2) an internal structure and available options which we believe are more flexible and have greater potential for future modification and extension. DFSIM does have its defects and limitations, which may be corrected in the future. Major improvement witt probably require updating and extension of the data base and development of improved estimates of component relationships. We believe the present version of DFSIM has had sufficient development and testing to justify its use in timber management. In this report we will provide an understanding of the nature and operation of DFSIM, and sufficiently detailed information to allow intelligent 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 simulator, methods of analysis, structure and operation of the program, limitations and prospective uses, and related background information. This is followed by a more detailed presenta tion of the mechanics of operating the program, program options, certain program components, and a sample yield tabie. A companion publication will present DFSIM yield 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 Reukema of the Pacific Northwest Forest and Range Experiment Station, who provided helpful advice and review during analyses.

6 The Data Sources, Assembly, and Editing We canvassed interested organizations and compiled a list of data likely to be useful. We sought remeasured research plots, primarily those from thinning and fertilization experiments. We did not use inventory plots becavse of expected difficulties with smal l plot sizes, truncated diameter measurements, inadequate sampling of heights and ages, and similar characteristics common in inventory plots not specifically designed for use in yield table construction. The thirteen organizations which contributed data that appeared suitable for our purposes were: British Columbia Forest Service Bureau of Land Management Canadian Forestry Service Crown Zellerbach Corporation International Paper Company MacMil lan-bioedel ltd. Oregon Department of Forestry Oregon State University Pacific Northwest Forest and Range Experiment Station Roseburg Lumber Company University of Washington (includes cooperators in the Regional Forest Nutrifion Research Program) Washington Department of Natural Resources Weyerhaeuser Company Despite initial screening, the data we received were extremely variable in standards of measurement and lacked a consistent and compatible format and coding system. Particularly serious and widespread problems were inconsistent and inadequate sampling and measurement of heights and ages, and unreliable or missing information on stand characteristics prior to initial thinning. Some plots were revisited during 1975 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 feasible. All data were converted to the standard format and coding system. Assembly, editing, and conversion of data to a common system proved to be a massive task, requiring several employee-years of work by the Experiment Station and Weyerhaeuser Company. 2Arney, James D. and Robert 0. Curtis 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 D. R. Reimer, Chairman. West. For. and Conserv. Assoc., Portland, Oreg. Dec

7 Treatment of Understory Douglas-fir is relatively intolerant of shade, and stands often develop an understory of small, younger stems of cedar, hemlock, and true firs. These small stems have little effect on volume growth or harvestable volume, but their presence strongly affects calculations involving number of trees and average diameter. We attempted to exclude these smal l stems when they were clearly of a different age class from the main stand. We calculated plot means and s.tandard deviations of diameters for Douglas-fir and coded as "understory" any stem of an associated species which on its first appearance in the record was smaller than the plot mean diameter of Douglasfir at that time, less 2112 standard deviations. Such understory stems were excluded from all subsequent computations. Height Estimates Weaknesses and inconsistencies in height sampling and measurement were widespread and obviously critical to the planned analyses. Where reasonable samples were available for given dates, we fitted regressions of the form In (height - 4.5) = a + b (dbh)c in which a and b were coefficients estimated for each measurement date. A single overall estimate of c was used for all measurements on any one plot to provide consistency among curves for successive 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 expressed as functions of age (Curtis 1967). This "pooled" regression was used to estimate heights in cases where the height sample was lacking or grossly inadequate for a particular date, or where the curve for a particular date appeared inconsistent with those for other ages on the same plot. These relationships and the Bruce-DeMars (1 974) volume equatio n were used to assign an estimated height and volume 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.), where n = 40.0 (plot area in acres) with restriction n 2: 4. Site index (S) values were assigned to plots using H40, corresponding plot age b.h., and King's (1 966) site index curves. Although H40 is not identical with the stand fraction used by King, differences are usually small. If successive measurements bracketed age 50 b.h., we estimated site index by linear interpolation; otherwise, we used the estimate for the measurement age nearest 50 b.h. If the stand had been fertilized prior to age 50 b.h., we substituted the mean of the estimates for the associated control plots. 3

8 Plot Summaries Screening and Combining Growth Periods Individual tree records with assigned heights and volumes, plot values of H40 and site index, and information from the plot index file were used as input to a plot summary program. This program gave us (1) stand statistics at each measurement date for trees over 1.55-inch, 5.55-inch, and 7.55-inch d.b.h., (2) merchantable volumes to various size limits, and (3) corresponding values for periodic mortality, ingrowth, and cut. At this stage, some plots and individual measurements within plots were rejected. These included: 1. Plots less than SO-percent Douglas-fir by basal area. 2. Excessively small plots. Plots were ranked by size relative to average diameter and the smallest were dropped. Minimum acceptable relative size was necessarily a compromise between the analyst's concept of desirable size and the realities of available data. Rejects included most 1/20-acre plots, and some 1/10-acre plots in stands of large average diameter. 3. Fertilized plots of marginal size lacking buffers between treatments. 4. Plots with obvious catastrophic mortality. 5. Plots with more than one age class in the main stand. 6. Plots with missing or obviously incorrect values, which prevented calculating a full set of stand statistics. (Additional deletions were made at later stages, when previously undetected errors or widely aberrant values were encountered.) The original measurements were made at intervals varying from 1 to 10 or more years. We attempted to combine these into growth periods of more nearly comparable length. We used King's (1 966) height-age equations to calculate years required for 10 feet of height growth at each initial age. Where possible, successive growth periods were combined to approximate this interval, subject to three restrictions: 1. No period could overlap a thinning or fertilization date. 2. No period could be less than 2.6 years. 3. No period could have basal area mortality per year exceeding five percent of the live basal area. Any period or combination of periods not meeting these requirements was / deleted. After screening and combining, there was still considerable variation in period lengths, whether measured in years or height increment. 4

9 Data Distribution After these operations (and subsequent occasional deletions), we had available for analyses 2,654 growth periods from 1,434 plots on 203 installations. Overall distribution of data is shown in tables 1-3 and figures 1-9. When all plots are considered, there is a reasonably good distribution across sites and ages. The distribution is much less satisfactory, however, when the data are subdivided by stand origin and treatment class, and when one remembers that multiple plots in a single installation are not really independent observations. In particular, there were little or no data for plantations older than about 40 years, for any stands over 80 years, for stands with repeated fertilization or long periods of observation following fertilization, or for older, thinned stands with a history of low initial density or early stocking control. TABLE 1-Number of growth periods used in DFSIM analysis, by stand origin and treatment Treatment Planted stand No PCT1 PCT Natural stand No PCT PCT Total No CT2 or fertilization CT, no fertilization , No CT, fertilized CT and fertilized ' 233 All treatments , ,654 1PCT (pre-commercial thinning) is any thinning 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 larger. 5

10 TABLE 2- Number of plots used in DFSIM analyses, by stand origin and treatment Planted stand Natural stand Treatment No PCT1 PCT No PCT PCT No CP or fertilization CT, no fertilization No CT, fertilized CT and fertilized Total All treatments ,434 1PCT (pre-commercial thinning) is any thinning made when the average diameter of the 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 larger. TABLE 3-Number of installations in DFSIM analyses represented by each stand origin and treatment1 Treatment Planted stand No PCP PCT Natural stand No PCT PCT No CP or fertilization CT, no fertilization No CT, fertilized CT and fertilized There were a total of 203 installations. Most contained multiple plots representing different treatments. 2PCT (pre-commercial thinning) is any thinning made when the average diameter of the stand is less than 5.55 inches. :JT (commercial thinning) is any thinning made when the average diameter of a stand is 5.55 inches or larger. 6

11 J: f t4 f f t4t 23 t23 f f f t t 2t f t bt t tt t ft I I t t 2t24 t t2292ttt t t t 2t22t n t * t I 21 2 t2tt flfi 4b b92%9339 ff ff ttffft tt tt2 HI HI t3732H232tn f f 94 9t393BI2t5f Ht t H IHf t 2 99t7 999S t91 2t2t t4f f t f f f f I 2 ff f 7t%79t H2 5f 2t4bt2H 22t f f t ai 3H n39922 flf3531 ff f4q Ht2 ff f ff f ttn H II f f f 10 fh H93943H I 122 I H f f I t Gl IH2t t3492t32247t tt574 f 3 t2t2 f %42H7t232f5454f t2 f I H 2 t42t3t34 t2h23t32t t 2 t3t 3 t21 2t f f m 1oo.oo as 2t22t323t tHf ttn f23t 4 2 f f 2 2 m f 2t t fit f 3 2"...2 2t 3t 2 t2 f f f f f f f: 9 f t tt42 I f 332b432H2 2 t f f t )( Gl 4 t5 3t l 4 t t ffl lf flf f f "0 f Jl f t2f f 9t 9t t c: 80,.00 H f f t! (i *2 9 f 3 *3* 9 t2*9 ftt 2t t 2t 2 tt H t2 f2t t2 f t t 40: Total Age Figure 1.-Distribution of growth periods by site index and age b.h., all data. 7

12 f ff I f f I f I f 2H 122 2* t2t2t f f f f 22 HH3f If f HI f I f I f If 21 tf t4 tff23 t22 f I 2 12 ffff I I 123 fff 2 f f I f I fl l: 2 12t t t t 2 I t f f I t f f f f 2 f f f 2 31 f 23 f H f ai t f Ht2f3H 52 tt2 t f f t f 0 10 tf 21 3tH 314 ff 14tU22 ft 4 f I f * I G) 2 12 t ff I f f I I 01 f f ft 2H Ht2 If 21 3f 2 2 <( tt f f I t4 ff If 31f t f G) Ul f f I'l If f 2 m I )( G) "0 f G).. (jj f fff f fl f f 3 *2 f f I 2 12 * f f flfl f *2* 3 I ffl f ffl f 2 t22t 21 ** 2 f f f I f f ** f f f I I * ll f H f 2 * * f * f f fl f f f f I Total Age Figure 2.-Distribution of growth periods by site index and age b.h., untreated natural stands. 8

13 Total Age Figure 3.-Distribution of growth periods by site index an d age b.h., untreated plantations. 9

14 :I a: U * 2 * I I H ** f H * I f I f f I f lb I 261 * HI I ff * * I 2 IH213 I f4 *32 I * * 21 2 * I ** 4 2 fb *61 b It 3ft * * I H 12 I 12 I 2* * f f I 311 f Ill * * f H] *2 f 1223 I 4H f I 10 G) I f * I 142 * 12 I I 01 H 112 f *91 f 2232 HIH5*13 21 f 33 f 2 f H ft < ff 2 3H f 2 I I G) Ill H * * 3 I 2 * * I 111 f I f H 2 I. I I I f I 2 2 Ill I I I 2 f f f I x f f ff G) f I f * Jf I "0 c:: **! * f (i f HI Total Age Figure 4.-Distribution of growth periods by site index an d age b.h., thinned (precommercial or commercial), natural stands. 10

15 :t ai Q), c * * 3 3 * 2f 2 f2 f2 f f 2f 2 f2h f f fh 5f 4f34t4ff 3 f 8J 8H8 16 f I f :H f f 0 It H f 6t f f f Q) ff*fl St f Ol Hfff 33b4 1 2f <( ff H5 2 f $ Ql f Hfff3 f m 2 >< f f f s f ff I 2 2 I * * f f f Total Age Figure 5.-Distribution of growth periods by site index and age b.h., thinned (precommercial or commercial) plantations. 11

16 * 2t 21 HH 2Ht f lf f f * I 3 4 I I I H224 2 I HIH3"l 2f4Hf I H I: H t II IH *2341 * Iff I * HHH f' 0 In 1' * 4 2 I f f Hff 3 t2 95t343932f Ol f 21 * f 22 t2t2 * nu t2t ft f * f 2 rn Ill * ff2l3t H f Ill 2 2 )( *2* 33tlrt t tt r:: G) *2 2*200 f 33 a: IH f G) H291 f 41 < f L G) *** f G) 2 I 2* * 2 41 f 42 " f '0 t2t 9f 9t (j * f Total Age Figure 6.-Distribution of growth pe riods by site index and age b.h., fertilized, unthinned, natural stands. 12

17 J: aj It G) 01 <( G) II Cll m x G) "D c ! 9 9 (j Total Age Figure 7.-Distribution of growth periods by site index and age b.h., fertilized, unthinned plantations. 13

18 J: m 0 10 Q) Ol <( Q) Ill Ill m )( Q) "0 c: Q).. ij H22Uf f f f fh2hf f 2 4f 33 f Total Age Figure B.-Distribution of growth periods by site index and age b.h., ferti lized and thinned natural stands. 14

19 I: ai U) (I *99* o9 <( (I fl ca lx x (I "D c s co Total Age Figure 9. -Distribution of growth periods by site index and age b.h., fertilized and thinned plantations.

20 b. Plantations. The user must supply the number (N 0.0 ) of al l successfully established stems.5 The program then assumes no further ingrowth and an arbitrary, very low mortality until. either the stand reaches a diameter of 5.55 inches or N 00 exceeds the estimated number of stems over 1.55 inches for the untreated, natural stand of the same site and age (a condition likely to occur only in plantations with extensive natural fill-in). If the latter occurs, the natural stand estimate is substituted. c. Precommercially thinned stands, natural or planted. The number of stems (N 00 ) left after precommercial thinning and age at precommercial thinning are specified by the user. The program then assumes no ingrowth and an arbitrary, very low mortality until the stand reaches 5.55-inch d.b.h. 3. Quadratic mean diameter (D1.6). Quadratic mean d.b.h. of stems over 1.55 inches is calculated for each successive year, using function DIAMJ with H40, N 1 6, and specificat ions for _ precommercial thinning and fertilization. 4. Mortality. Any mortality occurring during juvenile stand development is excluded from estimates of cumulative mortality given in later program summaries. Main Stand D.evelopment 1. Stand projection. After stand diameter reaches 5.55 inches, stand projection proceeds as follows:. - a. Increment in H40 (dh40) is estimated by function HTGROW, and successive H40s are estimated by adding successive dh40s to attained H40. b. Gross increments in basal area and volume are predicted by functions BAINCR and VINCR. These gross increments are subdivided into corresponding net increment and mortal ity using functions BAN ET and VN ET. If needed, increments are adjusted to keep volume/basal area ratios consistent with function VGRAT. c. Net increment in quadratic mean diameter (D) is estimated by function DIN CR. d. If needed, the three net increment estimates and associated mortality estimates are adjusted to maintain co nsistency among estimates. Live stand statistics are advanced by 1-year growth periods by summation of estimated increments. e. Number of mortality trees is calcu lated as the difference in numbers of live trees calculated from successive live stand diameters and basal areas. Diameter of mortality trees is calculated from the number of these trees and their basal area. Cumulative mortality is the sum of mortality increments since the stand reache'd a diameter of 5.55 inches. 5For very small diameters this introduces a bias, since function DIAMJ was derived using N1 6 rather than N 00. This becomes negligible for D1 _ 6 larger than about 4 inches. 18

21 Stand projections are made by summing estimated annual increments, as outlined above. The functions for volume increment, basal area increment, and diameter increment were derived as reg ressions using stand statistics at the midpoint of the measurement period as predictors (X.). This was done because I of the variable lengths of actual measurement periods in the data. Since values of the X; available for use in stand projections are those at the beginning of the 1-year projection period rather than the midpoint, estimates made using initial values are biased by an amount which depends on curvature of yield functions at that point. This bias is controlled by a procedure which calculates approximations to the midpoint values of the X. and then uses these to I calculate the final estimates of increments. 2. Fertilization. The functions for height, gross volume increment, gross basal area increment, and net stand diameter increment include a term which increases growth rate for a limited period following application of nitrogen fertilizer (subroutine XFERT). 3. Commercial thinning. The user can specify timing, type, and severity of thinning by several options as discussed in the section on program operation (appendix 1). If not otherwise specified, thinning follows a regime incorporated in the program (appendix 3), which we think is reasonable but not necessarily optimum. The user can modify this by specifying residual basal areas, did ratios to be used (did = (quadratic mean d.b.h. of cut)l(quadratic mean d.b.h. of stand before cut)), minimum basal area (in stems over 5.55 inches) at which the first thinning can be made, and minimum acceptable average diameter of cut trees. When a commercial thinning is made from above (did ratio for all trees over 1.55 inches is greater than 1.0), H40 is reduced by an amount which depends on the amount cut. The functions include terms which modify estimates following thinning. These involve one or more of the variables thinned versus unthinned, height increment since the most recent thinning, ratio of H40 to live stand D1.6, and relative density.6 Because much of the data lacks reliable information on stand statistics prior to the initial thinning or crown development, we were u n able to use expressions involving prethinning stand statistics, number and size of stems cut, or crown development as predictors of thinning response. 6 Relative density is expressed as the variable RD "" GI{D' ), where G is basal area in stems over 1.55-inch d.b.h., and Dis 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

22 4. Summary tables. A summary showing statistics for live stand, cut stand, residual stand, and cumulative values for cut and mortality for stems over 1.55-inch d.b.h. is produced for each thinning date and final harvest. Intermediate summaries are optional and can be requested at any specified age (appendix 1). Optional summary tables are provided for merchantable volumes 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 values are derived from the corresponding values in the basic output table (stems over 1.55-inch d.b.h.) by using the merchantable volume ratios (Subroutines VOLCON, MERCHV and MERCHT) given by Williamson and Curtis (1980). Note that cut totals for thinned stands do not include potentially salvable mortality. Simulator Performance How well does DFSIM represent reality? Unfortunately, we cannot provide an explicit answer. Ideally, a simulator should be tested against a sample of data which is independent of that used in its construction and representative of the range of possible conditions and treatments for which the simulator might be used. Although a large number of plot measurements were available, they came from a much smaller number of installations, and plots within one installation are certainly not independent. We could not draw a truly independent sample from the data without seriously impairing the data base available for constructing. the simulator. Therefore, we chose to use all available data for the original analyses. A second difficulty was the heterogeneous nature of the data. There was wide variation in length of observation period, initial age, number of serial observa tions per plot, number of plots per instal lation, and distribution of treatments by age and site. We could see no computationally feasible way in which a comparison over all data of predicted with observed values for each of the statistics of interest could be reduced to a simple, meaningful, and readily interpretable set of statistics. We therefore chose a limited number of installations, judged "best" by length of record and apparent reliabi l ity of measurements, to compare with simulator predictions. Each simulation began with observed plot statistics. Each time a thinning was made on a real plot, the simulated stand was thinned (when possible) to the same residual basal area and number of stems. Growth trends in net and gross volume and basal area; diameter of live trees; and number, basal area, and average diameter of mortality were compared graphical ly and by means of ratios of the form r:: (estimated increment)/i:: (observed increment). A partial summary is given in table 4. 20

23 Conclusions drawn from suc_h a partial comparison are necessarily incomplete and subjective. Certain installations showed consistent deviations from predicted trends. Some deviations clearly resulted from differences in height growth pattern. Some may have arisen from errors in estimating stand age and site index in very young stands. Some probably resulted. from differences in early stand history, site characteristics, or other attributes associated with physical location and not adequately expressed by the variables used. Initial comparisons appeared to show a tendency to overestimate mortality in young, thinned stands. There was also some tendency to underestimate growth in young stands on good sites which had received very early, repeated thinnings and had been maintained at low densities. This category is represented by the LOGS studies (Williamson and Staebler 1971 ) and a few similar installations. There were no low-site stands with similar treatments which had yet attained sizes allowing comparison with those on better sites. These instal lations had been highly selected for stand uniformity and good crown development, had received carefully controlled thinning, and had not exhibited the growth depression or "thinning shock" sometimes observed on poor sites. Stand descriptors in our equations may not satisfactorily distinguish these initial conditions from those associated with lesser response. ' We made some adjustments to the mortal ity computations, and to the increment functions for young, low density (RD less than 40), thinned stands. Within the limitations of our present data, we do not see a clear need for further modification. We think estimat.es are a good regional average, even though individual installations may differ considerably. Limitations DFSIM users should be aware of some uncertainties and limitations, which arise mainly from limitations of the basi.c data. These are not peculiar to DFSIM; similar qualifications apply equally to most other stand simulators and yield estimates. A fundamental limitation in any attempt to estimate development of intensively managed stands over an entire rotation is the simple fact that there are no stands now in existence, avai lable for sampling, which have developed to an advanced age under the type of management which seems likely in the future. Older stands had no regulation of competition in early life, and therefore commonly have restricted crown development and limited responsiveness to treatment. Some of our "thinned" stands represented treatments which many foresters would not consider reasonable thinnings. We had little data for repeated commercial thinnings in plantations or stands which had early density control. Comparison with the little data available from the LOGS studies and similar conditions suggests that potential benefits of systematic careful thinnings, begun early, in-stands which have not experienced severe competition, may be greater than indicated by our estimates. 21

24 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 Installation Age span Treatment Number Site class number (total age) Origin class of plots dvgross dggross dd 6 I Nat Th (145) Nat NT Th F Th+ F p NT Th F Th+ F Nat NT Th Nat NT Th II p NT (125) Th p NT 3 (0.83) (0.79) 1.16 Th p NT Th Nat NT T p NT 3 (0.87) (0.75) 1.12 Th Nat NT 3 (0.62) (0.47) 0.94 Th Nat NT Th p NT Th Nat NT Th p NT Th F Th+ F

25 TABLE 4-Summary of comparisons of DFSIM estimates with observed gross volume Increment, gross basal area increment, and net stand diameter increment, continued Observed plot statistics r.y est/r.y obs 1 Installation Age span Treatment Number Site class number (total age) 2 Origin 3 class of plots 4 dvgross 5 dggross dd6 Ill Nat NT (105) Th Nat NT Th Nat NT 3 (1.02) (0.89) 2.15 Th Nat NT 1 0, Th Nat NT Th Nat NT Th Nat Th Th+F Nat NT Th IV-V 306 "23 48 p NT (85 65) Nat NT Th p NT F Estimated increment/observed increment. 2Nat natural; P :: planted. 3NT :: no treatment; Th thinned; F = fertilized; Th + F thinned and fertilized. 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 mortality. 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 in feet at age 50 b. h. 23

26 Because of data limitations, we have assumed that response to late thinnings in older stands is representative of stands of similar age under a reg ular thinning regime (probably untrue). We have been unable to utilize stand condition prior to initial thinning as a predictor of response. We have assumed that height increment is not affected by juvenile stand density or early stocking control. For these reasons, also, our estimates of treatment response may be low. Relationships of mortality to stand attributes are weak, and estimates given by the mortality functions are unreliable. Since these estimates have a major influence in determining the upper limits of estimated stand densities and volumes in untreated stands, we have adjusted the mortality-density relationships to cause these estimates to stabilize at a density corresponding to the mean of the older untreated stands. This is somewhat higher than the "normal" of McArdle et at. (1961), but considerably lower than maximum densities attained by some individual plots. This assumption of a fixed upper density limit, applicable to all locations, is probably biolog ically incorrect (King 1970) but appears a necessary simplification. The basic data contained few plantations with less than 300 initially established stems per acre, few stands with early precommercial thinning to less than 300 stems per acre, few stands known to have had low initial stocking or strongly clumped stem distributions, and few stands treated with several applications of fertilizer. Predictions for conditions outside these limits are questionable extrapolations. Relation of DFSIM to DFIT DFSIM differs from the earlier program DFIT (Bruce, DeMars, and Reukema 1977) in data base, internal structure, and options available. DFIT was developed from a more restricted data base and relied heavily on theoretical relationships. DFSIM, with a more extensive though not entirely adequate data base, relies more on fitting empirically derived functions to the data. Because of differences in data, structure, and modeling approaches, it is inevitable that numerical estimates given by the two simulators will differ. Neither simulator has had sufficient extensive or directly comparable testing to indicate that one is "better" than the other. To us, the most striking point is not that estimates differ in some respects but that two completely different analyses using different data have produced estimates which are remarkably similar.7 This tends to give confidence in both. Compared to DFIT, the principal advantages of DFSIM are a broader data base, greater flexibility to represent a wider range of stand conditions and treatments, and greater potential for extension and modification. 7 Personal communication from Donald L. Reukema. 24

27 Future Development Data used in our analyses are from 1974 or earlier. Additional data on fertilizer response and the development of young stands with early density control are accumulating and should soon provide the basis for improving estimates. Although all components could certainly be improved, changes in many of them would have little effect on overall estimates. The really critical relationships are few: 1. Height increment function. Effects on height increment of stand origin, initial density, early density control, and fertilizer treatment need further investigation. 2. Gross volume increment, gross basal area increment, and net diameter increment functions. These need better data on thinning response, especially for low residual densities. Present functions appear excessively complicated, and simpler equations may be possible. The fertilizer response function may not correctly represent trends of response over time and possible interactions with other stand treatment and initial conditions. It does not consider possible differences associated with form of nitrogen and method and time of application. 3. (Net increment)/(gross increment) ratio functions. These mortality estimates are imprecise and poorly defined, and the present equations likely confound age and density effects. 4. Juvenile stand diameter function. Representation of the effects of precommercial thinning and fertilization could probably be improved. Two additional features would be desirable: the ability to generate diameter distributions corresponding to predicted stand statistics and estimates of the diameters of the largest 40 stems per acre. Application DFSIM is a "stand average" model derived from small research plots. It represents the development of relatively homogeneous, even-aged stands of one ' principal species and is not applicable to other types of stands. We regard it primarily as a means of summarizing results of numerous small thinning and fertilization trials. It was not designed as a means of projecting inventory data. It can, however, be used to estimate probable future development of existing stands, providing these are within the range of the data used and some judgment is used in application. We believe 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 under alternative management regimes. 25

28 2. Guides for stand management, including desirable stocking and sequence and timing of thinnings associated with initial number of trees planted or left after precommercial thinning. 3. Estimates of long-term production potential of managed stands. DFSIM users should recal l the limitations 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 estimates for stands over 100 years of age. Estimates for stands 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 thinning to less than 300 stems per acre, are outside the range of data. 3. Estimates for stands having frequently repeated fertilization or fertilized with more than 400 pounds of nitrogen per acre are extrapolations. Repeated thinning and fertilization in combination will soon produce stands outside the range of the data. The program provides for one precommercial thinning and one fertilizat ion during juvenile stand development (stand diameter under 5.55 inches). This number should not be exceeded. 4. When using simulations beginning with observed stand characteristics: a. Do not begin simulations with observed initial numbers and diameters of natural, unthinned stands at top heights of less than feet. If they are begun earlier, large errors will be introduced by the unknown ingrowth component. b. Simulations begun with observed number and diameter in very young plantations or precommercially thinned stands are sensitive to errors and inconsistencies in initial diameter and unusual heightfdiameter ratios. In very young stands, small absolute errors in starting diameters or in the corresponding DFSIM regression estimates represent large percentage errors; they will be carried forward in the simulation process. For plantations or precommercially thinned stands less than about 30-feet top height, it is preferable to begin simulations with observed number of stems (all stems, regardless of diameter) and accept the estimates of initial diameter generated by the program, even though these may differ somewhat from the observed initial values. Otherwise, substantial errors may be introduced through the biases (see footnote 5) and inconsistencies associated with diameter measurement for small trees and the extrapolation of diameter and number of trees functions to very young stands. c. Starting numbers and diameters are likely to produce unsatisfactory results if they (1) are obtained from excessively smal l plots (small tree samples), or (2) include understory stems of associated species, or (3) are based on measure ment to diameter limits different from those specified, or (4) are otherwise inconsistent with the basic data used in DFSIM. 26

29 d. The juvenile stand "approach to normal" trends in DFSIM are judgment relationships, which behave reasonably for stands that are fairly uniform and somewhat above or below the "normal" number of trees. Simulations for very dense or very open, natural untreated stands or stands with strongly clumped distributions are very uncerta,i n extrapolations. The yield table for a "natural untreated stand," produced by DFSIM when initial conditions are not specified by the user, corresponds to a traditional normal yield table. It represents the development of stands which were initially well stocked and which have had rio substantial non-suppression mortality. It is a convenient reference standard for comparing development under alternative regimes, but otherwise has only very limited application. This natural untreated stand or "normal" table represents an average of the untreated control plots in our data. The majority of these control plots were small and subjectively chosen for a degree of uniformity, stocking, and freedom from injury which occur only on selected small areas within wild stands. Volumes and basal areas shown are therefore higher and diameters smaller than for many wild stands. And, because severely damaged plots were excluded and many plots were observed for only relatively short periods, after initial selection, they have not in most cases had the groupwise irregular mortality and damage which in wild stands lead to stand irregularities and openings, a process which is much reduced under any consistent thinning regime. "Normal" stands are an occasional rather than a usual result of no management. Comparisons of estimates for managed stands with this "natural, untreated stand" table should not be interpreted as measures of the potential gain from management. Conclusion Development of a simulator such as DFSIM is an evolutionary process. This first version should be regarded as a framework for incorporating improved relationships as they are developed,.and integrating the results of many individual studies into regional estimates of potential yield and response to treatment. We anticipate continued modification and evolution. Metric Equivalents 1 inch (in) = 2.54 centimeters 1 foot (ft) = meter 1 square foot (ft 2 ) = square meter 1 square foot per acre (ft 2 /acre) = square meter per hectare 1 cubic foot per acre (ft 3 /per acre) = cubic meter per hectare 27

30 Literature Cited Appendix 1. Program Operating Instructions Bruce, David, and Donald J. DeMars Volume equations for second-growth Douglas-fir. 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 Douglas-fir managed yield simulator-dfit user's guide. USDA For. Serv. Gen. Tech. Rep. PNW-57, 26 p. Pac. Northwest For. and Range Exp. Stn., Portland, Oreg. Curtis, Robert Height-diameter and height-diameter-age equations for second-growth Douglas-fir. For. Sci. 13(4): King, James E Site index curves for Douglas-fir in the Pacific Northwest. Weyerhaeuser For. Pap. 8, 49 p. Weyerhaeuser For. Res. Cent., Centralia, Wash. King, James E Principles of growing stock classification for even-aged stands and an application to natural Douglas-fir forests. Ph. D. thesis. Univ. Wash., Seattle. 90 p. McArdle, Richard E., Walter H. Meyer, and Donald Bruce The yield of Douglas-fir in the Pacific Northwest. U.S. Dep. Agric. Tech. BulL 201, 72 p. Washington, D.C. Munro, Donald D Forest growth models-a prognosis. In Growth models for tree and stand simulation. Joran Fries, ed. Proc. IUFRO Work. Party S4.01-4, 1973, p lnternatl. Union For. Res. Organ. Reukema, Donald L., and David Bruce Effects of thinning on yield of Douglas-fir: Concepts and some estimates obtained by simulation. USDA For. Serv. Gen. Tech. Rep. PNW-58, 36 p. Pac. Northwest For. and Range Exp. Stn., Portland, Oreg. Williamson, Richard L., and Robert 0. Curtis Converting total cubic volumes of second-growth Douglas-fir stands to merchantable volumes. USDA For. Serv. Res. Note PNW-353, 14 p. Pac. Northwest For. and Range Exp. Stn., Portland, Oreg. Williamson, Richard L., and George R. Staebler Cooperative levels-of-growing stock study in Douglas-fir. Report No. 1 -Description of study and existing study areas. USDA For. Serv. Res. Pap. PNW-111, 12 p. Pac. Northwest For. and Range Exp. Stn., Portland, Oreg. DFSIM is written in FORTRAN IV and is operational on the CDC CYBER computer at the University of Washington Computer Center in Seattle, Washington. The program can be easily installed on the UNIVAC 1108, the IBM 360/370 series, and similar computers with minor modifications. On the CDC CYBER computer, DFSIM requires 42,300 (octal) words of memory and takes approximately 0.25 seconds of execution time per yield table. Execution time will vary depending on the number of years for the simulation and the types of yield tables produced. DFSIM reads input data from logical unit 5 and. writes output tables on logical unit 6. A generalized flow chart of DFSIM is presented in figure 10. A typical simulation setup with three stand simulations is illustrated in figure 11. An example of a yield table is illustrated in figure

31 .; Figure 10. -Generalized flowchart of DFSIM. 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 Grow stand to harvest to first time commercial thinning. without Yes commercial lll -.; inn in ;;;. ;;;: g:... (NDTHIN) Final harvest cut 29

32 EOF End offile card ENO Optional Control Cards Title Card Optional Control Cards Master Control Cant Title Card Optional Control Cards Title Card Figure 11.-DFSIM control card setup for three simulations. The minimum successful output from DFSIM is a yield table for all trees 1.6-inch d.b.h. and larger. The input conditions are listed at the beginning of the yield table. DFSIM Options At first glance, DFSIM can seem rather complex. This section provides an overview of the basic options and how they fit together. No atterr)t is made to cover all options and combinations. DFSIM has many options: two for stand type, four for juvenile stand history, 30 for commercial thinning, two for final harvest timing, two for fertilization, one for observed stand height/age relationship and eight for output tables. 30

33 EXAt.E D F S I " D F S I " VEION 1.0 PAG 1 DEFAUT THitNJ OO WITH feab.e V(ll YIEL t'in YIELD TABLE FOO OO-FIR 1.6 INCI S PLUS SITE INDX = 125. (50 YE II STAN ORIGIN -- NATt. STAND WILL BE PRCOtERClALLY THINN AT AG 11. TO 300. TRES PER AC. n SCOOED AG AT 1l HARST CU IS SO. Tl OOTP TABL WILL HAVE REOT AGS OTI THAN CUTING AGS. TH AVE DIAPTER CF ALL Cl TREES AT CCIAL THINNING I'T BE AT LEAST 8.00 INOS. TH BA ARA CU AT EA COIAL THIN'ING I'T BE AT LEAST 20. SOOA FEET PE ACR.. TH BASA ARA PE AC OF All TREES INCS PLUS tit BE AT LET SQ FEET BEOO Tl FIRST COI'IAL THINNIMJ CA (ICU. TOT BH LORY BA TRES CVTS CAl fii CVSt tlti CV411 AG AG HT40 HT DB MEA/A PE PER t l1 NE HHNEHH YR YR FEET FEET ltd SQ FT AC AC CV o.o o YEY ttotality VEY JUTALITY VEY ttotality VEY ttotality YEARY MOTALITY VEY ttotali TY YEARY MOTALITY YEARY tttality 1 I Figure 12.-Sample yield table for total stand, stand over 5.55-inch d.b.h., and stand over inch d.b.h. 31