44 FOREST GROWTH MODELS IN THE 1990s: FUNCTIONS, SOURCES, NEEDS James W. Flewelling, Robert 0. Curtis, and David M. Hyink
A growth model, as we use the tenn, is a system that attempts
to represent the development of trees and stands as a function
of time, initial conditions, site attributes, and stand treatment.
Growth models are not new. The old nonnal yield table was a
growth model of sorts. Managed stand yield tables have been
used in Europe for half a century or more. But these ''tradi­
tional" yield tables were quite inflexible, and any one yield
table could represent only one point within the range of possi­
ble conditions and management regimes.
The era of the traditional yield table is over. Modem growth
models became possible with the advent of the computer. Ma­
. chines have made possible the efficient analysis of masses of
how other stands will achieve nonnal stocking. Examples
are USDA Technical Bulletin 201 (McArdle et al. 1961)
and Schumacher (1930).
2. Empirical yield tables. These present average conditions
for specific areas or management regimes. Examples are
McKeever (1947) and Fligg (1960).
3. Stand yield equations. The early yield tables were con­
structed from means of plot observations categorized into
convenient cells and smoothed graphically. Later yield
tables predict stand volume as a function of other variables
and rely on regression techniques. Examples are Wiley
and Murray (1974) and Chambers (1980).
data, construction of flexible models capable of representing a
4. Stand growth and mortality equations. Growth and mor­
tion on demand of estimates for many combinations of site and
niques. They are components of systems that can be used
much wider range of conditions and treatments, and prepara­
stand conditions and management treatments. It is easy to for­
get how recent this development is. In the last two decades,
tality equations can be developed using regression tech­
for projecting existing stands. Examples are Curtis (1967)
computer growth models have progressed from mere academic
and King (1970).
5. Stand simulators. Complete sets of equations can be
ment process is far from over, and this paper will attempt some
development. The modeler usually goes through some ex­
exercises to practical tools in widespread use. The develop­
guesses concerning the extent and direction of changes, and
needs, for the next decade.
brought together in a computer program that predicts stand
tra steps to ensure that the overall results are valid. (Rey­
nolds et al. 1981). Examples are Hoyer (1975), Bruce et
al. (1977), and Curtis et al. (1981).
6. Tree growth and mortality equations. Growth and proba­
bility of death for individual trees within plots can be pre­
GROWTH MODELS
g
Growth models are efforts to quantify knowled e. They
serve two main purposes: (1) They are predictive aids to be
used in forest planning and in silvicultural decisions. (2) They
are a means of synthesizing hypotheses, knowledge, and ex­
perimental data into a consistent and understandable expres­
sion of forest behavior. Both purposes require that the model
summarize empirical knowledge in a framework consistent
dicted with regression equations. An example is Hamilton
and Edwards (1976).
7. Tree growth simulators. Tree growth simulators are usu­
ally categorized as either distance-independent or dis­
tance-dependent. An example of the fonner is Krumland
and Wensel (1981); of the latter, Mitchell (1975).
The early tables merely describe the mean behavior of an
with our understanding of biological processes.
existing population. Later works seek to extrapolate yield pre­
fU' may help us to conjecture their future. Some of the model
developments, categorized as in Hann and Ritters (1982), in­
tural practice. The latter attempt to answer a broader range of
1. Normal yield tables. These give yields under fully
pirical yield tables may be used to derive some crude algo­
The history of growth models and yield tables for Douglas­
clude:
stocked conditions and sometimes make predictions of
364
dictions to .broader ranges of density management and silvicul­
questions and are necessarily more complex.
In the future, yield tables will have only two uses. First, em­
rithms for short-tenn updating of inventories. Second, the
yield table fonnat will be used to display simulation results to
facilitate comparisons of projected growth for different re
gimes or different simulators. The latter application will be­
come less important as access to simulators becomes simpler.
The most visible change in simulators will be in packaging.
They will become more user friendly; they will adapt to many
different kinds of input; their output will be directly usable for
other analyses. Other big changes will be that many more fea­
tures of the forest stand such as log-mix tables and crown pro­
files will be predicted, and a wider array of silvicultural prac­
tices will be incorporated. A less visible change will be that
models will be calibrated using growth measurements from in­
ventory plots. How these changes come about will depend on
user needs, modeling philosophy, and data availability, as dis­
cussed below.
l. User needs. Growth models will be constructed to
meet the needs of the user. Buchman and Shifley (1983) have
written a guide to evaluating forest growth projection systems.
Their first criterion for evaluation is the "application environ­
ment." This is what the user "sees." Once the user has seen
some nice environments, he is likely to demand them for any
simulator that he uses. bepta (1984) outlines the systems envi­
ronment into which growth models must fit. In his operating
environment, the need to l'iave all growth projections work
from a given inventory system design is an overriding factor.
Buchman and Shifley (1983) also consider projection perfor­
mance, program design, and model design. ·
2. Modeling philosophy. There are major choices to be
made in the biologic design of a model, and modelers often
differ on how to proceed. The major choices are between stand
level and individual tree models, and· between detenninistic
and.stochastic models. Briefly, individual tree models contain
·lists of real or simulated trees; stand level models do not. De­
terministic models produ. e jD!ed answer for a given ques­
tion; stochast!
ls re
a slightly different answer each
time the qu 11it:tS re
..
3. Datfdvailability.
ff;Can model anything, but the an­
swers are .riot likel to bC correct unl ss the model is well
founded in goodtl ta: We, ·as a tree-growing community, must
install the kinds of experiments that 'Yill resolve critical que ­
tions of forest growth, and provide the data needed for model
fonnulation and model calibration. The cooperative efforts of
the past and those being planned for the future will be critical.
USER NEEDS
The user· is king! The user has been paying for forestry re­
search and growth model development for decades. It is time
the user got some silvicultural questions answered. Further­
more, the user now has a personal computer and has learned
that programs should be user friendly and do what the user
wants.
User needs can be divided into three distinct areas. First is
the application environment and program design. The second
area involves user questions that current models do not address
or for which results are uncertain. Third is the need for a speci­
fied accuracy. The third area will not be addressed here,
mainly because the authors have never seen anyone fonnally
make a decision on the size of experiments based on the accu­
racy desired in the result.
The authors hypothesize that the growth simulators of the
1990s will come in two different kinds of packages. The first is
the "neatly wrapped systems package" that is ready to go. The
Pae<ific Northwest is proceeding in this area now, though
slowly. An example is DFSIM (Douglas-fir Simulator), which
is widely available through Washington State University and
the agricultural extension offices (Baumgartner et al. 1984).
Recently a version of DFSIM has been packaged for use on
personal computers (Fight et al. 1984). But most systems have
a long 'way to go to become user friendly. T,he second type of
package is that envisioned by Depta (1984). Here, the growth
modules are in libraries of subroutines, which are accessed by
many different applications. Within Weyerhaeuser Company,
the second package will be used. One of the applications is
likely, however, to look very similar to the "neatly wrapped
systems package."
At present, there is no need to make critical decisions on
application environment and program design. The f!Ublic for­
estry research organizations in the Pacific Northwest have
rather freely shared data; growth equations, and programs.
This will probably continue. But development of user friendly
programs for widespread distribution is a step that for the most
part has not been taken. Public agencies, forestry cooperatives,
or "for profit" ventures could take this on. There will be a
demand for good user friendly programs, and it will be met.
Another aspect of the user environment is the input require­
ments for the model and the variables that it must estimate. A
growth model used as part of a planning system must operate
with infonnation that is or will be available to the system from
standard data bases, and must provide the estimates of "nona
standard" variables needed by the system. This does not mean
that it must use only values provided by past inventories; but it
must use values that are obtainable in inventories, and invenG
tory procedures must be coordinated with the input require­
ment of the growth model.
The models should provide estimates of stand development,
starting from bare ground, for a wide range of possible man­
agement regimes and stand treatments. They should provide
estimates of future development of existing stands, given pre­
sent stand characteristics, for a range of subsequent stand treat­
ments. Ideally, they should also provide estimates of expected
losses from pests, weather, and other factors. The information
produced should include tree size (diameters and heights) and
associated quality characteristics needed to convert biologic
Growth Models In the 1990s
365
·
production to product volume and value estimates suitable for
economic analysis.
The current Douglas-fir models are adequate for predicting
growth under certain conditions. These include uniform natu­
ral stands, natural stands with conservative late thinnings, and
unthinned plantations in their first two or three decades of de­
velopment. One silvicultural treatment for which we have
good information, at least for the short-term response, is nitro­
gen fertilization. But we would like to have more confidence in
model predictions for certain other conditions.
Conditions and treatments for which we are unsure of
growth rates and effects on yield and value include: (1) wide
spacings, (2) later thinnings in stands that have had early den­
sity control, (3) most types· of site preparation and early brush
control, (4) genetically selected stock, (5) multiple fertiliza­
tions over long periods, (6) stands with irregular and incom­
plete stocking, (7) stands with mixed species-either natural
fill-in or planted, (8) stands under attack by pathogens, with or
without control measures taken, and (9) pruning.
New methodology and information likely to appear in future
growth models include the ones discussed in the following six
paragraphs.
1. Alternatives or supplements to site index and regional
site curves as means of defining expected height growth. and
associated characteristics. This is important because height
growth is a driving variable in many simulators. Yet, height
growth is influenced by density, fertilization, site preparation,
brush control, and location factors such as soils and local cli­
mate.
2. Forecasts for growth of alternative species. Compara­
tive yield estimates will be made to aid in deciding whether
Douglas-fir is the best species to regenerate on a particular
tract.
3. Calibration. Precise estimates of silvicultural effects
require controlled experiments on uniform sites. Growth mod­
els constructed from such data may give biased estimates when
applied to average, less uniform conditions (Bruce 1977). The
only way to correct this is to measure the growth of the opera­
tion forest on a random or systematic basis and then adjust
the growth model to eliminate bias for those conditions for
which comparisons are possible. This is not a simple process.
There will be problems with data compatibility. Comparisons
will be possible only for limited portions of the range of possi­
ble conditions, and it will not be obvious which of the many
parameters of a complete growth simulator should be modi­
fied. But it must be done.
4. Tree characteristics and wood properties. Tree charac­
teristics relating to wood quality and to stem form will become
increasingly important. Traditionally, research data c nsists of
measurements on all diameters and a subset of heights. To our
knowledge, there has been no research on the errors that this
sampling process introduces into computations of volume
366
Flewelling, Curtis, Hylnk
growth. Given that the volume growth estimates were correct,
quality and value of wood from different regimes still could
not be compared. We need to know how management affects
tree form, branch size, proportion of juvenile wood, and ratios
of earlywood to latewood. In tum, we need to know how these
characteristics affect quality and value of wood and pulp.
Models of tree crown architecture, such as Mitchell's (1975),
look like the best approach to this problem. These models will
also produce estimates of biomass. Some sort of wood quality
estimates will be produced by the models of the next decade.
The research dollars we spend will determine their accuracy.
5. Variation in weather and climate. Weather is rarely
considered in growth analyses. Yet, temporal variation in
weather is probably the major cause of temporal variation in
growth rate. If weather data were included in growth analyses,
unexplained variation could be reduced and more precise esti­
mates of treatment effects would result. Similarly, explicit use
of the spatial variation in climate could lead to improved
growth models. These improvements would occur even though
climatic forecasts might not be directly used in predicting fu­
ture yields.
6. Quantification of the long-term effects of intensive man­
agement. Slowly, forestry is moving into an age where pre­
sent management techniques are influenced in some degree by
expectations for future rotations. The FORCYTE model (Kim­
mins et al. 1983) is a pioneering effort to combine a nutrient
cycling model with a traditional yield model to estimate effects
of management regimes on long-term productivity. There will
be more of this kind of thing in the future.
MODELING PHILOSOPHY
There are two specific choices that the modeler must make.
The ftrSt major choice is whether to use a stand-level model, a
distance-independent tree model, or a distance-dependent tree
model. Briefly, models that directly predict attributes, such as
growth per unit area, are called stand-level models. Distance­
independent tree. models contain lists of trees. Growth is as­
signed to each tree based on its size and the number and size of
other trees. Distance-dependent models go one step further:
predictions are based on the proximity of other trees. The dis­
tance-independent and the distance-dependent tree models will
be referred to as tree-level models.
The authors expect that all three types of models will still be
in use in the 1990s, and hypothesize that they will be combined
in a way to take advantage of the strengths of each. Daniels
(1980) discusses the possibility of collapsible models, where
compatibility between the models is built in. It is also possible
that simulators will be constructed that combine the basic mo­
del types. For example, Dahms (1983) has successfully com­
bined a stand-level model and a distance-independent tree mo­
del. There will be more hybrid models. Often they will be
designed by the person who designs the simulator-not by the
people who develop the component equations. The widely
used models of the next decade are likely to be evolutionary
descendants of the present models, and they need not be radi­
cally different in approach. In fact, some of the components
may not change at all. Some modifications will be added in the
form of specialized submodels to address new questions and
old questions that have not been satisfactorily handled.
Most users will agree that each type of model has some
the same answer each time for a given input and tell nothing
about the variation that nature will impose on the outcome.
Most individual tree models are stochastic in that they do not
produce the same answer each time for a given input. The sto­
chastic elements built into them are usually the mechanism by
which the models predict reasonable diameter distributions and
are not an attempt to model the stochastic nature of growth.
It will be difficult to model the stochastic nature of stand
growth with either stand-level or individual tree models. Pre­
strengths and some weaknesses. Past experiences and personal
diction of catastrophic mortality is particularly difficult and
which type of model is best for a given application. Luckily,
from regular (suppression) mortality (Hamilton 1980). Fur­
ing diverse model types, it may be that this is a noncontro­
tality and of catastrophic mortality are significantly different.
modeling biases often work to prevent a strong consensus on
under the .hypothesis that the simulator can be constructed us­
versy.
The authors' personal view is that stand-level models will be
a very important component of growth simulators for the next
decade. This view is stated only for western Washington
Douglas-frr in managed second-growth stands or plantations,
important. Catastrophic mortality must be handled separately
thermore, the data bases required for analyses of regular mor­
Most models in the 1990s will be inherently deterministic.
The individual tree models will continue to be stochastic, but
they will act as deterministic models in simulations for large
areas. Separate models for catastrophic mo ality will probably
be attempted; however, it will be difficult·to implement these
and is based on the model attributes of (1) simplicity, (2) ade­
models in conjunction with the deterministic model that will be
sented, (3) desirability of estimating total stand growth di­
ous forest inventory (CFI) data to evaluate a set of stochastic
quacy for the relatively simple stand conditions to be repre­
the heart of the simulator. It would be possible to use continu­
rectly, (4) compatibility with average stand values generated
functions that would in turn be applied to the standard deter­
nient experimental unit. This choice is subjective and arguable;
tempted, perhaps including variation in weather. But this
by inventories, and (5) compatibility with the plot as a conve­
it cannot be said that it is right and others wrong.
There are several Douglas-frr models in use in the Pacific
Northwest. Most appear to work reasonably well for those con­
ditions for which ample data are available for construction and
checking of models, and most produce similar estimates for
these conditions. It has been demonstrated that all three model
types can produce most of the information desired in the ma­
jority of management application .
Some forest management questions cannot be addressed
ministic functions. This or other stochastic models may be at­
exceedingly complex problem will probably not be given a
great deal of attention in the Douglas-frr region. Possibly after
successful models are developed in other regions, they will be
·
tried here.
DATA AVAILABILITY
Numerous minor improvements in modeling methodology
are possible and will no doubt be made over the next few
with the present generation of stand-level models: individual
years. Major improvements, and reliable forecasts for manage­
data in constructing the stand-level model come from plots
pendent on improvement in basic data.
tree models must be used. Consider a case where most of the
where the trees are more or less uniformly spaced. Now ask
what would happen if a thinning were performed that removed
every third row in a plantation. A distance-dependent model
ment practices much different from those of the past, are de­
Data needs are not a matter of mere quantity of data. There
is a huge amount of data already in existence for coastal Doug­
las-frr. But much of the existing data do not represent the con­
would have to be used. But to evaluate that treatment, it would
ditions of primary interest for the future, and procedural differ­
spatial restrictions-say a conventional thinning treatment that
much of the existing data difficult to use in combined analyses.
have to be compared with a thinning treatment that lacks these
removes a third of the trees more or .Jess uniformly distributed
ences among organizations and past poor quality control make
over the area. If users have a good reason fo using the stand­
Data are needed that can provide good response estimates for a
wide range of spacings; for thinnings systematically applied to
predicted growth of the individual tr.ee·model to con­
plantation management and wood properties; and for the best
level model for conventional thinning, they could easily adjust
the total
form to that of the stand-level model. Under that circumstance,
the same adjustment would be applied to the individual tree'
g
projections for the more radical thinnin scheme.
The second major modeling choice is whether models will
be deterministic or stochastic. Deterministic models produce
stands with early spacing control; for relationships between
cUITent practices rather than for the average of the past. Data
are needed in areas that are controversial: growth per acre of
genetically improved stands; comparative growth of different
species; and effects of management on growth and product
value.
Growth Models In the 1990s
367
The most important type of data needed is "treatment re­
ing conditions in the operational forest. Such data provide esti­
sponse" data. This addresses the chang in growth that results
mates of current growth and mortality rates, which are the re­
(Curtis and Hyink 1985). To define the functional form of rela­
the only conditions sampled are those now existing in the oper­
relationships, controlled experiments need to be installed.
Therefore, such data generally cannot provide quantitative es­
be designed to produce some stand conditions not now present
little confidence in extrapolations to possible regimes and fu­
from a specific treatment applied to a defined stand condition
tionships, estimate regression coefficients, and identify causal
These must include treatments not now in general use and must
sult of management treatments in the recent past. But, because
ational forest, treatment effects are confounded with location.
timates of response to specific treatments, and one can have
in the operational forest. Such experiments are essential for es­
ture conditions different from those that produced the present
tions and regimes radically different from those that produced
Inventory and Analysis unit of the Pacific Northwest Forest
Most of the treatment response data available up to 1974
gion (USDA Forest Service), should be useful in calibrating
timating treatment effects and for predicting growth for condi­
the present forest.
forest. CFI data, however, such as that collected by the Forest
and Range Experiment Station and the Pacific Northwest Re­
were assembled as part of the cooperative effort that led to the
growth models, estimating stochastic variation, and cqnstruct­
data for natural stands, with and without relatively late thin­
level (Beers and Miller 1964, Flewelling and Thomas 1984).
DFSIM model. This showed that there were large amounts of
ing mortality models. Growth must be computed at the plot
ning entries, and for natural unthlnned stands with nitrogen
Of all forestry data, these are the most underutilized.
data available for wide initial spacings, older plantations, or
a carefully planned program. Efficient use must be made of
fertilization. At that time (and today) there were relatively few
In general, new experiments should be established as part of
plantations receiving any form of treatment.
research dollars. Because of costs, the need for stability, conti­
lated in existing studies and some new studies have been estab­
ity control, such activities are best planned and carried out
In the last decade, additional measurements have accumu­
nuity, and consistency in procedures and designs, and for qual­
lished. The data now in existence and potentially available for
jointly through regional cooperatives. The Stand Management
decade ago. The data for modeling fertilizer response now ap­
Cascades.
tion Research Program at the University of Washington and the
equate data bases as a result of their own efforts. All concerned
analysis are considerably more extensive than those available a
pear reasonably adequate, thanks to the Regional Forest Nutri­
Cooperative is the big hope for new data on the west side of the
Few if any individual organizations have or can develop ad­
British Columbia Forest Productivity Program. The coopera­
can benefit by pooling their data; furthermore, the regional co­
data that fill part, but not all, of the need for information on
pooled data. Anyone who has ever been involved in such ef-
able from thinning studies.
cies and differences in data standards, measurement pro­
for new studies specifically designed to ftll gaps in present
organizations and among studies within organizations. Coop­
tive levels-of-growing-stock studies are now producing unique
growth-growing stock relationships. Additional data are avail­
There are still major gaps, however, and there.is still a need
knowledge. One glaring example is the paucity of good data
for individual tree models. At f1rst blush, there would seem to
operative may play an important role in the analysis of the
forts is keenly aware of the difficulties caused by inconsisten­
cedures,
and
experimental
designs
that
exist
among
erative efforts can promote the use of sound designs, compati­
ble measurement procedures, and high quality control stan­
be a lot; most research plots have individually tagged trees,
dards.
ments and root measurements are hard to get. But perhaps
ries? First, the data collected must be compatible and consis­
proving model formulation and testing alternative formula­
ventories should pay more attention to small trees and to
specifically aimed at how spatial arrangement affects growth
be needed, research should start measuring such things as ex­
and spatial coordinates aren't hard to get. Crown measure­
more crucial is the lack of experiments directed toward im­
tions. There is limited experimental data for Douglas-fir that is
(Smith 1978). But clumping experiments such as those with
red pine (Stiell 1982) have not been tried in the Douglas-ftr
region. The argument that our data already contain trees grow­
ing under every level of competition should not preClude direct
experimental manipulation of individual tree competition; sta­
tistical analyses based on trees should have trees as the experi­
mental unit.
Another need is for survey-type or ''growth trend'' data.
This comes from inventories or growth plots that sample exist­
368
Flewelling, Curtis, Hylnk
How should data be collected in experiments and invento­
tent in measurement standards. This probably means that in­
sampling young stands. Because wood quality information will
ternal stem characteristics, tree form, and crown parameters
that modelers may want to use later. Some of these measure­
ments are quite inexpensive, and will be worthwhile even if
not all are used.
SUMMARY
The growth models of the next decade will be hybrid de­
scendants of today's growth models. The big changes will be
·
in their packaging and in their capabilities. The actual im­
provement in these capabilities will depend on ( l) what experi­
ments are established in this decade, (2) whether the right vari­
Fight, R. D., I. M. Chittester, and G. W. Clendenen. 1984. DFSIM with
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Flewelling, I. W., and C. E. Thomas. 1984. An improved estimator for mer­
model components are shared, (4) whether growth models can
Fligg, D. M. 1960. Empirical yield tables. Forest Survey Note 6. British Co­
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be calibrated with suitable data, and (5) whether the laud-man­
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Lakehead University, Thunder Bay, Ontario.
Hamilton, D. A., and B. M. Edwards. 1976. Modeling the probability of in­
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