Forest-Management Modelling - Environmental Modelling: Finding Simplicity in Complexity - page 371

23.3.4 Ingrowthandregeneration 23.4.1 Validationandcalibration

Models of forest regeneration that provide reasonable
estimates of tree species composition and density after a
disturbance have been difficult to develop. Gap-dynamics
models in the JABOWA family tend to use an approach
of generating many small individuals in a predetermined
proportion based on their prevalence in the seed bank or
in the overstorey before disturbance and letting them die
in early steps of the simulation (Botkin, 1993). Empirical
stand models typically have no regeneration function or
a crude one that applies ingrowth to the smaller size
classes based on proportions of a previous stand (e.g.
Solomon et al ., 1995). Miina et al . (2006) provide an
overview of the techniques used to empirically predict
ingrowth and regeneration. One effective alternative to
empirical equations is to use imputation techniques based
on extensive regional databases (Ek et al ., 1997).
Developments using knowledge-based models to pre-
dict composition of understorey after a minor disturbance
or a newly regenerated stand after a major disturbance
show some promise. Yaussy et al . (1996) describe their
efforts to catalogue ecological characteristics of various
species of the central hardwood forest of the United
States and the individual-tree regeneration model devel-
oped from those characteristics. Ribbens et al . (1994)
developed a spatially explicit, data-intensive regeneration
model, Recruits, which calculates the production and
spatial dispersion of recruited seedlings in reference to
the adults and uses maximum likelihood analysis to cal-
ibrate functions of recruitment. However, this program
requires mapped data of adults and transect sampling of
seedlings, so it is unlikely to be useful in management
applications. A knowledge-based model of oak regenera-
tion developed by Loftis and others (Rauscher et al . 1997)
does show promise using expert knowledge of ecological
characteristics of tree species in the Appalachian region
to predict composition of a new cohort 10 years after a
major disturbance (Boucugnani, 2005).

To be useful, a model needs to depict regional trends
accurately. If a model is inaccurate, inappropriate man-
agement recommendations may be made or resource
availability under or overestimated. This importance of
proper validation and calibration is well illustrated in
Maine. For example, Randolph et al . (2002) suggested
that commercial thinning be delayed 10 to 15 years after
a spruce-fir stand reaches a dominant height of 15 m
and there were relatively few benefits of precommercial
thinning based on simulations made by the north-eastern
variant of the FVS growth-and-yield model. However,
Saunders et al . (2008) found that FVS vastly underpre-
dicted the growth of thinned stands, while overpredicting
the growth of unthinned stands. Consequently, Saunders
et al . (2008) recommended that precommercial thinning
is beneficial on most spruce-fir sites and commercial thin-
ning is best applied when the dominant height reaches
12 m based on simulations made by a recalibrated version
of FVERSUS.
Proper validation and calibration is often not done
because it is time-consuming and requires users to
have long-term data available. Validation is also diffi-
cult because selecting the proper statistical test is not
straightforward and various results can be obtained when
different tests are used (Yang et al ., 2004). One technique
that has worked well for model validation is the equiv-
alence test of Robinson and Froese (2004). Froese and
Robinson (2007) demonstrated the use of this technique
for validating an individual-tree, basal-area-increment
model. The method requires the researcher to select
indifference thresholds for both the intercept and slope of
the equivalence test. Rather than use a particular statisti-
cal test to validate a model, Yang et al . (2004) suggest that
statistical tests should be combined with other validation
techniques, particularly how well a model fits new and
independent data.
Commonly, after a validation exercise, model calibra-
tion is attempted to improve predictions. Calibration can
range from relatively simple single-equation modifiers
that adjust predictions to more closely match observa-
tions to entire recalibration of the full model. An effective
methodology for entire recalibration of the full model
uses a Bayesian optimization framework and has been
well demonstrated for calibrating complex mechanistic
models (Gertner et al ., 1999; Van Oijen et al ., 2005; Deck-
myn et al ., 2009). The current wide use of mixed-effects
models has made local calibration of equations relatively
easy. The use of this technique has been demonstrated

23.4 Implementation and use

Growth models are widely used for a variety of purposes.
In using a growth model, important considerations need
to be made to ensure proper behaviour. Some of the most
important considerations are validation and calibration
(see also Chapter 2), visualization, and integration with
other software systems (see also Chapter 27). Each of
these aspects is discussed further below.