Forest-Management Modelling - Environmental Modelling: Finding Simplicity in Complexity - page 367

controls canopy water interception, radiation extinction,
transpiration, and carbon gas exchange (Breda, 2003).
Even today, basic physiological parameters are unavail-
able for several tree species, which can make using a
mechanistic model challenging. An interesting alterna-
tive to parameterizing each individual equation used in
a process-based model from the literature or with new
data is the use of a Bayesian optimization technique. This
technique has been demonstrated several times and often
with promising results (Van Oijen et al ., 2005; Svensson
et al ., 2008; Deckmyn et al ., 2009). In this approach,
Markov chain Monte-Carlo simulation is used to vary
the model parameters and calibrate model predictions to
observed data. The further application of this technique
and increased availability of climate data should help
increase the use of mechanistic models for representing
forest management, particularly under climate change
(Schwalm and Ek, 2001). When properly parameterized,
mechanistic models can be just as effective or even better
than empirical models in short-term simulations (Miehle
et al ., 2009). However, mechanistic models can struggle
with long-term projections because of the difficulty in
representing mortality accurately (Hawkes, 2000).

and STAND-BGC such that both models ran simultane-
ously in parallel and a user selected the degree of coupling.
An example of an empirical growth equation with a phys-
iologically derived covariate is given in Baldwin et al .
(2001), who related site index to NPP from a process-
based model and allowed it to vary during a simulation.
Henning and Burk (2004) provide an example of an
empirical equation with a physiologically derived external
modifier and found it improved projections. Allometric
hybrid models rely on simplified representations of physi-
ological processes and empirical equations that relate tree
size to biomass. CroBAS and 3-PG are two examples of
allometric hybrid models. Both models use the concept
of light-use efficiency to relate light interception to gross
primary production (GPP), which avoids the complica-
tions of a detailed canopy-photosynthesis equation. In
addition, 3-PG avoids estimating respiration by assuming
NPP is one-half of GPP, which has been supported by
some empirical studies (Waring et al ., 1998). Allometric
equations are used to convert typical forest inventory data
into biomass and to estimate carbon allocation. However,
using a mean tree approach like 3-PG to accomplish this
can result in a significant bias as the diameter distribution
becomes more varied (Duursma and Robinson, 2003).
Relative to purely empirical models, the degree of
improvement achieved with a hybrid model has varied.
At the stand level, hybrid models have been quite effective
at improving predictions (Battaliga et al ., 1999; Snowdon,
2001; Dzierzon and Mason, 2006), whereas less modest
gains have been achieved at the individual tree level
(Henning and Burk, 2004; Weiskittel et al ., 2010). The
range of the reported improvements can vary widely at
both the stand and tree levels because of the breadth
of conditions covered by evaluation data, the length
of the simulations, and differences in the adequacy of
the empirical model. Interestingly, Henning and Burk
(2004) found climate-dependent growth indices almost
as effective as the process-based ones, while Snowdon
et al . (1998) found just the opposite. Regardless, the use
of hybrid models will likely continue to increase in the
future as the understanding of physiological processes
improves and the complexity of questions facing forest
managers broaden.

23.2.3 HybridModels

Hybrid models combine features of both empirical and
mechanistic approaches. This approach relies on the
robustness of empirical models, while increasing their
ability to extrapolate and avoid limitations with site index.
Hybrid models have been suggested as the most effective
means for representing the effects of forest management
because they provide output of interest to forest man-
agers and avoid the heavy data requirements of most
mechanistic models (Landsberg, 2003a). Several hybrid
models have been developed for single-species, even-aged
stands like CroBAS (Makela, 1997), DF.HGS (Weiskittel
et al ., 2010), and SECRETS (Sampson et al ., 2006). One
widely used hybrid model is 3-PG (Landsberg and War-
ing, 1997), which has been parameterized for a variety of
forest types (Landsberg et al ., 2003).
Three primary classes of hybrid model frameworks cur-
rently exist, namely: (i) empirical growth equations with a
physiologically derived covariate; (ii) empirical equations
with a physiologically derived external modifier; and
(iii) allometric models. The degree of hybridization within
each of these classes varies greatly, so an exact classifica-
tion of a hybrid model is difficult. For example, Milner
et al . (2003) linked the Forest Vegetation Simulator (FVS)

23.2.4 Knowledge-basedModels

Knowledge-based or rule-based systems are a special case
of modelling in which the components being modelled
and the interactions between them are not necessarily
represented mathematically. Approaches such as these