Forest-Management Modelling - Environmental Modelling: Finding Simplicity in Complexity - page 365

models describe the development of a forest based
on regression equations parameterized from extensive
datasets, while mechanistic models represent the key
physiological processes such as light interception,
photosynthesis, and respiration to predict growth.
Hybrid models combine features of both empirical
and mechanistic models to take advantage of strengths
offered by each approach. Knowledge-based models use
rule-based systems and may not rely on data in the
same way as the previous approaches. Each approach is
described below.

of stand age and site index. These yield tables were
generalized into compatible growth yield equations that
predicted changes in stand volume as a function of initial
stand conditions and age (Buckman, 1962; Clutter, 1963;
Moser, 1972). Some widely used whole-stand growth
models are DFSIM (Curtis et al ., 1981), TADAM (Garcıa,
2005a), and GNY (MacPhee and McGrath, 2006).
Whole-stand models are most appropriate for evenly
aged stands of a single species. Although techniques have
been developed to represent management activities with
whole-stand models (Bailey and Ware, 1983; Pienaar
et al ., 1985), they are not the most efficient approach,
particularly when multiple thinnings are intended to
be represented. However, whole-stand models continue
to be developed using modern statistical techniques
(Barrio-Anta et al ., 2006; Castedo-Dorado et al ., 2007) as
they are easy to use, relatively robust, and can be more
accurate in long-term predictions (Cao, 2006).

23.2.1 EmpiricalModels

Empirical models depict trends observed in measure-
ment plots that are established in forests. Consequently,
empirical models are usually only as good as the data
used to develop them. To be effective for modelling pur-
poses, the data must cover the extremes of the population
they are intended to represent, be extensive, and include
measurements that likely describe the inherent variability
of the observations. Due to regional differences, resolu-
tion of datasets, and the statistical approaches used, a
vast number of empirical models currently exist. Most
empirical models operate on five- to ten-year time steps,
but annualized models exist too (Weiskittel et al ., 2007).
In addition, most empirical models rely on site index,
average dominant height at a certain base age (gener-
ally 50 years), as a measure of potential site productivity
(Skovsgaard and Vanclay, 2008). Therefore, the largest
differences in empirical models are their spatial resolution
and treatment of competition.
Most empirical models are developed to operate at the
stand level, which is a relatively uniform collection of
trees that are similar in size, composition, and location.
Stands are generally 1 to 50 ha in size and are the basic
spatial unit at which most management decisions are
made. Based on their spatial resolution, three primary
classes of empirical models exist: (i) whole stand; (ii) size
class; and (iii) individual tree.

23.2.1.2 Size class
A forest is generally made up of trees of varying sizes,
so a size-class model divides each stand into multiple
groups of similar-sized individuals, which are projected
through time. Some of the most common size-class mod-
els are stand-table projections (e.g. Trincado et al ., 2003),
matrix-based (e.g. Picard et al ., 2002), and diameter-
distribution models (e.g. Qin et al ., 2007). Stand-table
projections and matrix-based approaches are similar
in that the frequencies of trees in each cohort are
projected through time by estimating the probability
of moving from one group to another. A diameter-
distribution approach uses statistical probability distri-
butions to describe the frequency of trees in different
size classes and their changes through time. The Weibull
probability distribution has been commonly used because
it is flexible, relatively easy to integrate, and the param-
eters can be determined in multiple ways (Cao, 2004).
Some examples of size-class models are FIBER (Solomon
et al ., 1995) and CAFOGROM (Alder, 1995), which are
both developed for mixed-species forests. However, most
size-class models are again best suited for even-aged,
single-species and unmanaged stands.

23.2.1.1 Whole stand

Whole-stand models describe the stand in terms of a few
values like total volume, basal area, or the number of
individuals per unit of area and predict the change in
these attributes over time. Whole-stand models are the
simplest type of empirical model and have the longest
history of development. One of the earliest examples
of a whole-stand model in North America is the yield
tables of Meyer (1929), which described growth in terms

23.2.1.3 Individual tree

An individual-tree growth-and-yield model depicts the
changes in each tree located in a particular forest. These
models provide the highest resolution of predictions, but
require the most data for both development and appli-
cation. Since the individual tree is the focal point, these