Forest-Management Modelling - Environmental Modelling: Finding Simplicity in Complexity - page 368

use a symbolic representation of information to model
systems by effectively simulating the logical processes of
human experts (Reynolds et al ., 1999). Knowledge-based
systems have the advantages that they do not necessarily
require the specific, detailed data that many simulation
models do, and they can be adapted to situations in
which some information may be lacking entirely. As
such, they can be very useful in providing assistance
to decision makers who must analyse situations and
choose actions without complete knowledge. Schmoldt
and Rauscher (1996) point out that knowledge-based
systems also prove useful as agents to codify institutional
memory, manage the collection and delivery of scientific
knowledge, and train managers through their ability to
provide explanations of their reasoning processes (see also
Chapter 18). All these characteristics make knowledge-
based models extremely useful in forest management.
One example of a knowledge-based system that has been
developed is the NorthEast Decision model (NED) (Twery
et al ., 2005). This is a series of interconnected models
including several growth-and-yield models that allow
users to easily address a variety of management objectives
and compare a range of alternatives.

is strongly correlated with tree diameter at breast height
(DBH), this relationship varies by species and stand con-
ditions so additional covariates are commonly included.
Tree DBH accounts for the majority of the variation in
tree height, even across a large range of stand conditions.
Hanus et al . (1999) found DBH to explain between 36%
and 83% of the original variation for several conifer and
hardwood species in south-western Oregon. In general,
hardwood heights tend to be harder to predict because of
the lack of a true leader and the difficulty of measuring it
accurately. Constructing a well-behaved tree-height allo-
metric equation requires selecting an appropriate model
form and an extensive dataset that covers a range of stand
conditions. Some researchers have found that includ-
ing national and state champion trees in their dataset
significantly improves the equation's predictive power.
Tree growth is strongly linked to crown size, which is
often expressed as crown ratio (CR) or the ratio of crown
length to total tree height. Consequently, crown vari-
ables are commonly included in several equations used
in growth-and-yield models. However, crown measure-
ments are significantly less common than observations
of total tree height. Although CR has been more com-
monly modelled (Belcher et al ., 1982; Wykoff et al ., 1982;
Hynynen, 1995; Hasenauer and Monserud, 1996; Soares
and Tome, 2001), Hann and Hanus (2004) found that
height-to-crown-base (HCB) equations produced more
precise predictions of crown recession when compared to
CR equations. A properly formulated CR model should
be constrained to give predictions between 0 and 1,
while an HCB equation should give predictions that
do not exceed the total tree height. Consequently, the
most common model form used to model CR and/or
HCB has been the logistic form because it can be con-
strained to asymptote at 1 or total tree height (Ritchie
and Hann, 1987; Hasenauer and Monserud, 1996; Hanus
et al ., 2000; Temesgen et al ., 2005; Ducey, 2009). Unlike
allometric height equations where tree-size variables pre-
dominate, tree size and measures of competition are of
equal importance in CR/HCB equations (Hasenauer and
Monserud, 1996; Temesgen et al ., 2005). Crown ratio and
HCB are generally much harder to predict than total
tree height, particularly for hardwood species (Hasenauer
and Monserud, 1996). Consequently, significant biases in
predicting CR or HCB can be incurred, which can have
important implications for long-term growth projections
(Leites et al ., 2009).
Several key variables used in growth-and-yield models
rely on estimates of crown width. For example, the crown-
competition factor of Krajicek et al . (1961) requires an

23.3 Components of empirical models

Empirical models are widely used by forest managers.
In particular, individual-tree-based empirical models are
becoming the new standard as they are flexible and
the most effective approach for representing a range of
stand structures, especially uneven-aged (Peng, 2000)
and mixed-species stands (Porte and Bartelink, 2002).
Consequently, it is important for forest managers to
understand the components of empirical models and the
limitations associated with each one.

23.3.1 Allometricequations

Allometric equations are a key component of several
hybrid models but in empirical models they are often
used to fill in missing values, predict hard-to-measure
attributes like volume and, in some cases, estimate growth.
Allometric equations can take many forms depending on
their intended use. In empirical models, the primary
allometric equations are for total tree height, height to
crown base, crown width, stem form, and biomass.
The use of allometric equations to predict total tree
height is quite common and they have taken multiple
forms (see Huang et al ., 1992). Although total tree height