Amaro A., Reed D., Soares P. (editors) Modelling Forest Systems
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08Amaro Forests - Chap 07 25/7/03 11:05 am Page 76
76 H. Kotze
Fig. 7.1. Location of Komatiland Forests in South Africa.
South African Forest Company Limited (SAFCOL). The plantations cover approxi-
mately 130,000 ha and comprise various pine species mainly grown for sawtimber.
A small area of eucalyptus is used for the production of special products for niche
markets. The plantations are spread over a number of physiographical regions with
varying geology and climate.
The objectives of the growth and yield research programme in Komatiland
For
ests are to develop a set of growth and yield models that can be used for resource
description, growth and yield predictions for management planning purposes and
the analysis and development of optimum stand-level management regimes.
Figure 7.2 shows the components in the growth and yield cycle. Models and
simulation systems ar
e the end-products of the growth and yield programme.
Therefore, the field programme has been designed to meet the requirements of mod-
els for stand growth, tree volume and taper, stand structure, response to silviculture
and site quality.
The purpose of this chapter is to describe the strategy for growth and yield
r
esearch for Komatiland Forests by describing the past and current situation and
indicating how the programme should develop towards the future.
The Field Programme
Due to its government-based background, with intense involvement in past growth
and yield research in South Africa, Komatiland Forests inherited most of the histori-
cal data on long-term spacing and thinning trials, which started in 1936. More
recently, since the late 1980s, a series of new spacing trials has been established and,
since 1995, a stratified permanent sample plot (PSP) programme has been started.
The field programme has been designed to gather data for the requirements of
08Amaro Forests - Chap 07 25/7/03 11:05 am Page 77
77 Strategy for Growth and Yield Research
• Implement models in simulator
• Develop optimization systems
Simulation systems
• Stratification
• Plot establishment
• Measure and maintain
Field programme
• Data capture
•
• Update database
• Data summary
Data management
• Fit models
•
•
Modelling
Verification
Test polymorphism
Verify and benchmark
Fig. 7.2. Components of the growth and yield cycle.
stand-level modelling. New data augment existing historical data in order to pro-
vide for more accurate growth models. Table 7.1 shows how the various types of
data are used to develop the required model components.
The field programme consists of long-term spacing trials, PSPs, silvicultural
r
esponse trials and ad hoc destructive volume and taper sampling. Inventory data
are also used for some model components. In a field programme, long-term trials
and PSPs should be well stratified over the resource base. Stratification factors of
importance are species, working circle, site types, productivity classes and age
classes. A detailed 1:10,000 site classification system is available for bottom-up strati-
fication purposes. This classification provides detailed descriptions of climate class,
soil group, soil depth, depth limiting material, geology and other terrain descriptive
variables. A top-down stratification framework was also developed by the forest
Table 7.1. Model components and their different data sources.
Thinning Management Silviculture
Spacing control inventory response Destructive
Model components trials PSPs data data trials sampling
Stand growth
Dominant height
Average height from
dominant height
Basal area
Survival
Growth response
Thinning response
Thinning
BA thinning ratio
Stand structure
DBH distribution
(Dmin, Sdev)
Average height by DBH class
Products
Tree volume and taper
Live crown height
08Amaro Forests - Chap 07 25/7/03 11:05 am Page 78
78 H. Kotze
industry for the whole summer rainfall area (Kunz and Pallet, 2000). This classifies
the forest area in terms of physiographical regions, i.e. groupings of geology and cli-
mate classes. PSPs are located so that they represent the various strata proportional
to the species area.
The aim of the field programme is to establish at least one spacing trial per
species per physiographical r
egion. The historic spacing trials were mostly of the
correlated curve trend (CCT) (O’Connor, 1935) and Nelder 1a (Nelder, 1962) types,
with the current spacing trials being of the Triple-S CCT type (Bredenkamp, 1990). It
is also aimed to establish at least 40 PSPs per species per physiographical region.
Currently there is about one PSP for every 400 ha. A PSP is approximately 40 m ×
40 m in size and contains at least 40 trees at rotation age. PSPs are established inside
existing stands, about 40 m away from the roadside. Du Plessis et al. (1997) summa-
rized the guidelines for the establishment and maintenance of the field programmes.
For minor species, with small areas, additional data are sourced from neighbouring
companies, belonging to the industry-based Mensuration and Modelling Research
Consortium (MMRC). A biennial measurement cycle is followed, using the same
measurement team as far as possible. Table 7.2 shows the current extent of the field
programme and indicates data available from historic sources and the MMRC. The
field programme continues to develop along with our understanding of site com-
plexity and the requirements for developing each model component.
Data Management
Research data follow three distinct steps from the field, through to the database and
to the models. In the field, trees are measured on demarcated plots. Tree diameter at
breast height (DBH) is measured with a DBH tape and all heights with a Vertex hyp-
someter. Individual tree measurements are verified against the previous set of mea-
surements. Measurement data are recorded on paper field sheets, or on hand-held
electronic data-capturing devices. In the office, data are captured (downloaded) on
electronic media to a standardized format. Data are again verified by range checking
and distribution plots. For growth modelling purposes, the data are summarized to
stand-level variables. At the end of each measurement cycle, a measurement report
is compiled, which summarizes all relevant parameters.
Table 7.2. Extent of the field programme.
Species
P. ellxcar
Variable P. patula P. elliotii P. taeda hybrid E. grandis Other (7) Total
% of area (130,000 ha) 46.4 26.5 6.7 5.3 4.1 11.0 100
Spacing trials
Current 2 1 0 1 3 2 9
Historic 3 1 1 0 0 1 5
MMRC 2 0 0 2 0 0 6
PSPs
Current 169 109 0 18 27 28 351
MMRC 52 66 42 0 50 61 271
Sample trees for taper
Historic 358 180 0 100 174 0 812
MMRC 170 100 100 0 0 420 790
08Amaro Forests - Chap 07 25/7/03 11:05 am Page 79
79 Strategy for Growth and Yield Research
Data must flow through the above steps speedily and without error. As mea-
surement data are also collected over a very long period of time, continuous and
careful data management is of the utmost importance. In the MMRC, this has been
realized to be an important need for the whole industry, and a joint general growth
and yield database is under development. In order to ensure consistency in the
industry, great efforts were made to develop common standards for the database
(Kotze, 1995). The data-management process for spacing trials has also been well
described in Kotze and Groenewald (1995).
Growth Modelling
Komatiland Forests adopted a stand-level modelling approach because all our
forests are planted, even-aged, single-species stands. Stand-level models can be clas-
sified under stand models, which is a general term to denote equations or systems
of equations developed for providing information on forest growth and yield. Stand
models are essential for decision making under intensive forest management, pro-
vide a means for evaluating treatment alternatives, and are but one component in
comprehensive systems for the management of forests. Stand-level models predict
stand growth and yield as a function of stand age, site index and stand density.
They can generally be applied with existing inventory data and are computationally
simple. They can be combined with procedures for predicting diameter distribution
to estimate product mixes. Stand-level models are somewhat inflexible for analysing
a wide range of stand treatments and are not likely to give reliable results outside
the range of conditions included in the sample plots on which they are based. There
are a number of essential properties which stand-level models must exhibit. These
are analytical compatibility between growth and yield, invariance for projection
length, and numeric equivalency between alternative applications of the equations
(Pienaar et al., 1988).
Various yield prediction models, with different input requirements, can be used
for management planning purposes under varying cir
cumstances, e.g. the classical
biological stand-level growth models (Chapman–Richards type) and the stand-level
yield prediction and projection models (Schumacher type). Remeasured data from
spacing trials are suitable for the Chapman–Richards-type growth models, and PSP
data are, in turn, more suited for the Schumacher-type growth models. Table 7.1 indi-
cates the model components required and which data can be used to develop them.
Growth and yield research has been carried out in South Africa since the early
1920s.
A number of researchers – O’Connor (1935), Craib (1939) and Marsh and
Burgers (1973) – did pioneering work in stand-density management, especially with
the CCT trials. Many others developed models or model components from trial,
inventory and other data. The theory and technology pertaining to growth and yield
models have changed over time, and numerous function types and model architec-
tures have been used over the years. Kotze (2001) has summarized all the available
models and their coefficient sets pertaining to South Africa.
Many of the existing models used in Komatiland Forests are based on data from
the old CCT trials started in 1936. They ar
e still the most suitable models, because
there are no models based on more recent data. The purpose of a growth and yield
research programme is to ensure that relevant data become available for the devel-
opment of more accurate models. That is why a series of new spacing trials was
installed in the late 1980s and a PSP programme was started in 1995.
The best existing models and their coefficient sets are selected for each species
and r
egion combination. These are packaged into a model configuration for ease of
08Amaro Forests - Chap 07 25/7/03 11:05 am Page 80
80 H. Kotze
Use enumeration data
Age
1
, Hd
1
, BA
1
, TPH
1
Predict from SQ variable, age, regime
Hd
1
, BA
1
, TPH
1
Bucking of the stand table
From mean tree
Reconstruct stand table
Optimized product breakdown
Calculate volumes?
More thinnings?
Thinning?
Calculate thinning %
and removals
Project to age of next operation
Hd
2
, BA
2
, TPH
2
Enumeration data
Y
N
N
Y
Fig. 7.3. Multi-component growth and yield model framework.
use and reference. These functions can work together in a simulation framework
(Fig. 7.3). Stand growth and yield are normally projected from a calibration point
where inventory data provide the calibration age (Age
1
), dominant height (Hd
1
),
basal area per hectare (BA
1
) and stems per hectare (TPH
1
). If such inventory data do
not exist, then a calibration point is created before the first thinning age. Each stand
has a default site index value at base age 20 years (SI
20
) and this is used to estimate
height at Age
1
. TPH
1
is estimated by multiplying planting density (TPH
0
) with a
default survival percentage (Surv%). BA
1
is estimated with a Schumacher-type basal
area function from Age
1
, TPH
1
and Hd
1
.
The most problematic part of growth and yield prediction is to project basal
ar
ea over time in thinned stands. An example is provided, showing the current
models in use. The following multi-step process is used:
1. Project Hd, TPH and BA from calibration age to thinning age. The most used
functions ar
e given below.
1a. The Chapman–Richards-type height growth function (Richards, 1959):
(1)
Age
Age
1
1-
e
1-
e
HD
2
= HD
1
β
3
2
β
β
β
β
1
1
2
where HD
1
is the dominant height at Age
1
, the calibration age; HD
2
is the projected
height at Age
2
; and β
1
to β
3
are parameters to be estimated.
1b. The Clutter–Jones survival function (Clutter and Jones, 1980):
1
)
)
)
)
+
+
2
(
⋅
(
⋅
(
(
(2)
Age
1
100
Age
2
100
2 1
TPH
where TPH
1
is the stems per hectare at Age
1
, the calibration age; and TPH
2
is the
projected stems per hectare at Age
2
.
β
β
3
1
β
3
−
⋅
β
+
β
1
2
TPH=
08Amaro Forests - Chap 07 25/7/03 11:05 am Page 81
81 Strategy for Growth and Yield Research
1c. The Schumacher-type stand-level basal area function for unthinned stands
(Schumacher, 1939; Pienaar and Harrison, 1989):
(3)
Age Age
2 1
where BA
1
is the basal area per hectare at Age
1
, the calibration age; and BA
2
is the
projected basal area per hectare at Age
2
.
1d. The Chapman–Richards-type basal area function for unthinned stands (Pienaar
and Turnbull, 1973):
(4)
(5)
TPH
1
where BA
t
is the basal area per hectare removed in the thining; BA
b
is the basal area
before the thinning; TPH
t
is the stems per hectare removed in the thinning; and
TPH
b
is the stems per hectare before the thinning.
4. Advance the calibration point to an age just after the thinning (Age
1
):
ln ln
ln
2
1
Age Age
2 1
ln HD
1
ln HD
1
0
HD
2
Age
2
t
HD
2
BA
1
ln
ln
k
t
TPH
TPH
b
BA
t
BA
b
BA
2
=⋅A
BA
2
1 exp
]
where and are parameters to be estimated.A k t m, ,
0
2. Reduce the TPH according to the thinning schedule. A typical thinning schedule for
pine sawtimber is as follows: plant at 1372 trees/ha, a survival percentage of 89% is the
default. Thin at age 8 years to 650 stems/ha, at age 13 years to 400 stems/ha, at age 18
(
years to 250 stems/ha and clearfell at 35 years.
3. Estimate the BA remaining after thinning with Field’s thinning ratio function
[
(Field , 1978):et al.
)
)
1
(
−
)
2
)
TPH
Age Age
2 1
((
−
β
0
⋅=
Basal area (m
2
/ha)
0
5
10
15
20
25
30
35
40
45
50
BA 1200
BA 650
BA thinned
TPH
TPH
)
(
(
+
2
ln
β
β
4
⋅
⋅
+
)
)(
−
)(
(
)(
−
) (
1
−
m
)
)
+
⋅
β
1
)
+
(
(
⋅
ln
+⋅
+⋅
β
5
exp
β
3
−
=
0 5 10 15 20
Age (years)
Fig. 7.4. Basal area after thinning using the index of suppression.
08Amaro Forests - Chap 07 25/7/03 11:05 am Page 82
82 H. Kotze
● Hd
1
: Hd after thin = Hd before thin;
● TPH
1
: TPH after thin = TPH remaining as prescribed in the thinning regime;
● BA
1
: BA after thin = BA before thin BA removed.
5. Project dominant height as indicated in Equation 1 above from Age
1
to the new
Age
2
.
6. The assumption is made that there is no mortality between intense and frequent
thinnings. Ther
efore, TPH remains constant until the next thinning.
7. Basal area response after thinning is one of the most difficult model components
to develop and to explain. The basic assumption is that a stand thinned fr
om, say
1200 stems/ha to 650 stems/ha, will have a lower basal area than an equivalent
unthinned stand standing at 650 stems/ha (Fig. 7.4). The hypothesis for basal area
growth after thinning is that the thinned stand will eventually catch up with the
unthinned stand (Marsh and Burgers, 1973). This type of growth response, in which
data are available for both the unthinned and thinned curves, can only be obtained
from formal thinning response trials as, for example, in the old CCT trials.
Three approaches have been defined to model this basal area response, namely:
7a. The index of suppr
ession, used in conjunction with the Chapman–Richards-type
models (Pienaar and Shiver, 1984).
BA
2
= BA
(
1 – IS
2
)
(6)
u
(
AGE
2
−
AGE
1
)
β
1
Age
1
IS
2
=
IS
1
⋅e
–
β
0
BA
IS
1
=−1
a
BA
ut
where BA
a
is the basal area per hectare after thinning at Age
2
; BA
u
is the basal area
per hectare of the unthinned stand growing at the same stand density to which the
stand is thinned to at Age
2
; Ba
ut
is the basal area per hectare of the unthinned stand
at the age of thinning; IS
1
is the index of suppression at the age of thinning; and IS
2
is the index of suppression at Age
2
.
7b. The stand-level thinning response term used with the Schumacher-type func-
tions (Pienaar and Harrison, 1989).
1
1
2 2
ln
(
BA
1
)
+ ⋅
Age
− +
β
⋅
(
ln
(
TPH
)
− ln
(
TPH
1
)
)
β
1
2
Age
1
BA
2
= exp
+⋅
(
ln
(
HD
2
)
− ln
(
HD
1
)
)
+
β
⋅
ln
(
TPH
2
)
−
ln
(
TPH
1
)
(7)
4
β
3
Age Age
1
2
β
7
+⋅
ln
(
HD
2
)
ln
(
HD
1
)
+
β
6
⋅
TPH
tt
Age
Age
β
7
t t
β
5
− ⋅
−
Age
1
Age
2
Age
1
TPH
Age
2
a
7c. The age-adjustment method, when only unthinned curves are available. This is
an algorithmic method and is based on observations by Marsh on South African
CCTs (Marsh and Burgers, 1973). Marsh’s hypothesis states that the increment of a
thinned stand equals that of an unthinned stand of the same density and basal area,
but at an earlier age. The effect is that the growth rate of the thinned stand after the
thinning is initially faster than that of an unthinned stand until the difference in
basal area is made up. This hypothesis works well, except where excessive suppres-
sion has been allowed to develop between thinnings. Alder (1980) and Crockford
(1995) have described the yield prediction procedure.
8. A number of other variables can be derived from the basic growth curves, namely
08Amaro Forests - Chap 07 25/7/03 11:05 am Page 83
83 Strategy for Growth and Yield Research
quadratic mean DBH, mean tree volume, mean tree-based whole stand volume,
mean annual increment, stock tables with a DBH distribution and average height by
DBH class and product volumes. The details of these variables are not discussed.
Simulation Systems
The growth and yield research cycle is completed when the model configurations
have been implemented in growth and yield simulators. These simulators are
forestry planning tools and have different roles, for instance they are used in man-
agement planning systems (e.g. the G&Y Shell; Nel, 2002) or as stand-alone sys-
tems for forestry scenario analyses (FORSAT; Kotze et al., 2001), the Pruning
Scheduler (Kotze and Vonck, 1997) or for optimal bucking of stands (
WINCUTUP;
Vonck, 1997).
Recommendations
The key for success is to find an effective methodology for the development of each
component in the growth and yield cycle and to maintain continuity over a long
period of time. Each aspect of the growth and yield research programme requires its
due attention. The emphasis is on an efficient and cost-effective field programme.
Data are sourced from a well-stratified field programme for each model component.
Industry interaction is aligned with the company objectives as far as possible to
enable maximum benefit.
The empirical stand-level modelling approach is recommended, because these
models can be easily implemented in simulators and can be calibrated with data
that ar
e readily available in the planning database. However, not all the basal area
and basal area response after thinning model types as illustrated in the paragraph
on growth modelling can be directly applied to (for example) the PSP data from
thinned stands. It is recommended that other modelling approaches be applied for
this specific data source.
It is recommended that Komatiland Forests supports other research institutions
in South
Africa currently working on other modelling strategies, such as process-
based models, until they can be applied in a practical manner. It is also recom-
mended that joint modelling exercises be coordinated between member companies
in the MMRC for the processing of pooled data. This will be beneficial, especially for
minor species covering small areas.
References
Alder, D. (1980) Forest Volume Estimation and Yield Prediction, Vol. 2. FAO Forestry Paper 22/2,
Rome.
Bredenkamp, B.V. (1990) The triple-S CCT design. In: von Gadow, K. and Bredenkamp, B.V.
(eds) Proceedings of a Symposium arranged by the Forest Mensuration and Modelling Working
Group in Collaboration with the Southern African Institute of Forestry and the Eucalyptus gran-
dis Research Network on ‘Management of Eucalyptus grandis in South Africa’, pp. 98–205.
Clutter, J.L. and Jones, E.P. Jr (1980) Prediction of Growth after Thinning in Old-field Slash Pine
Plantations. US Department of Agriculture, Service Research Paper SE-217, pp. 1–8.
Craib, I.J. (1939) Thinning, Pruning and Management Studies on the Main Exotic Conifers Grown
in South Africa. Department of Agriculture and Forestry, Government Printer, Pretoria,
179 pp.
08Amaro Forests - Chap 07 25/7/03 11:05 am Page 84
84 H. Kotze
Crockford, K.J. (1995) Yield models and tables for Pinus patula, Pinus elliottii and Pinus taeda in
Zimbabwe. Zimbabwe Bulletin of Forestry Research 12, Forestry Commission, 51 pp.
Du Plessis, M., Chiswell, K.E. and Morley, T. (1997) Criteria for the Inclusion of Permanent Sample
Plots in the Mensuration and Modelling Research Consortium, Version 1. Mensuration and
Modelling Research Consortium, South Africa, 30 pp.
Field, R.C., Clutter, J.L. and Jones, E.P. Jr (1978) Predicting thinning volumes for pine planta-
tions. Southern Journal of Applied Forestry 2(2), 59–61.
Kotze, H. (1995) Standards and Formats for Data and Databases. CSIR Report FOR-C-299, 47 pp.
Kotze, H. (2001) A Summary of Growth and Yield Models in South Africa. SAFCOL Research,
South Africa, 29 pp.
Kotze, H. and Groenewald, W.H. (1995) Progress Report: a Data Manipulation System for Growth
and Yield Trials. CSIR Report FOR-I-616, 74 pp.
Kotze, H. and Vonck, D.I. (1997) A growth simulator and pruning scheduler for Pinus patula in
Mpumalanga–North Province, South Africa. In: Amaro, A. and Tomé, M. (eds) Empirical
and Process-based Models for Forest Tree and Stand Growth Simulation. 21–27 September,
Portugal, pp. 205–221.
Kotze, H., Kassier, H.W. and van der Merwe, D.G. (2001) FORSAT Specification, Design and
Implementation Document. SAFCOL Research, South Africa, 90 pp.
Kunz, R. and Pallet, R. (2000) A Stratification System Based on Climate and Lithology for Locating
Commercial Forestry Permanent Sample Plots. ICFR Bulletin Series 01/2000, 17 pp.
Marsh, E.K. and Burgers, T.F. (1973) The response of even-aged pine stands to thinning.
Forestry in South Africa 14, 103–110.
Nel, J.H. (2002) A Generic Shell for Growth and Yield Models. AfriGis Environmental Solutions,
South Africa, 69 pp.
Nelder, J.A. (1962) New kinds of systematic designs for spacing experiments. Biometrics 18,
283–307.
O’Connor, A.J. (1935) Forest research with special reference to planting distances and thinning.
British Empire Forestry Conference, South Africa, 30 pp.
Pienaar, L.V. and Harrison, W.M. (1989) Simultaneous growth and yield prediction equations
for Pinus elliottii plantations in Zululand. South African Forestry Journal 149, 48–53.
Pienaar, L.V. and Shiver, B.D. (1984) An analysis and models of basal area growth in 45-year-
old unthinned and thinned slash pine plantation plots. Forest Science 30, 933–942.
Pienaar, L.V. and Turnbull, K.J. (1973) The Chapman–Richards generalization of Von
Bertalanffy’s growth model for basal area growth and yield in even-aged stands. Forest
Science 19, 2–22.
Pienaar, L.V., Harrison, W.M. and Bredenkamp, B.V. (1988) Yield Prediction Methodology for E.
grandis Based on Langepan CCT Data. University of Georgia, 36 pp.
Richards, F.J. (1959) A flexible growth function for empirical use. Journal of Experimental Botany
10, 290–300.
Schumacher, F.X. (1939) A new growth curve and its application to timber yield studies. Journal
of Forestry 37, 819–820.
Vonck, D.I. (1997) WINCUTUP User’s Manual. SAFCOL Planning and Development, South
Africa, 6 pp.
09Amaro Forests Part 2 25/7/03 11:05 am Page 85
Part 2
Mathematical Approaches and Reasoning
All models reflect scale in some way. Models may be developed at one particular scale and
applied at that scale. Other models may be developed and applied at multiple scales. Some
models may be developed at one scale and applied at another. Scale may be an explicit com-
ponent in a model or merely implied by the structure and nature of the model. Regardless of
how scale is used or functions within a model, a model cannot be assessed or evaluated
without some consideration of scale. As models become more ‘realistic’, it is likely that
issues revolving around scale will become more acute. Thus, it is important to continue to
develop and refine tools for modelling within and across spatial, temporal and hierarchical
scales.
Most models of forest systems that have been developed are state models. They describe
or pertain to the conditions of the system of inter
est. Most process models are state models,
as are some empirical models. An interactive model is sensitive to changing conditions and
allows the user to become a part of the modelling exercise, from the initial conceptual and
design phase of model development to final use and application. It is likely that an increas-
ingly sophisticated public will expect models of all types to be more interactive in nature.
Society’s expectations of how forest models can be used and what information they will
pr
ovide can be incongruous with the design and intent of developed models. Sometimes this
occurs because society is asking different questions or perhaps broader questions than the
models are capable of addressing. At other times there is inadequate continuity between the
scientific work of model development and what society needs or wants. Additionally, some-
times society’s questions or priorities change. Therefore, it is important to develop modelling
methods or approaches that address the current issues that society is facing as well as being
flexible enough to accommodate future concerns.
Usually, the development of a forest model is initiated by developing a simple submodel
or component that will form the basis of the full model. Fr
om this point forward, the mod-
eller confronts the tension that exists between simplification and aggregation. On the one
hand, forest models are simplifications of forest reality. Thus, models that become too com-
plex lose their usefulness. On the other hand, the need and desire for more realistic models
tend to promote the aggregation of submodels and components into more complex model
systems. Clearly, modellers must use a development process that aggregates submodel com-
ponents such that the proper balance between model simplicity (for the sake of usefulness)
and complexity (for the sake of reality) is achieved.
85