l)"i11 - University of Oxford

CFI OCCASIONAL PAPER
Number 20
PLANNING, PERFORMANCE AND
EVALUATION OF GROWTH
AND YIELD STUDIES
edited by
H.L. Wright
1983
1:11- OD .
Commonwealth Forestry Institute
University of Oxford
Proceedings of the meeting of
IUFRO Subject Group 54.01
Oxford. September 1979
ISBN 0 85074 062 2
ISSN 0141-8181

INTRODUCTION
LIST OF PARTICIPANTS
- i -
TABLE OF CONTENTS
PAPERS PRESENTED (in alphabetical order of author)
Where is the ground?
Do future establishments of permanent
sample plots in Britain need to follow
past practice to meet the requirements
of forest management?
Portable data terminals for data
collection in the field
Collecting growth data
Growth functions for radiata pine
plantations
Sample plots and experiments in crop
development studies
A caliper for use in tropical rainforest
management
A stem analysis machine under
development
Stem profile analysis
The permanent sample plot system of the
New Zealand Forest Service
Comparison of two stand growth models for
northern hardwoods
Estimation of the volume of a stand using
a tariff procedure
A flexible yield and management model for
spruce in the Belgian Ardennes
A stand growth model as a tool in studying
management options for MAB-rainforest
ecosystem projects and for temperate
forests
Application of a factorial design to a
thinning experiment in Eucalyptus grandis,
with intermediate results
Data collection in tropical forests
Bruce, D.
iii
iv
Christie, J .M. , and
Edwards, P.N. 4
Edwards, P.N. 10
Ferguson, I.S. 15
Ferguson, I.S. 25
Gallagher, G.J., and
Q'Brien, D. 46
de Graaf, N.R. 56
Howell, R.S., and
Stickland, R.E. 61
Lin, C.J. 62
McEwen, A.D., and
Goulding, C.J. 74
Monserud, R.A. , and
Ek, A.R. 83
Rennolls, K., and
Tee, v. 91
Rondeux, J. 100
Schneider, T.W., and
Alder, D.
Schonau, A.P.G.
Singh, S.P.
110
120
140

Growth and yield analysis of thinned
uneven-aged spruce and fir stands
in Maine
Quantifying forest science with biomass.
I-Site productivity
Quantifying forest science with biomass.
II-Conifer thinning studies
- ii -
Solomon, D.S., and
Seegrist, D.W.
Young, H.E., and
Ribe, J.H.
Young, H.E., and
Ribe, J.H.
149
157
166

- v -
Gallagher, G. (Or) Research Branch, Forest and Wildlife Service EIRE
Department of Fisheries and Forestry
1/2 Sidmonton Place
Bray, Co. Wicklow
Goulding, C.J. (Dr) Forestry Research Institute NEW ZEALAND
Rotorua
de Graaf, N.R. (Dr) Forest Research Officer of University of
Wageningen, Netherlands
Stationed at:
CELOS (Centre for Agricultural Research in SURINAM
Surinam)
P.Q. Box 1914 Paramaribo
Holte, A. Norwegian Forest Research Institute NORWAY
Box 61, 1432 As-NLH
Howell, R. Forestry Commission Research Station UK
Alice Holt Lodge, Wrecclesham, Surrey
Johann, K. (Or) A-1131 Wien AUSTRIA
Forstliche Bundesversuchsanstalt
Tirolergarten
Kenk, G. (Dr) Forstliche Versuchs-und Forschungsanstalt GERMANY
Baden-WUrttemberg, Abt. Waldwachstum
Reichsgrafenstrasse 12 7800 Freiburg
Lee, H.S. Forest Department MALAYSIA
Kuching, Sarawak
Liu, C.J. (Or) Department of Forestry (00731) USA
University of Kentucky,
Lexington, Kentucky 40546
Masson, J.L. Silviculture & Management GHANA
FAO/GHA/74/013
P.O. Box 209, Takoradi
Malleux, J. Forest Inventory Officer MOZAMBIQUE
MOZ/16/007
P.O. Box 4595, Maputo
Meng, C. (Dr) Department of Forest Engineering CANADA
University of New Brunswick
Fredericton, N.B.
Miller, H.G. (Or) Department of Peat and Forest Soils OK
Macaulay Institute for Soil Research
Craigiebuckler, Aberdeen
Mitchell, C.P. (Dr) Forestry Department UK
Aberdeen University
St. Machar Drive, Aberdeen
Monserud, R.A. (Or) USDA Forest Service USA
Intermountain Forest and Range Experiment
Station
1221 S. Hain St.
Moscow, Idaho, 83843

Sutter, H.
Thallon, K.P.
Tint, Kyaw (Or)
Turnbull, K. (Or)
Wright, H.L.
- vii -
National Forest Survey and Inventory
BUX!79!O 11
UNDP, Rangoon
Forestry Commission Research Station
Alice Holt Lodge
Wrecclesham, Farnham, Surrey
Dept. of Forestry
Arts and Science University, Rangoon
College of Forest Resources
University of Washington
Seattle, Wash. 98195
Commonwealth Forestry Institute, .
South Parks Road, Oxford
BURMA
OK
BURMA
USA
OK

- 3 -
To avoid bias in volume estimates in inventories, it is necessary to
use the same definition of ground level in the volume table sample as in
the inventory. I know of instances where this has not been done.
There are many arguments favoring either of my two main definitions-­
(1) average ground level or (2) ground level on uphill side of tree. I
favor the second because more foresters measure trees in inventories of
some kind than in growth studies. Furthermore, growth studies are made by
scientists who should deal easily with changing levels of basal area
determination. Finally, most trees can be measured 1.3 m above the ground
level on uphill side of trees, while some cannot be measured 1.3 m above
average ground level.
Standardization of the definition of d.b.h. is good but is not complete
until a standard definition of ground level has been accepted.

- 9 -
Fries, J. 1967. Variation in Forest Stands as a basis for the Planning
of Experiments. Paper to Section 25 IUFRO Congress 1967 Munich.
Hamilton, G. J. 1976. Pennanent Sample Plots in Britain. Paper to
IUFnO 54.01 meeting Warsaw in Permanent plots in forestry growth and
yield research. Department of Forest Yield Research No 43 1976.
11 September 1979

*The Wolf in Sheep's Clothing
- 11 -
The availability of computers enabled the forester to send
his collected measurements away without doing any calculations.
He then had much more time available for measuring the
experiments, and all the time-consuming calculations were done
by the computer. The procedure is now: the forester measures
the trees; writes the measurements on paper; sends the paper
to the computer centre; the data is copied into the computer
by punch-operators; the computer prints out the results; these
are returned to the forester for checking. This procedure is
widely used, but it has 2 obvious problems.
Errors may be introduced to the data while it is being
copied to the computer. Secondly, the delays caused by the
postal service, and pressure of work on the punch-operators,
may mean that the forester receives the results so long after
he measured the experiments that he is no longer in the area,
he has forgotten all about the data, and therefore cannot
check the data.
*If you go down to the woods today, you're sure of a big
surprise.
Portable data terminals eliminate the first problem and
reduce the second. A portable data terminal is a box which has
a keyboard and a display similar to a calculator, but which
also contains permanent solid state memory, usually 8K bytes or
more. It has some intelligence, and a battery. Sorne models are
available with casette tape memory in place of the solid state
memory, but these are not suitable for forest use for obvious
reasons. To send the data to the computer centre, the portable
data terminal is connected to an acoustic coupler, and the data
can be sent via a Post Office telephone to the modem at the
computer centre.
With a portable data terminal, the forester now uses the
following procedure:he measures the trees; enters the data into
the portable data terminal; sends the data via the Post Office
telephone to the computer; the computer calculates the results;
and the results are posted back to the forester. The possible
errors introduced by copypunching have been eliminated, as have
possible delays of getting the data into the computer. And half
the postal delays have been eliminated as well! The forester
can expect his results back within 3 days.

- 16 -
Sophisticated analytical aids such as forest simulation and linear programming
models are widely used in these plantations (Research Working Group
No. 2, 1978; Elliott 1978). Various growth functions are incorporated in
these models. However, because of the rapidity of changes in silvicultural
and other practices, difficulty has been experienced in trying to ensure that
these growth functions adequately reflect the impact of new practices, as well
as old.
The aim of this paper is therefore to review past practices in the collection
of growth data and developments in the estimation of growth functions, and
to examine the problems and advance possible solutions for future data collection
and estimation of growth functions.
GROWTH FUNCTIONS: AREAS PLANTED PRIOR TO 1970
Prior to 1970, the progressive changes in establishment and thinning
practices which had occurred in Australia and New Zealand had had comparatively
little impact on the pattern or magnitude of growth on a given site. Admittedly,
1970 is not a rigid dividing line for all plantations, radical changes having
been initiated somewhat earlier in some plantations, and later in others.
Existing data
In aggregate, the areas planted prior to 1970 constitute a relatively
homogeneous type for the purposes of sampling growth and estimating growth
functions for a particular plantation. Many organisations have already developed
growth functions which are deemed appropriate for these areas. If not,
data from permanent inventory or other sample plots are generally available to
estimate them. While these data frequently span a wide range of ages, the
coverage with respect to site, stocking, and severity and timing of thinning may
be less than ideal. The accuracy of some of the measurements also leaves a
lot to be desired, especially in the case of top height (McEwen 1978; Ferguson
1979). Nevertheless, initiation of new systems of data collection for these
areas iSiunlikely to be warranted, unless to fill major gaps in coverage. In
many cases, the major problem is how best to reduce the burden of continuing
measurement, especially where permanent inventory systems I,ave been established.
Cooperation and data pooling
Some scope exists for cooperation between organisations in pooling data
and thus improving coverage and sample size. Unfortunately, previous attempts
at interchange or pooling of Monterey pine data in Australia have foundered
because of concern to protect commercial interests, rivalries between the
technical staff of different organisations, and the ability of some organisations
to rely on growth functions prepared by others. To be fair, however, there are
also limitations to the ability to pool data usefully. Differences in data
definition or measurement techniques create problems. Substantial differences
in growth are also believed to exist between different regions. Moreover, a
diversity of approaches to the formulation and estimation of growth functions,
and the construction of simulation models, also has its advantages at this early
stage of development.

- 21 -
Other examples of greater variability in field practice may also be cited in
relation to initial spacing, initial survival, and spacing in thinning operations.
The expected value of the dependent variable in the growth function should
reflect this inevitable variability found in field practice.
Temporal differences between silvicultural experiments and routine practice
are also potentially important, although they have received little recognition
to date. In research reported elsewhere (Ferguson 1979) the effect of climatic
conditions on annual increment in gross basal area was quite marked in plantations
of Monterey pine in the Australian Capital Territory. Thus an experiment
established under favourable climatic conditions may well yield very different
results in relation to fertilizing to one which suffered a sequence of drought
years.
The potential effects of interactions between the effects of standards of
work, space and time are obviously considerable and would inevitably arise in
field practice.
Davidson and Martin (1967) carried out research into the magnitude of the
differences between experimental and farm yields in agriculture. Farm yields
ranged from 57 to 72% of experimental yields in wheat farming, which involves
relatively large areas in Australia. Experience in Australia and New Zealand
suggests that similar values occur in plantation forestry, but no systematic
study of the problem has been made.
Clearly, in the light of these problems, data collected from experiments
alone cannot be expected to provide a satisfactory answer for extending growth
functions. Initially, such data will have to be used, because no other sources
exist, and subjective adjustment factors will have to be applied to the resulting
estimates of growth. In the longer run, however, data will have to be obtained
which reflect field results. Experimental data must therefore be seen principally
as a bridging device for planning until the field data are available.
Bayesian estimation
The future of proposals to sample growth occurring in field practice would
have limited appeal if one had to wait for 20 years or more to accumulate
sufficient data to attempt the estimation of the new growth function. Fortunately
the use of Bayesian estimation offers a means of overcoming this problem. In
particular, it enables estimation to proceed sequentia11y, progressively improving
the growth function as additional data become available. While neither of
the examples of Bayesian estimation available to date (Leech 1978, Fergu50n 1979)
bear directly on the type of problem under discussion, Leech's work provides a
useful analogy.
Leech studied the effect of thinning on yield for Monterey pine plantations
located in South Australia. The data included both thinned and unthinned plots,
with an average of about 10 successive measurements in each plot. Given such
a small number of observations in the first-stage, estimation of the parameters
relating to the effects of thinning on yield was clearly impracticable in any
direct way. However, the unthinned plots were used to estimate a function
relating yield to age and site, using generalized least squares. This provided
reasonably precise estimates of the parameters concerned. The paramet?r
estimates and associated variance-covar;ance matrix were then used to derive
the parameters of a prior probability function for use in the Bayesian estimation
of the parameters, including additional thinning parameters, for each thinned
plot. This sequential analysis worked well and enabled tests of the significance
of the thinning parameters to be carried out. Without it, the analysis would
have been impossible.

- 25 -
IUFRO Subject Group S4.01, Mensuration, Growth and Yield,
Meeting in Oxford, September 16 - 22, 1979
GROWTH FUNCTIONS
FOR
RADIATA PINE PLANTATIONS
lan S. Ferguson
Department of Forestry
Austral ian National University
Canberra, Austral ia
SUMMARY
Gross basal area increment functions were estimated by general ized least
squares from annual data derived from 85 permanent plots. The preferred
functions incorporated thinning and cl imatic variables, as wel I as age,
site index, and forest.
Noisy data prevented the same detai I being incorporated in height
functions, but an anamorphic function relating to top height to age and site
index was estimated using general ized least squares.
Both functions seem satisfactory in their properties. Tests using
independent data from Kowen Forest indicated that smal I biases may exist,
although the direction of these biases alternated over time.
(Keywords: growth functions, general ized least squares, radiata pine,
thinning variables, cl imatic variables.)
INTRODUCTION
This paper reports the results of part of the research carried out under
contract for the Forests Branch of the Austral ian Capital Territory (A.C.T.).
The research contract involved the estimation of growth and related functions
suitable for the development of a simulation model of forest growth and
yield for A.C.T. plantations. This paper, however, deals only with the gross
basal area and top height functions; other work relating to mortal ity and
diameter distributions wi I I be reported elsewhere.
GROSS BASAL AREA
Gross basal area is defined as the sum of the basal area of living trees
plus that of the accumulated\trees of which have died or were removed up to
that point in time.

- 28 -
Thinning was incorporated in Equation (2) in a purely mechanical way
which avoided introducing further coefficients. The exponential term is
essentially a discounting factor which takes account of the diminishing
increment with age. The thinning variable (T) was defined as the proportion
of standing basal area retained after thinning and was incorporated thus:
' -p(CA/T)-A ) (4)
8 = n exp 0
Clearly, the effect of thinning wi I I only be felt in the year of thinning,
under this formulation. No lagged effects could be examined because of the
gaps in the annual series of measurements. The coefficient Aa in Equation (4)
is the intercept on the horizontal axis and hence Equation (4) can be
simplified to:
f B = n* exp-pA/T
Where n* = n exp pAo
This reduces the number of coefficients to be estimated and is tenable
provided A o can be estimated by other means, as is the case.
Cl imatic variables examined included various forms of rainfal I defined
as different periods of the year. However, prel iminary investigations
suggested that annual rainfal I and seasonally effective rainfal I were worth
pursuing further. Seasonally effective rainfal I is defined (Mi I lett 1944)
as the rainfal lover the months August to December inclusive, plus that over
the months March to May inclusive. Booth (pers. comm.) also provided an
annual "growing index" for each of the four forests based on earl ier work by
Fitzpatrick and Nix (1970). The index was calculated from mean weekly data
on rainfal I and evaporation, appropriately weighted to reflect their impact
on growth. Since the three variables developed here are mutually exclusive,
the symbol R wi I I be used to denote anyone in terms of the form of the model.
Whi le several variants were examined, the most satisfactory form was as
follows:
Equation (6) impl ies, of course, that both no and nl incorporate
the value of n* in Equation CS).
?irst-stage resuLts
Using seasonally effective rainfal I as the cl imatic variable, comparisons
were made between Equation (6) fitted with and without the thinning variable.
For the permanent yield plots, inclusion resulted in a 4.7% reduction in the
total residual sum of squares across at I 60 plots, and a reduction could be
seen in the overwhelming majority of results for individual plots. However,
two of the AFS plots showed substantial increases in the residual sums of
squares, reducing the difference to 2.2% over al I 85 plots. Although these
reductions may seem smal I, the number of observations affected by thinning is
only 10 to 15% of the total. Moreover the actual dates of thinning within
the year were unknown in the case of the permanent yield plots whereas
the model assumes the effect to be felt for the entire year in which thinning
occurred. Thus, whi le the mpdel may not reflect the exact magnitude of the
impact it does at least recognize an effect which all foresters know to occur.
(5)
(6)

TABLE 3.
Coefficient
bZ
bS
- 31 _.
ESTIMATED VALUES OF COEFFICIENTS IN EQUATION 6 AND ASSOCIATED
STANDARD ERRORS.
Seasonally effective Growing index /
rainfat t
Estimated Standard Estimated Standard
value error value error
-1.416 .604 -1.815 .481
.152 .025 .148 .020
.00207 .00016 .136 .008
.00259 .00017 .150 .008
.00266 .00029 .167 .032
.00322 .00023 .166 .011
.0241 .0009 .0231 .0009
Whi le it is obvious from Table 3 that not at I the coefficients b3 to b6
are significantly different from one another, there are some significant
differences and the pattern does seem to be sensible, as wi I I be apparent
from later graphical analyses.
The properties of these two models are virtually identical and it wi I I
therefore be sufficient to illustrate those of the model using seasonally
effective rainfal I. Figure I was prepared from the above results, holding
rainfal I constant for Uriarra Forest, and examining four different levels of
site index in unthinned stands.
The trends in Figure I are in accordance with expectations of growth
behaviour. Figure 2 was prepared holding site index and rainfat I constant,
and show the trends for the four forests in unthinned stands.
The ordering of the four forests in Figure 2 may seem curious but
nevertheless may be sensible, given that al I are based on the same level of
rainfall.
The relative impact of thinning on basal area increment is shown in
Figure 3, for three different thinning intensities for a given forest and site
index.
The trends in Figure 3 seem reasonable. Thinning at earl ier ages may
tend to have less impact because there are proportionately more suppressed
and dominated stems to be removed. Following first thinning at earl ier ages,
later thinnings may have more impact because there are relatively fewer of
these stems in the stand. However, the severity of later thinnings tends
to be less which may even the impact.

t-
:z
- 34 -
FIGURE 3
PROPORTION OF BASAL AREA INCREMENT AGAINST AGE
FOR VARIOUS THINNING SEVERITIES
W 0.8
::E
W er:
(.)
z
1 .0 --------------- T • 1.0
T • 0.8
<
w 0.6
et:: T • 0.6
<
-J
<
(J)
<
CD
u.. 0.4
0
z UR I ARRA "'FORES T
0
t- St TE INDEX 24.0
0::
0 0.2
a..
0 et::::
a..
. 4 10 15 20 25
AGE (YEARS)
:30 3S 40

- 36 -
In al I cases, errors have been converted to an annual base to al low
comparison across periods of measurement of differend lengths. No clear
trends were apparent in relation to site class, in some periods biases
being consistent in sign and magnitude across al I site classes, whi le erratic
In others. Thus further discussion of the results may be confined to
comparisons across al J plots. Results for the seasonally effective rainfal I
model were essentially simi lar but the biases were larger although in the
same direction.
For periods of measurement 1958 to 1962 to 1971, the mean error proved
to be significantly different from zero, based on 't' tests at the 95%
probabi I ity level. However, the direction of the bias changed from one
period to the next. In the 1958 to 1962 the magnitude of the bias is not
large relative to average increment and could be ignored for practical' purposes.
However the bias in the period 1962 to 1971 is approximately 10% of average
annual increment.
The plots used in the tests are evenly distributed over a wide range of
ages at first measurement. The switching of the direction of bias is
therefore puzzl ing. Local foresters have suggested that the bias in the
final period may reflect the effects of a disorder cal led dieback which is
drought-induced and which was prevalent in Kowen Forest at the time.
Further investigations along the same I ines are underway using the
growing index model as a predictor. Attempts are also being made to obtain
further independent test data.
The Intercept (Aa)
Only 13 of the 85 plots had been measured prior to an age of 8 years.
The remainder therefore couid not be used to estimate the intercept Aa, the
age at which a positive basal area first occurs. AI I 13 plots had a nominal
initial spacing of 3.66 by 3.66 m (12 by 12 ft) but the values of site
index ranged from 22 to 27 m.
Graphs of gross basal area gainst age were prepared for each of these plots.
A curve was fitted by eye and extrapolated to the horizontal axis, enabl ing
the intercept to be read off. Nine of the plots had intercepts of 3 years;
the remainder 4 years. There was some tendency for this age to increase
with decreasing site index.
Both initial stocking and site index seem I ikely to affect the value of
this intercept but further data wi I I have to be collected to provide precise
estimates.
In the meantime, the fol Jowing estimates were based on the above results
and inferences drawn from spacing trials in the A.C.T. (Cromer 1961):
These estimates in Table 5 are Iittle better than educated guesses
but shoutd suffice unti I better data can be obtained.

- 38 -
Because top height was measured less frequently than diameter, some
20 of the plots had 13 to 17 measurements, 26 had 18 to 21 measurements, and
14 had more than 21 measurements. Some 10 plots had values of site index
in the range 16 to 19 m, a further 31 fel I in the range 20 to 23 m, and 19 in
the range 24 to 27 m.
First-Stage Estimation
As in the case of basal area functions, two-stage analyses of the top
height functions were carried out; the first stage involving the estimation
of the coefficients for each plot separately.
Fipst-stage models
Several alternative first-stage models were examined. Most were either
unsuccessful or patently unsatisfactory and can be summarized briefly.
A model based on Equation (3) was fitted using annual increment in top
height as a proxy for the instantaneous increment. Rainfal I was also
included as an independent variable. The results were entirely unsatisfactory,
any effect of annual rainfal I being obscured by the errors of measurement in
annual increment for top height. Indeed, the values of the other coefficients
were also poorly determined and sometimes of the wrong sing.
AI I other models examined were therefore based on the use of top height itself
as the dependent variable and ignored rainfal I or other growing condition
variables.
Other models which proved unsatisfactory were the logarithm of height/
reciprocal of age model, Korf's (1971) model, and the monomolecular model,
either because they did not possess a.sigmoidal shape (eg. the monomolecular)
or because the point of inflexion was inflexible.
The von Bertalanffy (1941, 1942) model has a sigmoidal shape and is more
flexible in relation to the point of inflexion. It was fitted to the data
both in an unconstrained (Equation 7) and a constrained form (Equation 8), the
constraint being that top height must equal the value of site index at age
20 years: I
H = [n/p{l_exp-p(l-m)A}]I-m (7)
H =
I
S[I-exp-p(l-m)A ] I-m
l_exp-p(l-m)20
Where H denotos top height Cm).
A denotes age (years).
S denotes site index (m).
And n, p, m denote coefficients.
(8)

TABLE 7.
- 43 .;.
ERRORS OF PREDICTION BASED ON EQUATION 9 FOR THE
PERIOD 1955 TO 1958
Site Classes
AI J
50 60 70 80 t:'lots
No. of plots 4 14 I1 6 35
Mea,n error* .73 -.16 .32 -.06 • I I
standard error .22 .32 .28 .36 .16
*Observed minus predicted.
As Table 7 shows, there was no obvious pattern in the sign or magnitude
of mean errors by site classes, and the standard errors were such that these
mean errors were not significantly different from zero based on ft' tests at
the 95% probabi Iity level.
Subsequent measurements of these plots were then used to carry out
further tests, but on a somewhat different basis. Where more than one
measurement exists for a plot, there are obvious advantages in making the
prediction conditional on al I of those past measurements. The most
appropriate way of accomplishing this is to form Bayes estimators of the
coefficients, which are weighted averages of the estimates in Equation (9) and
those estimates derived directly from the previous measurements themselves.
Predictions from Sayes estimators are biased but have the property of a
minimum average mean square error. The results for predictions derived from
the Saves estimators are summarized in Table 8.
The mean errors for each measurement period showed a consistent bias
across al I site classes but the direction of the bias again changed from one
measurement period to the next. The direction of the biases in these two
periods agree with those for basal area. The use of Equation (9) on Its own,
rather than Saves estimators, is unlikely to change the general thrust of
these results.

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Bertalanffy, L. von, 1942. Theoretische 8iologie.
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Carron, L. T., 1967.
radiata pine.
I 1 StoffwechseI,
A variable-density yield table of a plantation of
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Cromer, O.A.N., and L.T. Carron, 1957. The volume I ine with reference to
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62(1): 89-100.
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Ferguson, I.S. and J.W. Leech, 1978. General ized least squares estimation
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Leech, J.W., 1978.
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27-42.
Program GLS - generalized
For. Sc i. 24 ( I ) :
Mi Ilett, M.R.O., 1944. Rainfal I and increment of Monterey pine in the
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Mitscherlich, E.A., 1910. Das Gesetz des minimuns und das Gesetz des
abnehmenden Bodenertrages. LANDWIRTSCH. 38: 537-552.
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Regression Models. Lecture Notes - Operational Research and
Mathematical Systems. No. 55, Ed. - by M. Beckmann, Sprlnger-Verlag,
209pp.

- 49 -
Table 2. Pole stage experiments in Sitka spruce and
lodgepole pine (coastal).
Species Variable No. Pres.Age Treatment Rep.
age Term
LP+ Spacing at 2 20-22 ·4-7 4 Randomised
planting block
LP " 3 15-16 5 4 "
LP " 1 9 4 4 " with
S.spruce
SS+ " 1 20 8 4 Randomised
block
SS " 3 15-16 5 4 " "
SS " 1 9 4 4 " with LP
SS " 1 14 13 2 Nelder grid
SS " 1 20 8 4 LP cut out
LP Respacing 2 9-10 5 4 Randomised
at 3 m block
SS " 2 10-12 5 4 "
LP Respacing
at 8 m
3*** 14-28 8 2-3 Randomised
CCT
LP Thinning
in·tensity
2* 24-27 4 2 Randornised
block
** " 2 27-38 3-5 2-3 " "
SS Thinning type 2 27-31 2-6 2 " "
n
" 1 27 8 3 IUFRO series
SS Thinning/ 2 23-28 3x3 3 Randornised
fertilisation block
factorial
SS Fertilisation 30** 40-54 15 Composite
rotatable
LP " 4* 16-26 15
* experiment written off. + LP lodgepole pine (coastal)
SS Sitka spruce

- 62 -
STEM PROFILE ANALYSIS
C. J. Liu
Department of Forestry
University of Kentucky
Lexington, Kentucky 40546
U. S. A.
INTRODUCTION
This paper describes an application of spline techniques
for constructing stem profile, developing spline functions for
the analysis of tree growth, and examining growth patterns and
their relation to environmental conditions. A stem profile is a
sequential set of taper curves. It provides a mathematical model
for studying both the secular and the dimensional developments of
a tree. When presented graphically, a stem profile depicts a
tree's dimensional changes over time. Results of this study
reveal that there is a strong relationship between local weather
conditions and tree growth. It is important, therefore, to consider
effects of environmental factors in growth modeling.
METHOD AND PROCEDURES
Spline approximation is an interpolation by a class of coordinates
functions which may be described as sets of cubic polynomial
segments with smooth joins. Instead of approximating a
given function f(x) over an interval [atb] by a single polynomial,
the interval [a,b] may be divided into n subintervals
[a,xl],[xl,x2], ••• ,[xn_l,b] and, then, f(x) may be approximated
by a different polynomial on each subinterval. To determine the
approximating function, g(x), it is required that: (1) in each
subinterval the approximation function g(x) be a polynomial of
maximum degree 3; (2) g(x) agree with f(x) at each of the n
points, xO·a,xl, ••• ,xn_l,xn-b; and (3) the first derivative

- 66 -
Error Introduced By Extrapolation
It is apparent that the use of spline extrapolation has
introduced a numerical error in estimated tree heights (Fig. 5).
However, errors in volume estimation thus induced are believed to
be negligible. While the history of the subject tree's height
growth remains unknown, there is no practical method to evaluate
the magnitude of this error except for the set of outermost
rings. The extrapolated height, using the outermost rings, can
be compared with the measured total tree height. For eight sample
trees studied, every extrapolated height was less than the
measured tree height but never exceeded 3% of error. The magnitude
of this error depends upon- (1) the ratio of stem height to
stem radius of the uppermost disc, and (2) the position and the
width of the ring by which the taper curve passes. Above all,
this extrapolation error can be minimized by maximizing the number
of sample discs.
CONCLUSION
Spline techniques are useful numerical procedures. This
investigation has employed spline techniques for construction and
analysis of a stem profile, a sequential set of taper curves.
This set of taper curves represents a mathematical model of a
tree's secular development. By examining a stem profile, foresters
can gain insights about growth trends and environmental
impacts on an individual tree. The use of spline extrapolation
tends to introduce some error, of varying magnitude, in height
estimations. This error can be minimized by maximizing the number
of sample discs. In this study, sufficient evidence supports
the assumption that tree growth is strongly affected by fluctuations
of cltmatological factors. It is suggested that effects of
environmental factors upon tree growth should be included in forest
modeling work;
LITERATURE CITED
Ahlberg, J. H., E. N. Nilson and J. L. Walsh. 1967. The theory
of splines and their applications. Academic Press, New
York. 284p.
de Boor, C. 1978.
log, New York.
A practical guide to splines.
392p.
Springer-Ver-
Liu, C. J. 1979. On single tree height increment with spline
approximation. (read at IUFRO S4.01-02 and S4.02-03 meeting,
Vienna, Austria, Septemter 10-14, 1979).

Figure 5 • The
tree.
- 71 -
stem profiIe
of t he subject
16. 50

- 76 -
Data Stored in the Computer System
The information which can currently be stored in the system in
each plot is described below, though not all plots contain all the
items despribed. The system is designed so that new items could be
incorporated at a later date.
The index file holds general plot details.
(a) Sample plot identification and location - plot number, forest
code, compartment number, latitude, longitude, altitude and a
local forest grid reference number.
(b) Details of the crop - species, establishment year, row and tree
spacing, site index, and codes for treatment, ownership and plot
status.
(c) Measurement details - number, last measurement age, and a volume
equation identification.
The measurement file of the plot holds the basic data.
(a) General details - month and year of each measurement, plot area,
height of pruning, and a general connnent.
(b) Individually identified trees - tree identification, distance
and bearing from a reference point. Data referring to a particular
measurement - diameter at breast height, total height, height to
base of green crown, and codes for height purpose, crown class,
stem quality, defect description and tree category (dead, felled,
windblown or residual tree).
(c) Diameter class distribution data. Instead of numbering each tree,
the number of trees at each measurement within each diameter class
can b e recorded for all trees or for a segment of the crop (e.g.
thinned trees), in which case the remainder of the trees would be
individually numbered. Each category is recorded separately.
(d) Height data for 'unnumbered trees - diameter at breast height, total
height, height to base of green crown, and height purpose code.
Supplementary Information
A "plot history sheet" contains environmental information and details
concerning the history and treatment of the plots. The sheet defines the
objectives of the experiment, the prescr,ibed treatment of the plot, and
cross-references any related plots. Environmental information is presented
on site, climate, geology and soils in a, descriptive manner, with room for
general remarks and warnings. The plot history describes the establishment
of the crop in detail, and every subsequent silvicultural operation.
This information is especially important for centralised research workers
who have no access to the actual plots and who therefore have no information
which could explain apparently anomalous results. Efforts are being made to
complete a sheet for every plot, and at the present .time these are not stored on
the computer. When an analysis is carried out, a preliminary selection of
plots can be made on the computer on the basis of plot location, species,
stocking, etc. A thorough screening of the selected plots can then be
carried out by referring to the plot history sheets.

COL: 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Optimal Sample Sizes
Optimum
Sample Sizes
Actual Sample
Sizes
Tariff
Estimate
Tariff
c. of V.
Estimate
from (17)
C .of V.
A
of V (C)
(same precision) (5\ precision)
CV/C
G = 30 Cv/C = 60 (CV/C = 30)
G G
A A
(m..i)
Species N n +n n V, (T) (m
J ) (\ )
V (C) n +n n n +n n n +n n
v 9 v v 9 v v 9 v v 9 v
Scots Pine 419 209 20 142.9 3.22 146.1 2.94 208 20 246 19 69 8
E. Larch 416 208 20 96.8 5.02 98.4 4.17 207 20 286 18 168 14
" 696 204 19 87.6 6.17 103.5 5.56 165 20 203 19 212 24 \0
0'
Norway Spruce 4750 240 21 549.2 5.11 588.2 4.60 326 16 407 14 265 14
It It 4080 272 27 714.8 4.90 735.4 4.44 350 23 432 21 286 18
.. If
808 202 20 160.9 4.07 160.2 3.82 244 18 331 16 148 11
If 4440 222 22 762.3 4.84 788.6 4.37 266 19 383 17 206 15
438 206 22 70.1 3.10 76.6 2.97 296 14 374 12- 131 6
Table 1. Summary of results for a number of stands from Rockingham Forest.

- 106 -
The selection index is (23.3 - 21.3) / 5.50 = 0.37, which
corresponds to a percentage of 78.5 in the normal distribution
so that the theoretical number of trees is 875 (= 1115 x 0.785).
639 stems (875 - 236) of d 23.7 cm are left after the proposed
removal. There is no problem to thin up to the 236 stems of
d 21.3 cm. On the other hand the thinning relative to the following
period cannot be realized according to the main stand, the
remaining number of sterns being insufficient (TEST = - 36).

Table 1
Stand constraints :
Results
NB.BOIS/HA
SURF TER
AGE INI.T
AGE FIN.
AGE =
HDOM =
N/HA =
DMOY =
DI00 =
D200 =
DECL =
G.AV =
G.AP =
GECL =
NECL =
TEST =
- 107 -
Abbreviations used in figure 1
HAUT DOM = top height (m x 10)
ANNEE PLANT. = planting age
AGE = stand age
DIAM INIT = initial mean diameter (mm) corresponding to
Silvicultural constraints :
the mean basal area of the stand
= number of sterns per hectare
= basal area per hectare (rn 2 )
= age at the beginning of simulation
= rotation age
CL.AGE = age classes (or thinning cycles)
AC.DIA = annual fixed diameter increment or "apparent"
increment (mm)
PC.BIO = "biological" increment (percentage of the "apparent"
increment)
age in years
top height (m x 10)
number of stems per hectare
diameter corresponding to the mean basal area (cm)
diameter of the 100 largest trees per hectare (cm)
diameter of the 200 largest trees per hectare (cm)
mean diameter of removed trees (cm)
basal area of the main crop per hectare before thinning
(m 2 )
basal area of the main crop per hectare after thinning
(m 2 )
basal area per hectare removed in thinning (m 2 )
number of stems removed per hectare
difference between calculated number of stems (from
normal distribution) corresponding to DECL and number
of stems to be removed NECL.

- 109 -
REFERENCES
Dagnelie, P.; Rondeux, J.; Thill, A., 1976: Tables dendrometriques.
Presses Agronomiques de Gernbloux, 128 p.
Delvaux, J., 1974: Contribution a l'etude de l'education des
peuplements XIII. Tables pour les eclaircies numeriques.
Sta. Rech. Eaux et Forets, Groenendaal-Hoeilaart.
Travaux. Serie B, nO 38, 31 p. + 33 annexes.
Gerard, P., 1975: Estimation en valeur des pessieres.
Bull. Soc. R. For. Belg., 82(4), 189 - 207.
Hiley, W.E., 1952: Numerical thinning: with special reference to
Japanese larch. Forestry 25(1), 10 - 18.
Nanson, A., 1967: Tables de la differentielle de selection dans
la distribution normale (0,1). Biornetrie-Praxirnetrie, 8(1),
40 - 51.
Rondeux, J., 1974: Simulation de l'evolution de peuplernents
forestiers dans le contexte dtune sylviculture intensive.
In : Growth models for tree and stand simulation. Research
note n° 30. Stockholm, Royal College of Forestry, 1973,
379 p.
Rondeux, J., 1977: Construction et utilisation de tarifs de
cubage "peuplernents" pour l'epicea (Picea Abies Karst.) en
Ardenne meridionale. Bull. Rech. Agron. Gernbloux, 12(4),
339 - 348.
Rondeux, J. et Delvaux, J., 1979: Tables de gestion et de recolte
"a la carte". Un modele simple pour I'epicea comrnun en
Ardennes beIges. Centre de Recherche et de Promotion Forestieres
I.R.S.l.A. Fac. Sci. Agr. Gembloux (sous presse).
Staebler, G.R., 1960: Theoretical derivation of numerical thinning
schedules for douglas-fir. For. Sci. 6(2), 98 - 109.
Thill, A. et Palm, R., 1976: Production de l'epicea commun dans
le Sud-Ouest de l'Ardenne belge. Note technique nO 28.
Gembloux, Centre d'Ecologie forestiere (I.R.S.I.A.), 42 p.

- 123 -
The use of an established stand was preferred since it would reduce the
total duration of the experiment by at least three years, and also any
possible error in the initial selection of the site. An eminently suitable
stand was available on Clan Syndicate in Compartment E.23 which had
been planted in February, 1967 at such an accurate espacement that the
error in one direction was not more than 15 cm in 450 m or 0,03 per cent.
After rejecting for practical reasons such factors as rotation length
and coppice management of the thinned trees, it was decided to use a factorial
experiment with intensity of thinnings, age of commencement of
first thinning, interval between thinnings and final stocking as the four
main factors. The tentative rotation length is set at 25 years and the
stools of all thinned trees are killed by chemical means immediately after
felling.
The minimum size of plot required was another factor which had to be
taken into account before the experimental design could be decided. In
Wattle Research Institute growth studies of stands of trees, it has been
found that a minimum of 10 trees per experimental plot are required to
provide satisfactory results, as long as the stands are uniform, have a
narrow range of diameters and allow for enough replications. This finding
is confirmed by Nemeth (1973) for Pinus taeda and P.eZZiottii on the
basis of a time-cost analysis, indicating that the most variable stand
would require plots with nine trees only. Unless a mean breast height
diameter (d b h) of over 50 cm is required at clearfelling, there is no
point in reducing the stocking lower than about 150 trees per ha.
According to Marsh and Burgers (1967) this stocking gives a mean d b h
of between 35 and 45 cm depending on age and site quality. Considering
this final stocking and a minimum of 10 trees in the experimental plot at
clearfelling, about 90 trees are originally required per plot if the
stand was planted at an espacement of 2,74 x 2,74 m or 1 329 trees per ha.
This gives a plot size of 677 m 2 or 0,0677 ha. In an arrangement of 9
rows of 10 trees at least 2 rows of surrounds are necessary and the gross
plot will be 13 x 14 trees = 182 trees or 0,1370 ha. Plotting each tree
in the chosen experimental area on a grid system indicated clearly that
it was possible to layout 81 plots in the area of nearly 15 ha. The
allocation of plots is illustrated in Figure 1 with the plot numbers shown
in the top left-hand corner.
The availability of 81 plots made varl0us designs feasible, but it
was decided that a single replicate of a 3 factorial, confounded in randomized
incomplete blocks of 9 units would be the most advantageous.
In Figure 1 the block boundaries are indicated by the dotted lines.
This design made possible the allocation of intensity of thinnings, commencement
of thinnings, interval between thinnings and final stocking as
main factors, each being represented at three levels. The sub-divisions
of the four main treatments are summarized on Figure 1, and their allocation
to the 81 plots ;s indicated by the numerical notation at the lower
end of each plot. Initially, thinning intensities of 30, 40 and 50 per
cent were suggested but rounding off and the necessary adjustments to
plot size made the relevant thinning percentages 32,0, 38,2 and 47,5 per
cent throughout from the first to the last thinning operation at the medium
final stocking. This resulted in five thinning operations for the
light intensity thinning, four for the medium and three for the heavy
thinning regime. Varying the starting age of the first thinning from
four, five and six years and the intervals from two, three and four

- 126 -
regression curve fitted of the heights on d b h separately for each block
of 9 units. The results showed that very little difference existed between
the curves for the 9 blocks. Objections against measuring only the
heights of thinned trees could be made, but from the second thinnings and
even in the first thinning of the highest intensity many dominant trees
were removed. In the thinnings the obviously suppressed, genetically
inferior trees and those with poor form or which were otherwise damaged
were removed first. Thereafter the spatial distribution of the trees
over the plot, heavy branching habit and stem crookedness were the main
considerations in marking trees to be removed in thinnings. In the plots
which were thinned at the high intensity, the latter considerations were
the main thinning criteria from the second thinning onwards, but for those
thinned at the lower intensities, these criteria were applicable mainly
only from the third thinnings on.
From the first enumeration, the measurements as well as the volume
calculations were made in imperial measure. For trees up to 25 cm d b h,
the volumes were calculated with the general volume regressions for E.grandis
(Schonau, 1971) and for larger trees with tables adapted from the original
South African alignment chart (Brent, 1956). The plot volumes are
the totals for each half inch d b h class calculated from the regression
heights and number of trees in the tallies. These calculations are made
each year and are at this stage only partly computerized. The main reason
for this non-computerization is lack of time and a satisfactory volume
regression for the larger trees. To obtain more data for the latter,
each year during the thinning at least 100 sample trees are measured according
to the WR I procedure (Schonau, 1972). During the last few years
these sample trees were all over 25 cm d b h.
Up to 11 years of age a number of lightning storms struck and killed
trees in at least seven instances. However, only one strike was so serious
that permanent damage occurred and in one plot the surviving trees
are rather confined to one side of the plot. Initial damage in the
form of severe bending by strong dry adiabatic winds occurred during the
first years, but no permanent damage ;s noticeable externally at present.
RES UL T S
No extensive report on the development from year to year will be given
in this paper, only the overall trend of the intermediate results at six
and ten years of age will be discussed together with an important finding
which could be of great importance if proved to be generally applicable.
The mean d b h of the experiment as a whole was 17,3 cm at six years and
25,0 cm at ten years of age. At these ages the mean height was 21,6
and 28,9 m and the mean annual increment (MAl) was 32,2 and 31,2 m 3 per
ha per annum respectively. The average standing volume up to 5 cm tip
under bark at ten years of age was 198,5m 3 per ha. The coefficients of
variation for these seven parameters were 2,18, 3,00, 0,95, 1,34, 5,80,
4,82 and 6,37 per cent respectively, indicating that the variation was
very small, increased slightly with age and that the experiment was very
uniform. In contrast the variation in the volumes of the first thinnings
were naturally much greater and the coefficient of variation was 13,65 per

- 131 -
interpolation makes it possible to quantify thinnings, other yields and
any stand parameter required for yield investigations.
It is not considered that the design discussed is the ultimate solution,
e.g. one of the main treatment factors could be dropped as superfluous
or too complicated. A 3 3 factorial with one or two replications
could then be used which would reduce the number of plots to 27 or 54.
On the other hand it could be found necessary thgt thinning intensity
should change with age, a third replicate of a 3 would then be a possibility.
However, at this stage the finding that mean annual increment is not
changed by thinning intensity, frequency or commencement of first thinning
is the most important result of this experiment. If the universal acceptance
of this principal for E.gpandis or any other eucalypt species can
be proved, then only a few other experiments will be necessary for satisfactory
thinning research under other site conditions. The fact that
the MAl remains the same over a wide range should make it a most useful
tool in the development of growth models. The great advantage of this
over the C C T approach is that it is based on statistical evidence and
not on various assumptions about basal area increment as made by some
authors (Marsh, 1957; Burgers, 1971; Marsh and Burgers, 1973). Also,
the possibility of regression analysis, response surfaces and interpolation
make this replicated trial a very rich source of information. In
conclusion, however, it should be noted that this is only a preliminary
analysis of a few intermediate data and that much work lies ahead to utilize
this experiment to its full advantage.
ACKNOWLEDGEMENT'
The encouragement by the Management of Hans Merensky Forestry Holdings
(Pty) Ltd and the continuous support of past and present staff at
Clan Syndicate (Pty) Ltd are gratefully acknowledged.
Prepared May, 1979.

Experiment SE.6 : E: GRANDIS
- 135 -
Plots :
Net = 9 rows of 10 trees = 90 trees
planted 2,74 x 2,74 m = 0,0677 ha
x 81 = 5,48 ha
Gross = 13 rows of
182 trees
x 81
TREATr··1ErJTS
"CLAN SYNDICATE"
CRAf·10tlD
A. Intensity of
Thinning
O. 32 %
1. 38,2 %
2. 47,5 %
B. Commencement
O. 4 years
1. 5 years
2. 6 years
C. Interval between Thinnings
O. 2 years
1. 3 years
2. 4 years
D. Final stocking
O. 148 trees per ha
1. 192 trees per ha
2. 236 trees per ha
=
Block E23
- - - - - Block boundary

- 136 ­
TABLE 2
Basic experimental thinning regimes indicated by number of trees per ha
remaining at various ages
Commencement
of thinning
4 years (80) 5 years (B1) 6 years (82)
Interval
between thinnings
Age
(yrs)
2 yrs
(Co)
3 yrs
(C1 )
4 yrs
(C2)
2 yrs
(CO)
3 yrs
(C1)
4 yrs
(C2)
2 yrs
(CO)
3 yrs
(C 1)
4 yrs
(C2)
Thinning
intensity
32,0%
(Aa)
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
901
620
413
281
final
901
620
413
281
final
901
620
413
281
final
901
620
413
281
final
901
620
413
281
final
901
620
413
281
final
901
620
413
28
final
901
620
413
281
final
901
620
413
281
final
4 827 827 827
5 827 827 827
6 502 827 827 827
7 502 502
8 310 502 502 502
9 310 502 502
Thinning 10 final 310 310 502
11 ... final 310
inten- 12 310 final 310
sity 13 final 310
14 final 310
38,2% 15 final
16 final
(A1 ) 17 final
18 final
Thi nning
intensity
47,5%
(A2)
4
5
6
7
8
9
10
11
12
13
14
694
369
final
694
369
final
694
369
final
694
369
final
694
369
final
694
36,9
final
694
369
fi nal
694
369
final
694
369
final
Final
stocking DO : 148 trees/ha °1 : 192 trees/ha 02 :
236 trees/ha

- 139 ­
TABLE 7
The effect of thinning intensity and time of the first thinning on
the timber volume removed during this latter operation in m 3 per ha
up to 5 cm tip diameter
Thinning
Commencement of thinning
intensity Mean 4 yrs 5 yrs 6 yrs
(80) (B1) (82)
32% (A O ) 20,3 16,5 22,5 21,9
38,2% (A 1 ) 29,0 24,6 28,6 33,8
47,5% (A 2 ) 44,2 34,2 45,5 52,9
Mean 25,1 32,2 36,2
Statistical details for Standard Least significant
interaction means error difference
P=O,05 P=O,01
1,419 4,07 5,46

- 152 -
that there would be no difference in accretion for the second
measurement period for these two treatments. However, the
common mean for these two harvesting cycles is different from
the mean for the 5-year harvesting cycle in the same period.
All other treatment means are assumed to be different.
The following notation is used in the statistical pro­
cedures. Let Y.. be the annual accretion in the k
k th compart­
1J
ment d urlng · t h e J.th measurement· per10d
for the l·th treatment.
The vector of average annual accretion for the k th compartment
in the i th treatment is denoted by lik = (Yilk' Yi2k' Yi3k'
Yi4k)' This applies to compartments with a complete set of
measurements. Let Zlk = (Y l1k ' Y12k' Y 13k ) for the two compartments
in the 5-year cycle that were measured in periods 1,
2, and 3 only.
The statistical model .for the means is:
for compartments in treatment 1
with complete set of measurements
(k = 1,2)
for compartments in treatment 1
measured in periods 1, 2, and 3
only (k = 3,4)
k = 1, •.• , 6
k = 1,2,3.
It is assumed that accretion measurements are dependent when
measured on the same compartment and that they have a common covariance
matrix. The vectors of measurements on different compartments
are assumed to be independent, that is:
E(Y'ik Yik') = r
= 0
if k = k'
if k 1- k'

- 155 -
RES U L T S
Because there are statistical differences due to treatments,
the maximum likelihood estimates of the treatment means in
Table 2 are the statistics of interest. These estimates suggest
that the accretion for the 5-year harvesting cycle may be different
from the accretion of both the 10- and 20-year harvesting
cycles. In the 5-year cycle, the four estimated accretion rates
are more or less the same. The largest accretion rates are in
the fourth period in the 10-year and the 20-year harvesting
cycles. This increase may be due to the removal of balsam fir
and the increase of hemlock, a faster growing species, into
the merchantable growing stock.
Although the treatments means are different statistically,
the differences in mean accretion rates are small. The differences
among the means of the four measurement periods may be
due to differences in growing conditions within the Reriod.
For management purposes, the overall mean of 2.42 ft /(acre.yr)
of accretion could be used.
Similar analysis can be performed on the mortality, ingrowth,
and net growth. However, the means in Table 1 suggest
little or no difference among the other growth components in
the three harvesting cycles. There are too few measurements
at the present time .to show distinct trends in the data.
The small differences in the accretion rates may be due to
the fact that the compartments in the three treatments had
about the same basal area before the first thinning and were
thinned to similar residual basal area. Also, the purpose of
thinning was not to maximize growth. The purpose was to change
species composition, obtain a balanced uneven-aged diameterclass
distribution, and to have a basal area of 100 to 120
ft 2 /acre midway through the operating interval.
These statistical procedures are applicable to any data
that can be described by a linear model where the data are
obtained from repeated measurements on permanent plots. A
computer program for the Incomplete Multivariate Model with
Correlated Errors will soon be available from the Northeastern
Forest Experiment Station, Broomall, PA 19008 U.S.A. l
1 Arner , S. L, and Seegrist, D. W.: MX4,A computer
program for th.e maximum likelihood estimator of the incomplete
multivariate normal linear model, In preparation.

- 157 -
QUANTIFYING FOREST SCIENCE WITH BIOMASS
PART ONE: SITE PRODUCTIVITY
Harold E. Young
Complete Tree Institute
School of Forest Resources
University of Maine
Orone, Maine 04469 USA
and
John H. Ribe
Woodlands Department
International Paper Co.
9 Green Street
Augusta, Maine 04330 USA
Prepared for: Meeting of 54.01, Mensuration Growth and Yield, IUFRO
Oxford, Great Britain
September 16-22, 1979

- 165 -
Young, H. E. and E. G. Stoecke1er. 1956.
interpretation mapping. Photo. Engr.
Quantitative evaluation of photo
22:137-143.
Young, H. E. 1971. Biomass sampling methods for puckerbrush stands. In
Forest Biomass Studies (H. Young ed.). University of Maine, Orono,
Maine. pp. 179-190.
Young, H. E. 1976. A summary and analysis of weight table studies. In
Olso Biomass Studies (H. Young ed.). University of Maine, Orono, Maine.
pp. 251-283.

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QUANTIFYING FOREST SCIENCE WITH BIOMASS
PART TWO: CONIFER THINNING STUDIES
Harold E. Young
Complete Tree Institute
School of Forest Resources
University of Maine
Orono, Maine 04469 USA
and
Donald C. Hoppe
Woodlands Department
Jar! F10restale Agropecuaria Ltda.
Belem, Para
Brazil
Prepared for: Meeting of S4.01, Mensuration and Yield, IUFRO
Oxford, Great Britain
September 16-22, 1979

Table I. Thinning Immature Softwood Stands on Meso Sites in Maine by Senior Industrial
Foresters Assuming (1) the existance of efficient economical machines for thinning
and (2) a market for all material thinned.

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Table 2 shows the range of differences, calculated as a percent, between
the actual field weight and the calculated weight for individual plots and the
relatively low difference when a group of six or more plots are combined.
Using the results of Table 1 as a guideline the marking instructions for
the second summer were to remove about 45% of the above ground biomass from
about 65% of the living trees primarily in the smaller diameter classes. The
only exception to this was that 50% of the biomass was to be removed from 50%
of the trees in the very dense young conifer stands. Table 3 shows the results
of the thinning during the second summer by age class of the stands. The standards
were achieved in the dense young stands but in the "normal" densities an
average of 10.5% more biomass was removed from 15.5% more trees than the marking
rules recommended. Table 4 shows the thinnings that would have achieved
the desired results in the "normal" stands. It is interesting to note the large
number of trees per acre that would be left compared to the number of trees
per acre recommended by the industrial chief foresters.
DISCUSSION
For this study stand selection depended on combinations of stand age and
moisture conditions. To expedite matters the field crews were directed to specific
areas known to be quite wet, such as bogs, or quite dry such as the vast
sandy area in Washington County. The time to locate a specific plot varied from
a few minutes to two or more hours. A more refined classification scheme involving
5-9 moisture regimes, or one based on landforms or one based on soil series
or groups of soils series would greatly increase the time required to locate a
series of plots extending over the desired age range for each member of the classification
scheme.
An experienced two person field crew can establish and then cut and weigh
all of the above ground material on a 1/100 acre plot plus sub-sampling in about
one-half day. In contrast it takes only about 30-45 minutes to establish and
measure the trees on the same size plot when weight tables will be used to estimate
the biomass. Inasmuch as approximately six 1/100 acre plots are necessary
to obtain a reliable estimate of the average biomass in a' stand when using weight
tables, the total time for the stand is about the same as that to destructively
sample a single plot.
Table 3 shows the margin by which the field crew failed to meet the thinnings
standard that had been established. This is primarily a planning error
by the senior author and to a much lesser degree the fact that the crew had no
prior experience with biomass. If the weight tables used in phase one had been
used to check the marking on the first few plots and possibly once a week thereafter
while field work was in progress the crew would have come closer to the
standard of thinning 45% of the above ground biomass from 65% of the living trees
as indicated in table 4.
Two silvicultural arguments that encourage a thinning program in fully
stocked immature conifer stands are (1) the very high density of young stands
which decreases rapidly with increase in age and (2) the corresponding tonnage
in standing dead trees with increase in age. The latter (Chase and Young 1976)
can be used for pulp increasing the productivity per acre.

Table 2. Comparison of Actual Plot Biomass and Calculated Biomass on an Acre Basis Using 1975 Data
O'of Ave. Dif. Between Range of Difference
Plots Calculated and Actual Between Actual and Calculated
Region Location Biomass as a Percent Biomass for Individual Plots
Northern St. Pamphi1e 7 +4.4% (-9.7%) - (+30.5%)
Ashland 9 +3.1% (-4.6%) - (+6.9%)
Telos 7 +6.1% (-9.4%) - (+26.5%) .....,
All 26 +4.5% (-9.7%) - (+30.5%)
Central Princeton 8 -1.1% (-18.0%) - (+18.3%)
Machias 8 -0.1% (-7.5%) - (10.5%)
PassaduDlkeag 10 +0.1% (-13.9%) - (+20.4%)
All 26 -0.3% (-18.0%) - (20.4%)
Southwestern Rangeley 6 +2.6% (-12.1%) - (+10.9%)
All 55 +2.2% (-13.9%) - (+30.5%)

Table 4. Average Thinning Conditions for 1975 Data to Achieve Thinning of 45% of Biomass by
Removing 65% of Trees 1.0" dbh and Larger
Oven dry biomass
in tons per acre
No. of stand- No. of trees
Age
Class
65% of trees
1.0" dbh and
larger
ing dead trees
1.0" dbh and
larger
Total trees
to be removed
per acre
45% of trees
1.0" dbh and
larger
Standing
dead Total
left per acre
1.0" 'dbh and
larger
.......
w
28-39
(normal) 2900 3900 6800 26.3 4.2 30.5 1500
40-74 2400 2100 4500 30.8 6.5 37.3 1200
..