Diameter accretion (uD.ccreoonl is the
periodic increase i n quadratic mean
diameter of those trees present at the
start of the period;
TECHNICAL COMMENTARY
On The Definition Of Stand Diameter
A Da ccrebon
Growth For Remeasured Plots
=
--
=---
V(G2 + G2mort)l(f..."(N2 + Nmort))
- VG1!(kN1)
Robert 0. Curtis and David D. MarshalF
=
V(G2 + G2Mort)l(kNl )
- YGI/(kNI)
Periodic increment o r periodic an­
where trees are measured to a very
where G2mort is the final (time of
nual increment in quadratic mean di­
small minimum diameter, so that in­
death) basal area of trees dying during
ameter at breast height (dbh) are sum­
growth need not be considered. The
the period, and Nmort is the corre­
mary statistics commonly used to
suggested terminology is similar to
sponding number of mortality trees.
compare growth and treatment re­
that generally accepted for volume
Diameter growth of the n lo.rgest trees
sponse in remeasured plots. Some
(and basal area) growth, as given by
(t..Dm) is the periodic increase in qua­
ambiguities associated with the defini­
B e e r s (1962), Marquis and Beers
dratic m e a n diameter o f a fixed
tion of periodic diameter increment
(1969), Husch et al. (1982), and Van
number n of the largest diameter trees
arise, however, in summaries and
Deusen et al. (1986). Because we are present at the start and end of the pe­
analyses of data from both research
dealing ·with averages of a tree dimen­
riod:
plots and from remeasured inventory
sion rather than with values per unit
plots.
area, the additive relationships that
Periodic diameter increment is often
exist for volume growth (and basal
calculated as the difference between
area growth) do not apply.
where
quadratic mean diameters at the be­
Net diameter growth (.:lDn.J is the dif­
D2NL
quadratic mean diameter of
ginning and end of the growth period.
ference in quadratic mean diameters
the largest n trees present at
Although the computation is simple
of trees present at the beginning of the
the end of the growth period;
and straightforward, the removal of
growth period and those present at
small trees by suppression mortality
the end:
d1NL
quadratic mean diameter of
can produce an artificial diameter
the largest n trees present at
A.Dnet
VG2JkN2 - YGl/kNl
"growth," similar to the effect of a low
the beginning of the growth
D2- Dl
thinning. This can be quite misleading
period; and
when diameter growth of high-density
where
n = some standard number, often
stands with substantial suppression
chosen to more or less
mortality is compared with that of
Dl
quadratic mean diameter at
correspond
to the lowest
low-density stands, or with radial
beginning of growth period,
number of trees expected to
growth observed on increment cores.
D2
quadratic mean diameter at
be present at rotation age in ..9:!
Although this phenomenon has
end of growth period,
any of the stand conditions ii
long been recognized (Baker 1950, p.
358), the magnitude of such effects is
or management regimes
G1
basal area at beginning of
sometimes not fully appreciated, and
being compared.
period,
there are no well-established conven­
::l
0
G2
basal area at end of period,
tions or definitions governing the sev­
.0
<(
eral alternative diameter-growth
Nl
number of trees present at
DISCUSSION
values that can be calculated. The lack
beginning of period,
of a standard terminology and anal­
Table 1 illustrates the magnitude
N2 = number of trees present at end
ysis for diameter growth may be a
and nature of differences that can
of period, and
major reason for conflicting results in
occur among values of alternative ex­
diameter growth response compar­
p r e s s i o n s of p e r i o di c d i a m e t e r
k
a constant
isons. This paper discusses some defi­
growth. The four alternative diameter
0.00545415 for English
nitions and briefly illustrates some re­
growth statistics were calculated using
units,
sults of their use.
data from the 1979-1983 growth pe­
0.00007854 for metric
riod in the Hoskins levels-of-growing­
DIAMETER GROWTII STATISTICS
units.
stock study (Berg and Bell 1979), and
At least four different diameter are the means of values for the 3 plots
Survivor diame ter grrr..uth (Wsurvivors)
growth statistics can be calculated. We in treatment 9 (unthinned) and the 3
is
the periodic increase in quadratic present these below, for the simple plots in treatment 5 (repeated thin­
mean diameter of those trees that situation (common on research plots) ning retaining 50% of the unthinned
were
present at both the start and end where measurements are made imme­
plot gross basal area growth).
of the period: diately before and after cutting, so If the ratio of thinned to unthinned
that cut trees do not influence the diameter growth is taken as an indi­
ADsurviv.m
computation of periodic growth; and YG2J(kS'2)
cator of response to thinning, very
=
=
=
=
=
=
:E
=
=
=
=
=
=
=
- Y(Gl - GlmartY(k(Nl - Nmort))
=
1
The authors are Prindpal Mensurationist,
Padfic Northwest Research Station, For­
estry Sciences Laboratory, Olympia, WA,
and Graduate Research Assistant, Oregon
State University, College of Forestry, Cor­
vallis, Oregon. Paper 2254 of the Forest Re­
search Laboratory, Oregon State Univer­
sity, Corvallis OR 97331.
102
WJAF 4(3)1989
Western J.
YG2·(k..Y2)
- Y(Gl - G1mort)i(k:.\f2)
where Glmort is the initial (beginning
of growth period) basal area of trees
dying during the period and Nmorl is
the corresponding number of mor­
tality trees.
Applied Forestry 4(3):102-103.
different conclusions can be reached
depending on. the diameter-growth
statistic used for the comparison.
The v a l u e of A.Dnet for the un­
thinned plots is greatly influenced by
the death of small suppressed trees. It
does not represent the actual growth
of those trees that are producing po­
tentially usable material anlj-w en
compared with the correspondrng
July 1989.
T01ble 1. Comparison of periodic di01meter growth st<1tistics for un th inned (treatment 9) and
thinned (treatment 5) plots in the Hoskins study, 1979-1983 growth period.
Statistic
t::.D-.
t::.D...
!::..0-=t::.D
. ,oo
Unthinned
4yr t::.D
Thinned
4yr t::.D
(em)
(in.)
(em)
2.41
1.24
1 17
2.87
(0.95)
(0.50)
(0.46)
(1.13)
3.38
3.20
3.12
4.14
.
value for thinned plots-leads to an
underestimate of the actual benefit
from thinning.
wsurvivors expresses the actual diam­
eter growth of trees present at the end
of the growth period. Comparison of
thinned vs. unthinned survivor diam­
eter growth provides a meaningful ex­
pression of the effect of thinning on
diameter growth of these trees. It is
also consistent with diameter-growth
estimates obtainable from increment
cores.
tl.D,C'C:n!tion has been used occasion­
ally (as by Berg and Bell 1979, who
r e f e r t o it a s "gr o s s d i a m e t e r
growth"), but its interpretation seems
less clear. Although for short growth
periods numerical values of llDa=eilan
are close to those of tl.D,urvivars' for
longer growth periods suppression
mortality can have a considerable ef­
fect on the former. llD,umvors is prefer­
able.
AD100 r e p r es e n t s the d i a m e t e r growth o f the 100 largest trees/ha (40/ ac). As would be expected, the effect of thinning on this stand component is less than on the average of all trees present but is still substantial. Effect of Ingrowth
If ingrowth is present, this will fur­
ther distort wnet as an expression of
actual growth, by an amount that de­
pends on the number of ingrowth
trees and on the position of the lower
limit of measurement relative to
average diameter of the stand. Values
of the other diameter growth statistics
are unaffected.
Effect of Cut Trees
Measurements on research plots are
usually made immediately after any
cutting and immediately before any
subsequent cut. Consequently, the
change om quadratic mean diameter
due to cutting can readily be separated
from periodic diameter change due to
growth pius mortality. In inventories,
however, cutting date and measure­
ment date are usually unrelated, and
trees may be cut at any time during
(in.)
(1.33)
(1.26)
(1.23)
(1.63)
Ratio of
thinned tlD to
unthinned t::.D
1.40
2.52
2.67
1.44
the growth period. This can have a
large effect on calculated values of
A Dnet· Growth periods may be rela­
tively long, and growth on cut trees
since the previous measurement may
be substantial, but measurements of
cut trees at the time of cutting are
u s u a lly not available. For thes e
reasons also, tl.Dsurvivors is more appro­
priate than tl.D,a:rerian as an expression
of stand diameter growth.
Choice of
n
component of the stand. Few st.mds
will be reduced below this number of
trees, so that .10100 values will be com­
paruble across most stand conditions
and treatments. Because this compo­
nent is much less influenced by thin­
ning than is the stand as a whole,
tl.DuJJ alone is not a sufficient basis for
evaluating diameter-growth response
to thinning.
tl.D:oo is an appropriate alternative
for species or regimes that do not pro­
duce large trees.
CONCLUSIONS
The common net diameter-growth
statistic is, by itself, often misleading
as a m easure of s t a n d diameter
growth and response to treatment.
This is true because net diameter
growth represents the combined ef­
fects of death of small trees, ingrowth,
and actual biological growth. Net di­
ameter growth is an essential statistic,
but it should not be used as the pri­
mary measure of biological diameter
growth response to treatment, and it
does not correspond to an average di­
ameter growth determined from in­
crement cores. A standard termi­
nology and additional diameter
growth statistics, as suggested above,
will aid in evaluation of treatment re­
sponses and avoid misinterpretation
of summary values.
A satisfactory description of stand diameter growth and diameter-growth response to treatment should include (1) net diameter growth, (2) survivor diameter growth, and (3) diameter growth of a standard number of the largest trees per unit area.
0
Diameter growth of spedfied crop
trees has sometimes been used in
comparisons of treatment effects
(Adams and Chapman1942, Berg and
Bell1979), and this procedure does in­
deed serve the purpose of character­
izing growth of that part of the stand
that is of primary interest in manage­
ment. However, selection of crop
trees involves a considerable element
of subjectivity, and inconsistencies are
introduced when crop tree numbers
differ between treatments or between
experiments (as is usually the case).
Several authors (e.g., Reukema
1979, Mitchell and Cameron 1985)
have used diameter growth of the n
UTE.RATURE CITED
largest trees as a summary statistic,
AoMAS, W. W., AND G. L. OiAP.'>fAN. 1942. Crop most commonly the diameter growth
tree measurements in thinning experiments. J. of the 250 largest trees/ha (100/ac).
For. 40:493-498. BAKER, F. 5. 1950. Principles of silviculture. Ed.
1bis avoids the subjective decisions
1. McGraw Hill, New York . 414 p.
involved in choice of crop trees. For
BEERS, T. W. Components of forest growth. 1962.
many regimes, values for the 250
]. For. 60:245-248.
largest trees/ha provide a reasonable
BERG, A. B., AND J. F. BELL. 1979. Levels-of­
growing-stock cooperative study in Douglas­
approximation of diameter growth of
fir: Rep 5-The Hoskins study, 1963-1975.
the "crop trees" expected to reach
USDA For. Serv. Res. Pap. PNW-130. 29 P·
final harvest. The combination of wide
HUSOI, B., C. L Mn.llR, AND T. W. BEERS. 1982.
initial spacing and heavy thinning
Forest mensuration. Ed. 3. Wiley, New York.
402 P·
may, however, often produce stands
MAJ\Qti!S, D. A., AND T. W. BEERS. 1969. A fur.
with less than 250 trees/ha as they ap­
ther definition of some forest growth compo­
proach final harvest age, as is now
nent s . J. For. 67(7):493.
common in extreme treatments in e-x­
MrrCHEU. K. K., AND!. R. CAMERoN. 1985. Man­
aged stand yield tables for coast"! Doup la -fir:
isting thinning studies.
Initial densitv and p recommeraal thinnmg.
We suggest that, for many species,
Land Y!anage'. Rep. 31. B.C. Ministry of For.,
suitable standards for calculating
Victor'.a. 69 p.
ADNl. are the 100 and 200 largest trees
R.R;KB{A, D. L. 1979. Fifty-year developme t of
Doug!as·fir stands planted at various spaangs.
(by diameter) per ha (40 and 80 largest
USDA For. Serv. Res. Pap. PNW-253. 21 p.
per ac). LlD100 corresponds to a com­
VAN DEUSE.'I, P. C., T. R. DELL, AND C. E .
monly used definition of top height
THO.\L-\S. 1986. Volume g rowth estimatio
and will provide consistent height and
from permanent horizontal points. For. Sa.
32:415--122.
diameter values for the top height
WJAF 4{3)1989
103