Height Growth and Site Index for
Douglas-fir in High-Elevation Forests
of the Oregon-Washington Cascades
ROBERT O. CURTIS
FRANCIS R. HERMAN
DONALD J. DeMAR
Abstract. Height growth and site index estimation curves were derived from stem analyses of 52 Douglas-fir (Pseudotsuga
menziesii (Mirb.) Franco var. menziesii) trees. Their height growth pattern differs from lowland Douglas-fir, and corresponding
differences in the pattern of volume growth must exist. Site index estimation procedures and growth information derived
from lowland Douglas-fir are not applicable to these high-elevation forests. Forest Sci. 20:307-316.
Additional key words. Measurement techniques, Pseudotsuga menziesii, volume growth.
THE HIGH-ELEVATION FORESTS on the
western slope of the Cascade Mountains have been
little studied. Most of the area has been relatively
inaccessible and considered of minor importance
for commercial timber production. With improved
road systems and intensified management, these
forests have recently become much more important
for timber production as well as recreational use.
The need for information on their characteristics
and productivity led us to undertake extensive
stem analysis studies, beginning in 1965.
One segment of our work deals with the height
growth pattern and site index classification of
Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco
var. menziesii). Though broadly classified as true
fir-hemlock, these high-elevation forests contain
substantial amounts of Douglas-fir, both as stands
and as scattered trees or groups intermingled with
other species. Douglas-fir is also frequently planted
on cutover areas within this zone.
The area corresponds to the “Abies amabilis
zone” of Franklin and Dyrness (1973), which
occurs on the western slope of the Cascade
Range at elevations from about 3,000 to 5,000
feet (1000–1500 m) in Oregon, to about 2,000 to
4,000 feet (600–1300 m) in northern Washington.
The forests are of mixed species composition.
Although some stands are even-aged, others are
composed of two or more distinct age classes. The
most abundant species are the tolerant Pacific silver
fir and western hemlock, whose growth is often
much influenced by past suppression and for which
conventional site index procedures are probably
inaccurate and possibly inapplicable. However,
Douglas-fir is a relatively intolerant species, and
when abundant, has usually developed under locally
even-aged conditions without overhead competition.
Conventional site index procedures which express
productivity in terms of height attained at a
standard reference age can therefore be applied.
Data were obtained by stem analyses of 52
selected dominant Douglas-fir trees at locations
in the Cascade Range between McKenzie Pass
in central Oregon and Stevens Pass in northern
Washington (Figure 1). An effort was made
to sample all identifiable habitat types within
this area, within the limitations imposed by
The authors are Principal Mensurationist, Mensurationist,
and Associate Mensurationist, Pacific Northwest Forest and
Range Exp. Stn., Forest Service, U.S. Dep. of Agric., Portland,
Oreg. Manuscript received Nov. 12, 1973.
volume 20, number 4 1974 / 307
existing stand conditions and species composition.
All locations represented unmanaged stands, mainly
old growth. The physical difficulty and cost of stem
analyses of very large trees necessarily limited sample
size. (Existing young-growth stands represent a small
fraction of the area and a very restricted distribution.)
The distinction between height growth estimation
and site index estimation made in this paper follows
Curtis et al. (1974).
Field Procedure
Each study location was selected for apparent
uniformity in site and stand conditions and was
about one-fourth acre in size, within a stand or
group of trees in which the dominants were
judged to represent a single age class. The tallest
dominant of each species was felled. Sections
were cut at stump height, 4.5 feet (1.3 m), (bh),
and at intervals up the stem. Section lengths were
usually 18 feet (5.5 m) within the merchantable
portion of large trees and and shorter in the
upper portion of the stem and in small trees.
Heights were plotted over ages for the
sections from each tree and interpolated
308 / Forest Science
heights obtained for each 10 years of age bh. (In
this paper, “age” is based on number of rings
present at bh.) These graphs were examined for
evidence of abnormal growth patterns suggesting
past stem damage, early suppression, or differences
in age class. As expected of an intolerant species,
the Douglas-fir data showed relatively few such
anomalies. The number of acceptable Douglas-fir
trees for which sections were available was, for each
of the tree ages indicated:
Table 1 gives the distribution of trees by classes
of height attained at age 100 (= H100).
Stem analysis procedures are discussed in more
detail by Herman and DeMars (1970) and in an­
other paper in preparation.1
Analysis of Data
Analysis followed that given by Curtis
et al. (1974) with modifications. Prelim­
inary analyses using individual age class
Francis R. Herman and Donald J DeMars. Stem Analysis
field and laboratory techniques for coniferous tree species.
Manuscript in preparation.)
1
regressions preceded fitting of conditioned
regressions to pooled data. Equations were
transformed before fitting by dividing by smoothed
standard errors of estimate (SEE) from the individual
age class regressions, to stabilize variances.
Principal differences from the earlier procedure
were use of a different height growth function and
fitting of site index estimation curves in segments,
to accommodate the wide range in ages and insure
reasonable behavior at the extremes.
“H100” represents total height of an individual
tree at age 100 bh, which is an estimate of site
index or “S100” (= the location mean of all
such heights for the specified stand component).
“H” represents total height at any specified
age. Regressions were calculated using the
variables (H100 – 4.5) and (H – 4.5) in feet, in which
subtraction of 4.5 (approx. 1.3 m) serves to place
these scales on the same basis as age (“A”), measured
from bh as origin.
Height Growth Curves. Initial trials used two
equations frequently found satisfactory for height
growth curves: the exponential function (H – 4.5)
bA c
= a (l – ebA
) given by Prodan (1961), Beck (1971),
and others; and the inverse polynomial (H – 4.5)
= A2/[a
//[[ + bA + cA2] previously used by King (1966)
for low-elevation Douglas-fir.
The first gave an excellent fit over the lower twothirds of the age range but diverged from the data at
advanced ages. The second was satisfactory over most
of the range but diverged somewhat at young ages.
volume 20, number 4 1974 / 309
Discussion
Height Growth Curves and Site Index Estimation Curves.
EquationIandFigure2representaconventionalsystem
of height growth curves describing the average pat­
310 / Forest Science
tern of height development of trees which actually
attain a specified height at specified age (site index).
However, if height actually attained at index age is
unknown and the objective is to estimate this from
height measured at some age other than the index
age, then the traditional procedure based on the
height growth curve is less efficient than one using
the regression (equations II and III) of site index on
age and height (Curtis et al. 1974). For comparison,
these last are shown in traditional height-over-age
format in Figure 4, but a more natural mode of
presentation is that in Figure 3.
The two systems of curves are expected to
coincide for the mean site index; to coincide at
index age only for all other site indices; and for
other ages, to diverge in a consistent manner as
site index diverges from the mean value. Our
curves (Fig. 4) approximate these conditions
though not meeting them exactly. (Dahms2 has
Walter G. Dahms. Gross yield of central Oregon lodgepole pine. (Manuscript in preparation.) since developed an
alternative fitting procedure which insures that these condi­
tions are met.)
2
since developed an alternative fitting procedure
which insures that these conditions are met.)
“Polymorphism” of Height Growth Curves. Height
growth curves corresponding to equation I are
“polymorphic,” with age of culmination of current
annual height increment varying from 27 years bh
for H100 = 60, to 22 years bh for H100 = 160.
Differences from simple proportionality become
more evident as age in-creases beyond the index
age, but are not striking and are less pronounced
than those found in similar analyses with some
other species (Beck 1971, Carmean 1972). Of
course, there may be differences associated with site
or stand characteristics which are not adequately
expressed by site index alone.
Choice of Index Age. Analyses were based on an index
age of 100 years bh (corresponding to a total age
of about 110), chosen on the bases of precedent
and the belief that rotations in these high-elevation
forests are likely to be relatively long.
Over a span of several decades about
volume 20, number 4 1974 / 311
index age 100 bh, there is little difference between the
site index estimation curves and the height growth
curves, and the latter are nearly proportional. For
a limited range of possible rotation ages, height
at rotation age should be nearly proportional to
H100. Although we derived another site index
estimation equation using index age 140 bh, the
system of curves based on index age 100 bh should
suffice for practical use for anticipated rotations in
the range of perhaps 80 to 150 years.
Possible Sources of Bias. The height growth curves
show sustained height growth to very advanced
ages. However, the upward bend in the graphical
curves at about age 260 seems unreasonable, and
the data contain relatively few trees beyond this
age.
312 / Forest Science
In addition to graphical curves based on all 52
trees, others were prepared for ages: (1) 0 to 250,
using the 31 trees older than 250 years; (2) 0 to
100, using the 13 trees 90+ to 200 years; and (3) 0
to 300, using the 10 trees over 300 years. Curves
from (1) and (2) differed little from those based
on all 52 trees; those from (3) suggested that these
few very old individuals differed somewhat from
the average growth pattern, having more prolonged
height growth.
This could merely represent sampling variation.
It could also reflect effects of recent climatic
change (Franklin et al. 1971), or the possibility
that the tallest individuals in very old stands
may frequently have unusually prolonged height
growth. If present, such effects would produce an
upward warping of the curves, probably important
only at the upper margin of the age range.
Shifts in relative tree position over time (Dahms
1963) should have little effect on average curves
within that portion of the age range in which there
is substantial overlap in tree ages (100 to 250 yr in
these data), but could introduce bias at younger
ages. Such bias is probably present but cannot be
evaluated with one sectioned tree of the species per
location. We think its practical importance is small
except at very young ages.
Age and Site Index Estimates. Site index estimates
for individual locations were calculated for
successive 10-yr measurements using both the site
index estimation equation and traditional inverse
estimation from the height growth equation. The
site index estimation equation gave the better esti­
mates of H100, and it was evident that estimates
made for ages less than about 20 yr bh had little
meaning (as expected from the low correlations
between H and H100 at these ages, Figure 5).
Better estimates might be possible using curves
constructed from younger stands, based on a more
carefully specified stand component identifiable in
young stands. As yet, relatively few such stands are
available for study.
Comparisons with Other Height Growth Curves.
The principal previous height growth curves for
Douglas-fir in the Pacific Northwest are those of
McArdle et al. (1930, 1961) and King (1966). These
were based on low-elevation Douglas-fir and differ
considerably both from each other and from our
new curves (Figures 6A and 6B) .
McArdle used the old guide curve
volume 20, number 4 1974 / 313
method, with little data below age 40; King’s curves,
prepared from internode measurements, should be
a more reliable expression of the actual course of
growth. McArdle used average height of dominants
and codominants; King used average heights of the
largest 20 percent (by diameter) from a group of
50 stems, at time of measurement; while we used
heights of the tallest tree per one-fourth acre in
mixed, old-growth stands.
314 / Forest Science
Since shape of height growth curves derived by
regression is not independent of the index age used
(Heger 1973), we also prepared graphical curves
using index age 50 bh, as in King (1966). These
differed only slightly from our curves based on
index age 100 bh and do not affect the comparison
in Figure 6.
These different systems represent development
over time of slightly different stand components.
Some differences would also be expected from
differences in method of construction, and
possibilities of bias exist in each. However, it
seems very unlikely that these could account for
differences in curve shape of the magnitude shown.
We conclude that our trees do have a different
growth pattern, characteristic of upper-slope sites
with their lower temperatures, higher rainfall, and
shorter growing season. Compared with our new
curves, McArdle’s site index curves can be expected
to overestimate site index of old stands and to
underestimate that of young stands (also true to a
lesser extent of King’s).
Slower height growth in youth and more
prolonged height growth in later life must be
accompanied by corresponding differences in
patterns of volume and basal area growth. Lacking
volume or basal area growth data for these stands,
we can make no direct estimates of corresponding
patterns of volume growth. However, the probable
nature of such differences can be inferred indirectly.
If a common relationship of cubic volume to stand
height is assumed for our stands and for those de­
scribed in Tables 1 and 3 in McArdle et al. (1961),
and if the trend of height over age indicated by
equation I for the same height at total age 100 is
substituted for McArdle’s height growth curve, the
comparison shown in Figure 7 is obtained (for
McArdle’s site index 110).
Since much of the Douglas-fir at high elevations
is in mixed stands rather than the pure stands
decribed by McArdle et al., the relationship
of stand volume to height probably differs
and the specific numerical values obtained are
probably biased. The comparison nevertheless
illustrates that differences in shape of the
height growth curve must be associated with cor­
responding differences in the volume increment
curve, and that McArdle’s yield estimates cannot
be safely applied to upper-slope Douglas-fir of the
same numerical site index.
Application. The new curves should be used for
Douglas-fir within the geographical and elevational zone represented by the basic data.
The height growth curves (equation I)
are the proper basis for arranging stand
volume or volume increment in age sequence by
sites when preparing yield tables, and for comparing
height growth patterns with other species or
localities.
Volume yields for a species are closely associated
with stand height and although the relationship is
curvilinear in young stands, it approaches linearity
with increasing age (and heights). Hence, heights at
an index age approximating probable rotation age (site
indexes) provide a means of stratifying stands into
productivity classes even in the absence of applicable
volume 20, number 4 1974 / 315
yield tables. Here, the appropriate estimate is given
by equations II and III.
For stand ages from about 80 to 200 yr, there is
little practical difference between estimates using
equations II and III and those obtained by the
traditional procedure of inverse estimation using
the height growth equation. However, differences
become important at younger ages and are
appreciable for ages over 200.
The equations are based on trees selected as
the single tallest undamaged dominant Douglasfir per one-fourth acre. In application to oldgrowth stands having widespread top damage, the
“undamaged dominant” requirement necessarily
takes precedence over any specific area standard,
and definition of site trees as “leading dominants”
should be adequate for stand classification in oldgrowth forests. The area estimate of site index is then
the mean of estimates of H100 made for several
well-distributed “leading dominants,” exclusive of
trees with major top damage or indications of early
injury or suppression.
Literature Cited
Beck, Donald E. 1971. Height-growth patterns and site index
of white pine in the southern Appalachians. Forest Sci
17:252—260.
Carmean, Willard H. 1972. Site index curves for upland oaks
in the Central States. Forest Sci 18:109—120.
Curtis, Robert O., Donald J. DeMars, and Francis R. Herman.
1974. Which dependent variable in site index-height-age
regressions? Forest Sci 20:74—87.
Dahms, Walter G. 1963. Corrections for a possible bias in
developing site index curves from sectioned tree data. J
Forest 61:25—27.
Franklin, Jerry F., and C. T. Dyrness. 1973. Natural vegeta­
tion of Oregon and Washington. Pac Northwest Forest &
Range Exp Stn USDA Forest Sery Gen Tech Rep PNW-8,
417 p.
, William H. Moir, George W. Douglas, and Curt
Wiberg. 1971. Invasion of sub-alpine meadows by trees
in
the Cascade Range, Washington and Oregon. Arctic
& Alpine Res 3:215—224.
Heger, L. 1968. A method of constructing site index curves
from stem analyses. Forest Chron 44:11—15.
. 1973. Effect of index age on precision of site index.
Can J Forest Res 3 (1) :1—6.
Herman, Francis R., and Donald J. DeMars. 1970. Techniques
and problems of stem analysis of old-growth conifers in
the Oregon—Washington Cascade Range. In Tree-ring
analysis with special reference to Northwest America. J.
H. G. Smith and J. Worral, eds. Univ B C Fac Forest Bull
7, p. 74—77.
King, James E. 1966. Site index curves for Douglas-fir in the
Pacific Northwest. Weyerhaeuser Forest Pap 8, 49 p.
McArdle, Richard E., and Walter H. Meyer. 1930. The yield
of Douglas-fir in the Pacific Northwest. U S Dep Agric
Tech Bull 201, 64 p.
, Walter H. Meyer, and Donald Bruce. 1961. The
yield of Douglas-fir in the Pacific Northwest. U S Dep
Agric Tech Bull 201 (rev.), 74 p.
Prodan, Michail. 1961. Forstliche Biometrie. BLV
Verlagsgesellschaft. 431 p., Munich, Bonn, Vienna.
(English translation published as Forest Biometrics. 1968.
447 p. Pergamon Press.)
About This File:
This file was created by scanning the printed publication.
Misscans identified by the software have been corrected;
however, some mistakes may remain.
316 / Forest Science