United States Department of Agriculture

Forest 

Service

Pacific Northwest 

Research Station

Research Paper

PNW-RP-603

March

2015

Development of Top Heights and 

Corresponding Diameters in HighElevation Noble Fir Plantations

Robert O. Curtis
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Author

Robert O. Curtis is an emeritus scientist, U.S. Department of Agriculture, Forest 

Service, Pacific Northwest Research Station, Forestry Sciences Laboratory, 3625 

93rd Avenue SW, Olympia, WA 98512-1101.

Cover photograph © 2014 by Walter Siegmund.
Abstract

Curtis, Robert O. 2015. Development of top heights and corresponding diameters 

in high-elevation noble fir plantations. Res. Pap. PNW-RP-603. Portland, OR: 

U.S. Department of Agriculture, Forest Service, Pacific Northwest Research 

Station. 20 p.

Height and diameter growth of noble fir (Abies procera Rehd.) trees included in the 

largest 40 stems per acre were compared in a study that included five precommercial thinning spacings plus no thinning, in each of eight replications, at elevations 

from 2,200 to 4,100 feet in the western Cascade Mountains of Washington and 

Oregon. Height growth rates were not affected by spacing. The unthinned treatment 

had slightly greater initial heights, a difference that probably arose from the method 

used to select leave trees in thinning. Height trends differed markedly from those 

given in Herman et al. (1978); which should not be used in plantations. Spacing had 

a considerable though highly variable effect on diameter growth of these dominant 

trees. New top height/age curves are presented, which can be used for interim site 

classification pending availability of data that includes a greater range of ages.

Keywords: Nobile fir, plantations, thinning

Summary

Height and diameter growth of noble fir (Abies procera Rehd.) trees included in 

the largest 40 stems per acre were compared in a study with eight replications of 

five precommercial thinning spacings plus an unthinned treatment. Elevations 

were from 2,200 to 4,100 feet in the western Cascade Mountains of Washington 

and Oregon. Seven installations were in the Abies amabilis Zone, and one in the 

Tsuga mertensiana Zone. Height growth rates were not affected by spacing. The 

unthinned treatment had slightly greater initial heights, a difference that probably 

arose from the method used to select leave trees in thinning. Spacing had a considerable though highly variable effect on diameter growth of these dominant trees. 

Height trends differed markedly from those given in Herman et al. (1978); which 

should not be used in plantations. Possible reasons for the difference are discussed. 

New top height/age curves are presented, which can be used for interim site classification pending availability of data that includes a greater range of ages.
1

Development of Top Heights and Corresponding Diameter in High-Elevation Noble Fir Plantations

Introduction

Background

Extensive harvesting in Pacific Northwest high-elevation true fir-hemlock forest 

began in the early 1950s. Early operations commonly followed practices that had 

been generally successful in lower elevation Douglas-fir (Pseudotsuga menziesii 

(Mirb.) Franco): namely, clearcutting followed by slash burning and planting—often 

with Douglas-fir. Many of these early plantations failed, and regeneration by 

natural seeding took place over an extended period of years.

In subsequent years, better species selection combined with improvements 

in nursery, site preparation, and planting practices greatly improved survival of 

planted trees and produced many successful plantations. 

Extensive precommercial thinning (PCT) began on national forests in the late 

1970s. A common practice was to thin at an early age to 350 to 400 stems per acre. 

There were concerns about the effects of number of residual trees on future stand 

development and the potential productivity of such stands. 

These concerns led to establishment of a spacing and yield study (C72) to 

compare the effects of thinning to a range of spacing on tree and stand development 

and to provide a basis for yield estimates for young managed stands. This study 

included 18 locations considered ready for PCT under then-current operational 

practice, located in the western Cascade Mountains and the Olympic Mountains. 

The overall study was described in more detail by Curtis et al. (2000) and Curtis 

(2008, 2013). 

Noble fir (Abies procera Rehd.) is a highly promising species for high-elevation 

sites, but one for which data on young stand development is largely lacking. The 

present report—unlike the 2013 report—is confined to a subset of the C72 data 

consisting of eight noble fir plantations (including some measurements not available for the 2013 report), plus very limited data from another study (C45). A ninth 

C72 noble fir plantation, Alpine, was not used because several treatments did not 

contain sufficient noble fir.

Previous Research

Franklin (1982, 1990) has reviewed past research on noble fir. Most of the existing 

knowledge is derived from observation of existing stands rather than from planned 

experiments. Demonstrated characteristics of the species are very slow juvenile 

height growth, followed by a long period of relatively rapid and nearly linear 

growth, with moderate height growth continuing to advanced ages. It is the least 

shade-tolerant of the true firs, being more or less comparable to Douglas-fir in this 

Noble fir is a highly 

promising species for 

high-elevation sites, 

but data for young 

stand development is 

largely lacking. 
2

research paper PNW-rp-603

respect. Noble fir can develop large trees of excellent stem form on relatively poor 

high-elevation sites and is highly resistant to snow breakage.

Harrington and Murray (1982) compared height growth patterns of noble fir 

with that of Douglas-fir and concluded that the long period of nearly linear height 

growth characteristic of noble fir could enable it to outgrow Douglas-fir on some 

sites, despite an initial disadvantage.

Herman et al. (1978) developed height growth (site index) curves for noble fir, 

based on stem analyses of an extensive sample of mature trees in naturally established stands.

Murray et al. (1991) compared height growth of young planted noble fir with 

the height growth estimates of Herman et al. (1978) and concluded that the young 

stands they sampled were growing much more rapidly than predicted.

Objectives 

The analyses here reported aimed to compare development of top height of noble fir 

(H40) among initial spacings, where H40 is defined as mean height of those noble 

fir trees included in the largest 40 trees per acre (by diameter) of all species present. 

Similar comparisons were also made of the mean diameters (D40) of noble fir trees 

in the top height component.

This definition was selected both because there is considerable precedent for 

use of top height, and because it provides an objective method of sample tree selection without the personal judgment element present when crown class is used as a 

basis. (Top height is very similar to, though not identical with, dominant height). 

Good estimates of trends of top height in relation to age are important for two 

reasons: (1) their relative position as expressed by site index provides a basis for 

productivity classification, and (2) top height and top height increment are important drivers in various stand simulation models.

Study area

Most data used here are from C72 installations located in the Oregon and Washington Cascade Mountains, on the Mount Hood, Gifford Pinchot, and Willamette 

National Forests. Elevations in C72 data used ranged from 3,000 to 4,100 feet. The 

C45 data (described below) are from a somewhat lower elevation (2,000 to 2,400 

feet) at a single location within the Gifford Pinchot National Forest. Seven of the 

C72 installations are in the Abies amabilis Zone (Franklin and Dyrness 1973), and 

two in the Tsuga mertensiana Zone (one of which, Alpine, is of limited usefulness 

because of insufficient noble fir in some treatments). The C45 data is transitional 

between the Abies amabilis and Tsuga heterophylla Zones.

Analyses compared 

development of top 

height of noble fir 

among spacings. 

Similar comparisons 

were made for mean 

diameters of noble fir 

trees in the top height 

component.
3

Development of Top Heights and Corresponding Diameter in High-Elevation Noble Fir Plantations

All installations used here are plantations, although some also contained 

substantial amounts of natural regeneration of associated species.

Study Design

C72—The C72 study design was randomized blocks, complete except for a single 

missing treatment in one installation (block). There are five thinning treatments 

plus no thinning in each block. Treatments and plot sizes are given in table 1.

Plots were square, with sides that were multiples of the desired spacing, to 

facilitate gridding of the area. Measurement plots were surrounded by buffers 

treated in the same way.

Plots to be thinned were gridded with string at intervals corresponding to the 

assigned spacing, and leave trees were selected as the best available tree within 

each grid cell.

Plots were measured at time of establishment, and at 5, 10, and either 19 or 20 

years after establishment. Heights were measured on a subset of trees, ranging from 

40 per acre in the unthinned, 50 percent in treatments 2 and 3, 60 percent in treatment 4, to all trees in treatments 5 and 6. Diameters were measured to the nearest 

0.1 inch on all trees 1.6 inches in diameter at breast height and larger. 

C72 installations are listed in table 2.

Table 1—Treatments and corresponding 

measurement plot size in study C72

Treatment Spacing Trees Plot size

Feet Per acre Acres

T-1 — — 0.200

T-2 7.9 700 .242

T-3 10.1 430 .234

T-4 12.8 265 .241

T-5 16.4 163 .302

T-6 20.9 100 .361

C45—This study was established as a completely randomized design, including a 

variety of species, at a single location. The spacings and plot sizes were similar to 

those in C72, though not identical. Unlike C72, spacing was established in 1980 

by planting, rather than by thinning. Some of the original C45 noble fir plots are 

unusable because of abundant natural regeneration of Douglas-fir that overwhelmed 

the original planting, which—on a south slope at a relatively low elevation—is not a 

typical true fir site. Ten plots were considered usable for present purposes. Measurement dates were 1992, 1997, 2001, 2005, and 2009. Ages at the 1992 measurement were 5 years at breast height (b.h.) and 15 years total.
4

research paper PNW-rp-603

Table 2—List of noble fir plantations in study C72

Installation

National

forest

Year

established Age b.h.

Total

age Elevation

Years Feet

Alpinea Mount Hood 1990 11 19 4,500

Cabin Gifford Pinchot 1994 7 14 3,000

Dog Creek Mount Hood 1991 13 20 3,600

Job Gifford Pinchot 1992 8 17 3,700

Marys Creek Willamette 1994 8 15 4,000

Memaloose Mount Hood 1992 13 24 4,000

Pointer Gifford Pinchot 1991 10 17 4,100

Twin Gifford Pinchot 1994 10 18 3,800

Age b.h. = number of annual rings at breast height.

a

 Not used because of insufficient noble fir in some treatments.

Data Summarization

Computation of H40 and D40

At each measurement, diameters of all live trees (all species) then present were 

sorted in descending order within each plot. Those trees in the largest 40-per-acre 

component (8 to 14 in number, depending on plot size) were sorted by species, and 

mean values for those noble fir included were taken as H40 and D40. Thus, these 

were not always the same trees. Also, means were frequently based on fewer than 

the above number of trees, because of the presence of naturally seeded stems of 

other species. 

When measured heights were lacking for some trees included in the largest 40 

per acre, values were assigned using height/diameter equations fit to all noble fir 

measurements on the plot.

Stand Age

There are three possible ages:

• Years from seed (total age)

• Years from planting

• Breast-high age (number of rings at b.h.)

Planting dates are available for both C72 and C45. Planting stock was 2-1 or 

3-0, according to records. Therefore, years from seed = years from planting + 3.

Breast-high age has the advantages that (1) in applications, it can be determined 

without knowledge of planting date, and (2) to some extent, it reduces the variable 

effects of early vegetative competition. There are some uncertainties in the data. In 
5

Development of Top Heights and Corresponding Diameter in High-Elevation Noble Fir Plantations

C72, age b.h. was estimated from ring counts on cut trees, which involve sampling 

error and trees that presumably were generally somewhat smaller than trees in the 

largest 40 per acre. In C45, breast-high age was estimated by backward extrapolation of a regression of the form: 

ln(H40) = a + b/(total age)0.5

Differences between estimated ages at b.h. and ages from seed derived from 

planting dates ranged from 7 to 11 years. This suggested 9 years as an overall 

adjustment for use in the absence of site-specific information.

In most but not all of the following comparisons, age from seed (total age) is 

used as the most reliable value.

Analyses of H40 in Relation to Age and Spacing

Except where specified, the following is based on the C72 data only.

Means of H40 from combined treatments, by installation—

Means of H40 were calculated for each measurement date at each installation, using 

the combined data for all treatments in an installation. Trends over age are shown in 

figure 1. Within the age range of the data, the trends are very nearly straight lines. 

There are substantial differences in the age ranges.

0

10

20

30

40

50

60

70

80

90

0 10 20 30 40 50 60

H

40 (feet)

Years from seed

Haller

Alpine

Dog Creek

Pointer

Job

Memaloose

Cabin

Twin

Marys Creek

C45

Figure 1—C72 + C45: trends of installation mean H40 over total age from seed, all treatments combined.

Within the age range of 

the data, trends of H40 

over age were nearly 

straight lines.
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research paper PNW-rp-603

Except where otherwise specified, means of all treatments within an installation were used in the following comparisons.

Values of H40 by treatments within installations—

Treatment values of H40 were plotted over age from seed, by installation and 

treatment, in the format shown in the example in figure 2. Other installations, not 

shown, showed more or less similar trends.

The trends were, in general, more or less parallel and fairly regular. Points of 

importance that stand out:

1. In general, relative values remained much the same over the age range. 

Differences present immediately after thinning were still present, though 

reduced, at the most recent measurement. (Memaloose was considerably 

more variable than other installations.)

0

10

20

30

40

50

60

70

15 20 25 30 35 40

H40 (feet)

Years from seed

No thin

TN-700

TN-430

TN-265

TN-163

TN-100

Figure 2—Trends of H40 over total age, by treatments. 
7

Development of Top Heights and Corresponding Diameter in High-Elevation Noble Fir Plantations

2. Means by treatment at the initial and most recent measurement are shown 

in figure 3. 

3. Treatment 1 (no thinning) was at or near the maximum in most installations, both immediately after thinning and at the most recent measurement. 

The one apparent exception is Cabin, in which treatment 1 was lowest. 

(Possibly this was a somewhat poorer site.) Differences in H40 at measurement 4 are primarily a continuation of immediate postthinning differences. 

4. A comparison1 of H40 for unthinned vs. thinned treatments at establishment was significant at the 0.05 level, but was no longer so at the 20-year 

measurement. Differences among thinned plots were nonsignificant at both 

measurements.

The apparent difference in postthinning H40 between unthinned and thinned 

treatments (2.37 feet) has a plausible explanation. The unthinned H40 is a mean of 

noble fir trees included in the largest 40 trees per acre, considering all trees on the 

entire plot without regard to spatial position. H40 values for thinned plots, in contrast, are calculated from leave trees that were selected as the “best” tree found in 

0

10

20

30

40

50

60

70

No thin TN-700 TN-430 TN-265 TN-163 TN-100

H40 (feet)

Treatment (target number per acre)

Measurement 1

Measurement 4

Figure 3—Treatment means of H40, with error bars for one standard error, at initial measurement 

and at 4th (most recent) measurement.

1

 ANOVA followed outline in Snedecor 1956, p. 294, with missing value for T-2 at Haller 

estimated as on p. 310.
8

research paper PNW-rp-603

each individual grid cell of area = spacing2. Thus, some trees that would have been 

in the largest 40 per acre in the absence of spatial constraints may have been cut.

No consistent trend of H40 with treatment (spacing) is apparent in the thinned 

plots.

Regressions of H40 on total age—

From figure 1 and other graphs, it appears that simple straight lines would likely 

give fits about as good as any alternatives, within the age range of the data. But 

these are unacceptable on logical grounds. Predicted H40 must approach 0 as Age 

approaches 0. And, H40 cannot increase without limit. 

The observed trends shown in figure 1 are more or less proportional (“anamorphic”). There are substantial differences among installations in the range of ages 

represented; consequently, a simple overall fit to pooled data would likely give a 

biased estimate of average curve shape. Adjustment using an index H40 (analogous 

to site index) at some greatest common age should eliminate the problem.

Figure 1 suggests that H40 at total age 35 is a value that can reasonably be 

estimated from the observed values by interpolation or minimal extrapolation, and 

the corresponding values of H40 are hereafter referred to as S35.

Figure 2 and similar graphs for other installations show that the principal difference is unthinned vs. thinned, and that differences among thinned plots are not 

consistent. It is here assumed that most stands to which the results may be applied 

will have had some sort of density control, and that overall means across treatments 

will suffice.

A considerable number of functional forms have been used to express the

H = f(age) relationship. Most require nonlinear fitting. With the limited age range in 

the data presently available, it seemed unlikely that one could distinguish between 

alternate forms. An equation that has had considerable use, meets the logical 

requirements of a growth curve, and that has the advantage of being easily fit (in 

logarithmic form) is:

H40 = aeb(1/Aget)^c

whence

ln(H40) = ln(a) + b(Aget)-c,

where Aget is years from seed and “c” can be estimated by successive 

approximation.

Let: S35 = H40 at index Aget = 35, estimated by interpolation or very limited 

extrapolation.

There was no 

consistent trend of 

H40 with spacing 

for thinned plots. 

Observed trends over 

age were more or less 

proportional.
9

Development of Top Heights and Corresponding Diameter in High-Elevation Noble Fir Plantations

Then:

ln(S35) = ln(a) + b(35)-c

subtracting:

ln(H40) – ln(S35) = b[(Aget)-c – (35)-c], 

whence:

ln(H40) = ln(S35) + b[(Aget)-c – (35)-c],

and

H40 = exp[ln(S35) + b[(Aget)-c – (35)-c],

which is a family of proportional (“anamorphic”) curves constrained to pass 

through the index points (35, S35). With the limited range of ages and number of 

installations available, it seemed unlikely that proportional vs. polymorphic curves 

could be distinguished.

Successive measurements on the same plot are not independent. Therefore, the 

usual measures of significance are not valid. Estimated equation coefficients are 

unbiased, and calculated values of the coefficient of determination (RSQ) and root 

mean squared error (RMSE) do provide a ranking of comparative goodness of fit, 

even though we cannot attach probabilities.

A number of regressions of the form:

ln(H40) – ln(S35) = b[Aget)-c – (35)-c]

were run, using the combined C72 and C45 data and various trial values of the 

exponent c. Selection of the “best” equation was a judgment call, based on (1) near 

minimum values of RMSE, plus (2) biologically plausible behavior when extrapolated for several decades. This used mean values for all treatments within each 

installation. Results suggested that c = 0.5 was appropriate.

A fit to the C72 installation mean values gave the equation: 

ln(H40) – ln(S35) = -14.5756(Aget)-0.5 – (35)-0.5) (1)

with fit statistics RMSE = 0.04958 and adjusted RSQ = 0.9639. Rearranging:

ln(H40) = ln(S35) – 14.5756[(Aget)-0.5 – (35)-0.5] (2)

and hence

H40 = exp[ln(S35) – 14.5756[(Aget)-0.5 – 0.1690)]] (3)

Figure 4 shows the curves corresponding to equation 3, plotted for S35 values 

of 35, 45, 55, and 65, which span the range of S35 values in the data. Figure 5 is the 

same, but overlaid on the individual installation growth trends. A similar regression 

using the C72 data only was not appreciably different.
10

research paper PNW-rp-603

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20 25 30 35 40 45 50

H40 (feet)

Years from seed

S35 = 35

S35 = 45

S35 = 55

S35 = 65

Figure 4—H40 over total age curves corresponding to equation 3.

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20 25 30 35 40 45 50

H40 (feet)

Years from seed

Figure 5—Curves from equation 3 (dotted) superimposed on observed installation trends of mean 

H40 (solid).
11

Development of Top Heights and Corresponding Diameter in High-Elevation Noble Fir Plantations

The pattern of residuals from equation 1 was reasonable, with no indication of 

bias or any trend. However, this is for the variable y = ln(H40) – ln(S35). The variable of actual interest is ln(H40) or, better, untransformed H40.

Figure 6 is a plot of the residuals from the detransformed H40 estimates, calculated from the C72 data using installation means and equation 3. Measurement 3 at 

Haller seems to be an unexplained outlier; otherwise the pattern appears satisfactory. Mean residual was 0.44 feet with standard deviation 1.35 feet. There was no 

indication of any relationship to S35.

A similar computation using equation 3 and all measurements, rather than the 

installation means, gave a mean deviation of 0.18 feet, with standard deviation 1.68 

feet. The pattern was similar to figure 6 except for somewhat wider dispersion, as 

would be expected.

Regressions of H40 on breast-height age (age b.h)—

Some additional noble fir data are available from study C45 (described in more 

detail by Curtis 2013b). These are from an initial planting spacing trial established 

in 1980 on the Wind River Experimental Forest, near Carson, Washington. This 

trial included both pure and mixed plantings of several species, including noble fir. 

Spacing ranged from 2 by 2 meters to 6 by 6 meters (6.6 feet to 19.7 feet). Data used 

here are a subset of the original noble fir plots and exclude a number of plots, originally planted to noble fir, which have been overwhelmed by natural Douglas-fir regeneration and now have fewer than five noble fir present in the largest 40 per acre.

-3.0

-2.0

-1.0

0

1.0

2.0

3.0

4.0

5.0

0 10 20 30 40 50 60

obs H40 – est H40 (feet) 

Years from seed

Figure 6—Plot of detransformed residuals from equation 3 over age.
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research paper PNW-rp-603

The C45 data involve some differences from C72 in that:

• The plots are at relatively low elevation (2,000 to 2,400 feet) on a south 

slope, and thus are on a lower and warmer site than C72 and at or below the 

lower margin of the Abies amabilis Zone.

• The plots developed a heavy cover of Ceanothus velutinus Douglas ex 

Hook, which may have restricted growth somewhat, prior to mechanical 

release in 1990.

• No direct measurements of age at b.h. are available. Values used were estimated by backward extrapolation of a regression of H40 on total age, fit to 

the overall means.

• Spacings were established at time of planting, whereas those in C72 were 

established by precommercial thinning of initially moderately dense stands.

The C45 installation trend in H40, shown as the dotted line in figure 1, is not 

greatly different from the others, although it has a slightly greater slope. If we 

hypothesize that some part of the difference arises from the known early Ceanothus

competition, the relationship should be improved by using age at breast height (age 

b.h.) rather than total age. Data plots show that this does in fact bring the C45 curve 

(dotted line) into a position consistent with the other installations.

H40 at total age 35 was used as the reference point in fitting equation 3 above, 

which provided the H40/total age curves shown in figure 4. An approximate 

conversion to similar curves of H40 over age b.h. can be made simply by relabeling the horizontal axis; on average, age b.h. is about 9 years less than total age. Or, 

equivalently, substituting the variable x = age b.h. + 9 for total age in equation 3 

produces the equation: 

H40 = exp[ln(S35tot) – 14.5756((age b.h.+9)-0.5 – 0.1690)]. (4)

The corresponding curves are shown as the solid lines in figure 7. Although 

these do not meet the logical requirement that H40 = 4.5 when age b.h. = 0, the discrepancy is small and of no importance for most purposes. Like equation 3, limited 

extrapolations to somewhat greater ages seemed reasonable.

Alternatively, a regression can be fit directly, using age b.h. rather than total 

age, and an index age b.h. = 35 – 9 = 26 (used to provide comparability).

A first attempt using the equation 1 form with exponent -0.5 was clearly 

unsatisfactory.

A more satisfactory fit was obtained with the equation:

ln(H40 – 4.5) – ln(S – 4.5) = ̶ 14.3663[((age b.h.)-0.5

 – 0.1961) + 10.8439((age b.h.)-1 – 0.03846)], (5)

On average, age at 

breast height was 

about 9 years less than 

total age.
13

Development of Top Heights and Corresponding Diameter in High-Elevation Noble Fir Plantations

with fit statistics RSME = 0.0563 and adjusted RSQ = 0.9652.

Rearranging the equation:

ln(H40 – 4.5) = ln(S – 4.5) – 14.3663((age b.h.)-0.5 – 0.1961) +

10.8439((age b.h.)-1 – 0.03846),

and

H40 = 4.5 + exp[ln(S – 4.5) – 14.3663((age b.h.)-0.5 – 0.1961) +

 10.8439((age b.h.)-1 – 0.03846)]. (6)

Here, 0.1961 = (26)-0.5 and 0.03846 = (26)-1, where 26 is the age b.h. corresponding 

to the value of S.

The corresponding curves for S26 = 35, 45, 55, and 65 are shown as dashed 

lines in figure 7. Within the range of the data, these are not appreciably different 

from those for equation 4, but diverge somewhat when extrapolated to greater ages 

although they are not radically different. Like equation 4, these do not meet the 

logical requirement that H40 approaches 4.5 as age b.h. approaches 0, but the discrepancy is evident only for ages b.h. less than 5, and is of no practical importance. 

The discrepancy arises from inclusion of the terms 260.5 and 26-1, used to force the 

condition that H40 = S at index age 26.

0

10

20

30

40

50

60

70

80

90

100

110

120

0 5 10 15 20 25 30 35 40 45 50 55

H

40 (feet)

Age at breast height (years)

Figure 7—Curves of H40 over breast-height age (solid), corresponding to equations 4 and 6 

(dashed).
14

research paper PNW-rp-603

Detransformed deviations, obsH40 – estH40, were calculated using equation 6. 

The mean deviation was 0.08 feet, with standard deviation of 1.66 feet. The pattern 

in relation to age b.h. was similar to that in figure 6.

Comparison with previous height growth curves—

Total ages were converted to corresponding breast-high ages, and installation 

means of H40 were then plotted over age at b.h. Figure 8 shows these trends superimposed on the corresponding height/age b.h. curves (dashed) for the best, medium, 

and poorest sites given in table 1 in Herman et al. (1978). The differences are considerable and show the same general pattern as does figure 4 in Murray et al. (1991). 

Namely, that the C72 and C45 data show much more rapid early height growth than 

do the Herman et al. curves. The 1978 curves are not suitable for site evaluation in 

young planted stands.

0

10

20

30

40

50

60

70

80

90

0 5 10 15 20 25 30 35 40 45

H40 (feet)

Age at breast height (years)

Figure 8—Observed trends of installation means of H40 over breast-high age (solid), compared with the height growth curves 

(dashed) for the poorest, medium, and best sites from Herman et al. (1978).

The data show much 

more rapid early height 

growth than do the 

1978 curves of Herman 

et al. The 1978 curves 

are not suitable for site 

evaluation in young 

plantations. 
15

Development of Top Heights and Corresponding Diameter in High-Elevation Noble Fir Plantations

Analysis of D40 in Relation to Age and Spacing

A similar series of comparisons was made for D40, the mean diameter of those 

noble fir included in the largest 40 stems per acre.

Development trends of D40 were plotted in relation to total age, by installations, and by treatments within installations. In general, growth rates were greater 

in thinned plots than in unthinned, although there was much variation among 

installations. In some installations, growth trends were nearly parallel, while in 

others, thinned treatments had markedly greater slopes than unthinned.

Figure 9 shows treatment means of D40 by treatment immediately after thinning (measurement 1) and at the 20-year measurement (measurement 4). As with 

H40, the data suggest that thinning initially decreased D40. The comparison of the 

unthinned treatment with the combined thinned treatments at measurement 1 was 

significant at the 0.05 level. This corresponds to the similar indication for H40, 

and can plausibly be attributed to the spatial constraints on leave tree selection 

used in the thinned plots but not in the unthinned. Unlike H40, the comparison of 

unthinned vs. thinned treatments remained significant at the 20-year measurement. 

Differences among thinned treatments were nonsignificant at measurement 1, but 

became so (p = 0.01) by measurement 4.

Figure 10 compares periodic annual increments (PAI) in D40, by treatments, 

for the 20-year period from measurement 1 through measurement 4. It is clear 

that periodic annual diameter increment of the 40 largest trees per acre increased 

0

2

4

6

8

10

12

14

16

No Thin TN-700 TN-430 TN-265 TN-163 TN-100

D40 (inches)

Treatment (target number per acre)

Measurement 1

Measurement 4

Figure 9—Treatment means of D40, with error bars for one standard error, at initial measurement 

and at 4th measurement.

Periodic annual 

diameter increment of 

the 40 largest trees per 

acre increased with 

spacing. 
16

research paper PNW-rp-603

0.50

0.45

0.40

0.35

0.30

0.25

0.20

0.15

0.10

0.05

0

No thin TN-700 TN-430 TN-265 TN-163 TN-100

20-year periodic increment in D40 (inches per year)

Treatment (target number per acre)

Figure 10—Treatment means of 20-year periodic annual increment in D40, with error bars for 

one standard error.

substantially with spacing, even though these trees were in a dominant position 

throughout. The relation of D40 PAI to spacing on thinned plots can be expressed 

by the regression equation:

periodic annual D40 increment (inches/year) = 0.282359 +0.007381(spacing) (7)

with RMSE = 0.08 and adjusted RSQ = 0.1332. 

Although D40 PAI clearly increased with spacing, the amount of increase was 

highly variable among installations. Presumably this variation is at least in part the 

result of differences in initial age and differences in site quality, but with only eight 

complete installations, no quantitative relationship can be defined. 

Discussion

The comparisons of these H40 results with Herman’s curves (fig. 8) are very similar 

to those made by Murray et al. (1991), although the method of selection of sample 

trees was not identical and the present data are based on remeasured plots whereas 

Murray et al. used stem analyses. Both show that young noble fir plantations 

established on clearcuts are making much more rapid early growth than did the 

old naturally established trees sampled by Herman et al. (1978). Herman’s curves 

should not be used with plantations.
17

Development of Top Heights and Corresponding Diameter in High-Elevation Noble Fir Plantations

The reasons for the difference are unclear, but several factors probably 

contribute:

• C72 plantations were established with vigorous seedlings on clearcuts, and 

were usually relatively free from early vegetative competition.

• The recent climate has been warmer and more favorable to tree growth than 

when the old trees used by Herman et al. (1978) were becoming established.

• The plantations included in C72 and C45 probably did not sample the poorest sites included in Herman’s sample.

• Herman’s curves were derived from stem analyses of old trees, of natural 

origin and unknown early competitive status. Biases could have been introduced by shifts in tree position over time.

H40 over age curves prepared from successive measurements will not generally 

be identical with curves prepared from stem analyses (ex: Dahms 1963) because 

of tree mortality and the shifts in tree relative crown position that occur over time. 

Differences are probably small when direct measurements and stem analyses cover 

similar short time periods, but can become large when the stem analyses are made 

on much older trees. Curves prepared from repeated measurements of H40 are 

preferred, even though the trees included may change over time, because they are 

consistent with height measurements made in the usual one-time field applications.

The new curves of H40 in relation to total age and age b.h. (figs. 4 and 7) can 

be used to estimate relative site quality in young noble fir plantations, and are much 

preferable to the older curves for this purpose. The curves for equations 4 and 6 

are almost identical within the range of the data (fig. 7), and either can be used. 

Extrapolations to greater ages are necessarily highly uncertain, but the curve shapes 

are at least plausible and more or less consistent with values for older ages given 

by Herman et al. (1978). Admittedly, eight locations is a weak basis, but this must 

suffice pending availability of more extensive data. 

The index ages used here (35 total and 26 breast high) are undesirably low, 

but are limited by the range of the presently available data. When data become 

available, an index age of 50 years b.h., which is now in use for a number of other 

species, would be much preferable.

There is no indication of a spacing effect on H40 in the C45 data. The C72 data 

do suggest that unthinned H40 is generally slightly greater than that in thinned 

stands, but that there is little apparent relation to spacing among thinned stands. 

Differences at the most recent measurement, though nonsignificant, appear consistent with differences present immediately postthinning. The difference between 

thinned vs. unthinned in C72 may be the result of the spatial constraints applied in 

The new curves of H40 

in relation to total age 

can be used to estimate 

relative site quality in 

young plantations and 

are much preferable to 

the older curves for this 

purpose.
18

research paper PNW-rp-603

selection of leave trees in thinning, which probably led to removal of some trees 

that would have been included in the largest 40 per acre in the absence of spatial 

constraints.

Unlike H40, there is a definite spacing effect on D40 increment. Even these 

dominant trees did respond to increased growing space.

The recent loss of the Twin and Mary’s Creek installations to unplanned thinning is unfortunate. Some years hence, we will need to decide whether continued 

measurement is justified. These would provide a continuation of H40 development, 

but would be useless for the original purpose of comparing the overall effects of 

alternate initial spacings.

It is well recognized (Franklin 1982, 1990; Harrington and Murray 1982) that 

noble fir characteristically has very slow juvenile height growth, followed by a 

long period of nearly linear growth, and substantial height growth continuing even 

at advanced ages. This implies the desirability of relatively long rotations for this 

species. Results in this study are consistent with previously reported information.

Acknowledgments

Thanks are due to David Marshall of Weyerhaeuser NR Co., Douglas Maguire of 

Oregon State University, and Peter Gould of the Washington Department of Natural 

Resources, for helpful reviews and suggestions.

Metric Equivalents

When you have: Multiply by: To find:

Inches (in) 2.54 Centimeters

Feet (ft) 0.3048 Meters

Acres (ac) 0.405 Hectares

Trees per acre 2.471 Trees per hectare

References

Curtis, R.O.; Clendenen, G.W.; Henderson, J.A. 2000. True fir-hemlock spacing 

trials: design and first results. Gen. Tech. Rep. PNW-GTR-492. Portland, OR: 

U.S. Department of Agriculture, Forest Service, Pacific Northwest Research 

Station. 122 p.

Curtis, R.O. 2008. True fir spacing trials—10-year results. Gen. Tech. Rep. PNWGTR-749. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific 

Northwest Research Station. 36 p.
19

Development of Top Heights and Corresponding Diameter in High-Elevation Noble Fir Plantations

Curtis, R.O. 2013a. True fir spacing and yield trials—20-year update. Res. Pap. 

PNW-RP-590. Portland, OR: U.S. Department of Agriculture, Forest Service, 

Pacific Northwest Research Station. 32 p. 

Curtis, R.O. 2013b. C45 Unit 7, noble fir spacing trial: analyses of 2009 data. 

Unpublished report. On file: U.S. Department of Agriculture, Forest Service, 

Forestry Sciences Laboratory, 3625 93rd Ave. SW, Forestry Sciences Laboratory, 

Olympia, WA 98512.

Dahms, W.G. 1963. Correction for a possible bias in developing site index curves 

from sectioned tree data. Journal of Forestry. 61(1): 25–27.

Franklin, J.F. 1982. Ecology of noble fir. In: Oliver, D.D.; Kenady, R.M., eds. 

Proceedings of the biology and management of true fir in the Pacific Northwest 

symposium. Institute of Forest Resources Contrib. 45. Seattle, WA: University of 

Washington, College of Forest Resources: 59–69.

Franklin, J.F. 1990. Abies procera Rehd. Noble fir. In: Burns, R.M.; Honkala, 

B.H. 1990. Silvics of North America. Vol. 1, Conifers. Agric. Handb. 654. 

Washington, DC: U.S. Department of Agriculture, Forest Service: 80–87.

Franklin, J.F.; Dyrness, C.T. 1973. Natural vegetation of Oregon and Washington. 

Gen. Tech. Rep. PNW-8. Portland, OR: U.S. Department of Agriculture, Forest 

Service, Pacific Northwest Forest and Range Experiment Station. 417 p.

Freund, R.J.; Littell, R.C. 1991. SAS system for regression. 2nd ed. Cary, NC: 

SAS Institute, Inc. 210 p.

Harrington, C.A.; Murray, M.D. 1982. Patterns of height growth in western 

true firs. In: Oliver, D.D.: Kenady, R.M., eds. Proceedings of the biology and 

management of true fir in the Pacific Northwest symposium. Institute of Forest 

Resources Contrib. 45. Seattle, WA: University of Washington, College of Forest 

Resources: 209–214.

Herman, F.R.; Curtis, R.O.; DeMars, D.J. 1978. Height growth and site index 

estimates for noble fir in high-elevation forests of the Oregon-Washington 

Cascades. Res. Pap. PNW 243. Portland, OR: U.S. Department of Agriculture, 

Forest Service, Pacific Northwest Forest and Range Experiment Station. 15 p.

Murray, M.D.; Coble, D.; Curtis, R.O. 1991. Height growth of young Pacific 

silver fir and noble fir established on clearcuts in the Pacific silver fir zone of 

western Washington. Canadian Journal of Forest Research. 21: 1213–1221.

Snedecor, G.W. 1956. Statistical methods. 5

th ed. Ames, IA: Iowa State University 

Press. 534 p. 
20

research paper PNW-rp-603

Glossary of Symbols and Acronyms

Aget = total age = years from seed.

age b.h. = breast-high age = number of annual rings at breast height

D40 = mean diameter (inches) of those noble fir included in the largest 40 (by

diameter, all species) stems per acre.

Exp(x) = ex.

H40 = mean height (feet) of those noble fir included in the largest 40 (by diameter,

all species) stems per acre.

RMSE = root mean square error = standard deviation of residuals.

RSQ = (multiple correlation coefficient)2 = coefficient of determination.

S35 = estimated H40 at total age 35.

S26bh = S26 = estimated H40 at breast-high age 26.

TN = target number of leave trees per acre.

adjRSQ = RSQ adjusted for number of variables = 1 ̶ ( 1 – (RSQ)(N ̶ 1)/(n – m – 1).

(Freund and Littell 1991, 23).

XY = product of X and Y.

ln(x) = natural logarithm (base e) of x.
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