United States Department of Agriculture / Forest Service

Rocky Mountain Research Station

Research Paper RMRS-RP-82WWW

October 2010

Dennis E. Ferguson and Clinton E. Carlson

Height-Age Relationships for

Regeneration-Size Trees in the

Northern Rocky Mountains, USA
Ferguson, Dennis E.; Carlson, Clinton E. 2010. Height-age relationships for 

regeneration-size trees in the northern Rocky Mountains, USA. Res. Pap. 

RMRS-RP-82WWW. Fort Collins, CO: U.S. Department of Agriculture, Forest 

Service, Rocky Mountain Research Station. 19 p.

Abstract

Regression equations were developed to predict heights of 10 conifer species in 

regenerating stands in central and northern Idaho, western Montana, and eastern 

Washington. Most sample trees were natural regeneration that became established 

after conventional harvest and site preparation methods. Heights are predicted as a 

function of tree age, residual overstory density, elevation, site preparation, habitat 

type series, and closest National Forest location. Equations are presented that can 

be used to predict heights at a given age or to predict the number of years required 

to reach a specified height.

Keywords: forest succession, conifer growth, natural regeneration, forest 

management, habitat types

Authors

Dennis E. Ferguson is a Research Silviculturist with the USDA Forest Service, Rocky 

Mountain Research Station in Moscow, Idaho. 

Clinton E. Carlson is a Research Silviculturist (retired) with the Rocky Mountain 

Research Station in Missoula, Montana.

Acknowledgments

We thank Raymond J. Boyd, Ward W. McCaughey, and Leon Theroux for their help 

with study design and data collection.

Available only online at http://www.fs.fed.us/rm/pubs/rmrs_rp082.html

Rocky Mountain Research Station

Publishing Services

Telephone (970) 498-1392

FAX (970) 498-1122

E-mail rschneider@fs.fed.us

Web site http://www.fs.fed.us/rm/publications

Mailing address Publications Distribution

Rocky Mountain Research Station

240 West Prospect Road

Fort Collins, CO 80526
USDA Forest Service RMRS-RP-82WWW. 2010. 1

Introduction

Secondary succession that follows disturbance is a period of rapid change in northern 

Rocky Mountain forest environments. During this period, shrubs, forbs, and grasses are 

responding to increased sunlight, moisture, and nutrients. Several conifer and a few deciduous tree species are regenerating, and residual overstory trees are adjusting to changes 

in stand conditions. All these vegetative lifeforms are competing within and among themselves to various degrees.

Also, many chance occurrences can play a role in altering the direction of secondary 

succession in regenerating stands. Among these factors are weather patterns, seed and cone 

insects, seed predation, small mammal activity, animal browsing, various diseases, and 

abiotic damages. Silvicultural treatments to favor conifers such as shrub control, thinnings, 

and plantings can have substantial impacts on succession that last for many decades.

It is important in the northern Rocky Mountains to understand conifer height-age relationships during the approximately 20-yr regeneration period that follows disturbance. The 

information can be used to estimate regeneration heights, determine the number of years 

for regeneration to reach breast height (4.5 ft) or conversely estimate total tree age from 

breast height age, and make decisions about the need for treatments to control competition.

This report provides information on regeneration height-age relationships for 10 conifer 

species in central and northern Idaho, western Montana, and part of eastern Washington. 

These data have been reported elsewhere (Ferguson and others 1986; Ferguson and Carlson 

1993), but new analytical techniques are now available that improve predictions of heightage relationships.

Study Design

The data come from three studies that looked at regeneration success following timber harvest in the northern Rocky Mountains. The first study was conducted in the grand fir (Abies 

grandis), western redcedar (Thuja plicata), and western hemlock (Tsuga heterophylla) 

habitat types of northern Idaho during 1975 to 1976 and was used to develop version 1 

of the regeneration establishment model (Ferguson and others 1986). Data were collected 

during a second study in central Idaho Douglas-fir (Pseudotsuga menziesii), grand fir, and 

subalpine fir (Abies lasiocarpa) habitat types, and from Douglas-fir and subalpine fir habitat types in northern Idaho during 1979 to 1982. Data were collected during the third study 

in Douglas-fir, grand fir, western redcedar, western hemlock, and subalpine fir habitat types 

in western Montana during 1979 to 1982. Data from studies 2 and 3 were combined with 

data from study 1 to develop version 2 of the regeneration establishment model (Ferguson 

and Carlson 1993).

A stratified random design was used to select stands that were harvested 2 to 20 yr prior 

to sampling. Stratification variables were habitat type series, site preparation, and regeneration method. In studies 2 and 3, history of western spruce budworm (Choristoneura 

occidentalis) defoliation was also a classification variable. Although stands were used to 

select study areas, the focus was on sampling microsites within stands.

After obtaining stand histories and stereo aerial photographs for each selected stand 

from Ranger District files, either transects or a sampling grid was used to systematically 

locate about 25 plot centers per stand. In Idaho, transects crossed through areas observable 

on aerial photographs that varied in aspect, overstory density, site preparation, or topographic position. In Montana, a sampling grid was used to locate plot centers.

Each sample point was the center of a 1/300-acre circular fixed area plot and a variable radius plot for sampling the overstory (if present) with a 10 basal area factor prism. 

Each plot was made as independent as possible by recording plot attributes: slope, aspect, 
2 USDA Forest Service RMRS-RP-82WWW. 2010.

type of site preparation, topographic position, residual overstory density by species, and 

habitat type (Cooper and others 1991; Pfister and others 1977; Steele and others 1981). 

Systematically spacing plots also helped maintain independence among plots within stands 

because plots were dispersed throughout the stand. The year of harvest, geographic location, and elevation were stand variables that did not differ among plots within a stand.

Within the same stand, plots could have different “years since last disturbance” due 

to the timing of site preparation. Untreated plots were last disturbed when the stand was 

harvested. Mechanically prepared or burned plots were last disturbed when the site preparation took place, which could have occurred after the harvest year.

All established conifer regeneration on plots in the Idaho studies was counted by species; in Montana, up to 10 established trees were recorded per plot. Minimum heights were 

0.5 ft for shade-tolerant species and 1.0 ft for shade-intolerant species, which roughly correspond to the heights of 3-yr-old trees. Maximum size for all regeneration was 3.0 inches 

diameter at breast height (dbh). Tree heights were measured as of the end of the previous 

growing season to ensure that all trees were sampled during a field season by the same 

criterion.

Tree height to the nearest 0.1 ft, tree age at groundline (end of the previous growing 

season), and tree condition were recorded on a subsample of regeneration called best trees, 

which were chosen by the following rules:

• Select the two tallest trees on the plot regardless of species.

• Select the one tallest tree of each additional species present on the plot.

• If the first two rules do not result in at least four trees, select in order of descending 

height from any remaining trees until four trees, if present, are chosen.

Shrubs, forbs, and grasses were characterized by recording average height and percent 

plot coverage, similar to Daubenmire (1959). These data were not used to predict regeneration heights because it was not possible to retrospectively determine coverage during the 

life of the tree; however, the Idaho data were used to develop a model of secondary succession for shrubs, forbs, and grasses (Moeur 1985).

Data Analysis

Data were analyzed with SAS version 9.2 using methods for mixed models (Littell and 

others 1996). PROC MIXED was used to predict regeneration heights as a function of 

age, site variables, and overstory competition. Study areas were designated as a random 

variable because each site represented a sample from a larger set of possible sites. The 

SUBJECT statement was used to account for the correlation among plots within stands.

The significance of independent variables was evaluated using t-ratios and F-values 

at the P = 0.05 level. Akaike’s information criteria (AIC; smaller is better) was used to 

compare models that had different independent variables but the same dependent variable. 

Transformations of variables were explored to achieve homogeneity of error variance and 

obtain additivity of effects (Kirk 1982). Preliminary analyses showed that the natural log 

(ln) of height and age were the best transformation for these two variables.

Stands were assigned to a class variable for the nearest U.S. Forest Service National 

Forest (NF). Other researchers have found NF useful in modeling forest growth because 

it divides the study area into units that can account for variation in latitude, longitude, climate, and soil (Ferguson and Carlson 1993; Wykoff 1982, 1986). The interaction of aspect 

and slope was modeled after Stage (1976).

Before fitting regression equations, the data were screened to exclude advance regeneration (trees that had germinated more than 3 yr before the harvest). Also eliminated were 

tree species with only a few observations, which resulted in 10 conifer species available 
USDA Forest Service RMRS-RP-82WWW. 2010. 3

for analyses. Table 1 shows common and scientific names of conifer species in this study, 

as well as minimum establishment heights.

Visual inspection of height-age plots revealed a bias in the sample design because mean 

tree height increased with increasing age, but then unexpectedly declined beyond a certain age. It is likely that tall trees were absent at older tree ages because they had grown 

beyond the 3.0 dbh threshold. A combination of inspection of height-age plots by species 

and examination of mean heights by age by species was used to reveal ages beyond which 

the data were suspect. Therefore, trees were eliminated with ages beyond 13 yr for western 

larch; 14 yr for Douglas-fir; 15 yr for ponderosa pine, western white pine, and western redcedar; 16 yr for lodgepole pine; 17 yr for Engelmann spruce and grand fir; 18 yr for western 

hemlock; and 20 yr for subalpine fir.

Results

A total of 8824 trees were used in the analyses. Table 2 shows the number of trees by 

species, habitat type series, NF, and site preparation. A summation of the number of trees 

by geographic area shows that 686 trees were sampled in central Idaho, 5721 trees in northern Idaho, 227 trees in eastern Washington, and 2190 trees in western Montana. Western 

hemlock had the fewest trees in the sample (346), and grand fir had the most (3100), comprising about one-third of the total number of trees.

It is clear from Table 2 that height estimates cannot be made for all combinations of 

species and NF locations. Species do not occur uniformly across the landscape, and even 

where they do occur, their occurrence is low toward the extremes of their environmental 

niche (Daubenmire 1966; Rehfeldt and others 2008).

Table 1. Common name, scientific name, and abbreviation for conifer species in this 

study.

 Minimum

Common Scientific establishment

name name Abbreviation height (ft)

Ponderosa pine Pinus ponderosa Dougl. PP 1.0

ex Laws. var. ponderosa

Western larch Larix occidentalis Nutt. WL 1.0

Lodgepole pine Pinus contorta Dougl. LP 1.0

ex Loud.

Engelmann spruce Picea engelmannii Parry ES 0.5

ex Engelm.

Douglas-fir Pseudotsuga menziesii DF 1.0

var. glauca (Beissn.) 

Franco

Western white pine Pinus monticola Dougl. WP 1.0

ex D. Don

Grand fir Abies grandis (Dougl. GF 0.5

ex D. Don) Lindl.

Western hemlock Tsuga heterophylla WH 0.5

(Raf.) Sarg.

Subalpine fir Abies lasiocarpa AF 0.5

(Hook.) Nutt.

Western redcedar Thuja plicata Donn RC 0.5

ex D. Don
4 USDA Forest Service RMRS-RP-82WWW. 2010.

Height-age equations

Table 3 lists variables used in regression analyses to predict regeneration heights. 

Table 4 shows multiple regression equations for predicting height from age, residual basal 

area, elevation, slope, habitat type series, NF, and site preparation. Interpretation of the 

partial regression coefficients can be done with all other variables in the equation being 

held constant.

Tree age is the best predictor of height. The smallest coefficients (shorter trees) for age 

are subalpine fir and western redcedar. Shade-intolerant species—ponderosa pine, western 

larch, lodgepole pine, Engelmann spruce, Douglas-fir, and western white pine—had larger 

coefficients than subalpine fir and western redcedar. Western hemlock had the largest coefficient for age of the 10 species.

For all species except Engelmann spruce, residual basal area was associated with shorter 

heights when all other variables were held constant (Table 4). Western redcedar heights 

were least negatively impacted by residual overstory basal area, while ponderosa pine and 

lodgepole pine had the largest reductions in heights associated with basal area.

Increasing elevation was associated with shorter heights for western larch, lodgepole 

pine, western white pine, grand fir, western hemlock, and western redcedar when all other 

variables were held constant (Table 4). Overall, the interaction of slope and aspect was 

not a significant predictor of tree heights, but slope was important for lodgepole pine and 

grand fir.

Table 2. Number of sample trees by species, habitat type series, National Forest location, and site 

preparation. Species are listed in the approximate order of shade tolerance, from least (left) to 

most tolerant (right). Species definitions are found in Table 1.

Species

Habitat type

series* PP WL LP ES DF WP GF WH AF RC Total

PSME 252 55 106 4 251 0 8 0 1 0 677

ABGR 256 131 190 92 427 46 899 0 22 6 2069

THPL 57 94 62 76 299 129 1205 2 21 308 2253

TSHE 2 97 90 93 264 160 834 337 61 137 2075

ABLA 33 163 394 335 246 20 154 7 396 2 1750

National Forest PP WL LP ES DF WP GF WH AF RC Total

Bitterroot 51 5 36 6 62 0 3 0 15 0 178

Boise 113 0 48 16 27 0 26 0 3 0 233

Clearwater 32 50 54 133 323 137 1152 0 59 209 2149

Colville 3 10 63 2 49 1 76 6 3 14 227

Deerlodge 2 45 25 5 83 0 0 0 5 0 165

Flathead 0 81 18 6 64 4 10 0 7 0 190

Gallatin 0 0 96 7 17 0 0 0 5 0 125

Helena 0 0 55 0 67 0 0 0 10 0 132

Kootenai 19 83 62 43 51 33 33 25 64 30 443

Lolo 150 167 193 22 218 5 136 1 51 14 957

Nez Perce 62 17 31 77 80 0 252 0 25 8 552

Panhandle 2 75 110 220 402 175 1333 314 211 178 3020

Payette 166 7 51 63 44 0 79 0 43 0 453

Site preparation PP WL LP ES DF WP GF WH AF RC Total

None 149 133 250 69 586 163 1560 181 184 178 3453

Mechanical 222 161 325 202 351 81 631 64 133 84 2254

Burn 192 197 219 259 447 65 638 70 134 107 2328

Roads 37 49 48 70 103 46 271 31 50 84 789

Total 600 540 842 600 1487 355 3100 346 501 453 8824

* PSME = Pseudotsuga menziesii habitat type series. ABGR = Abies grandis series. THPL = Thuja plicata

series. TSHE = Tsuga heterophylla series. ABLA = Abies lasiocarpa series.
USDA Forest Service RMRS-RP-82WWW. 2010. 5

Table 3. List of variables used in analyses of data, means, and extreme values.

Abbreviation Explanation Mean Min/Max

height Tree height (ft) 2.5 0.5 to 22.9

age Tree age at groundline (yr) 8.5 3 to 19

ba Residual plot basal area (ft2

/acre) 18.5 0 to 380

elev Stand elevation (nearest 100 ft) 46.9 24 to 74

slo Plot slope ratio (percent/100) 0.23 0 to 0.99

delay Number of years from harvesting 2.2 -3 to 17

or site preparation to germination 

of the tree

Table 4. Coefficients for equations that predict tree heights. The form of the equation is:

Height = exp (ß0

 + ∑ßiXi). Height is tree height in feet, age is tree age at groundline, ba is point basal area in ft2/acre, elev is 

stand elevation to the nearest 100 ft, slo is plot slope ratio (percent/100); and PSME is Douglas-fir habitat types, ABGR 

is grand fir habitat types, THPL is western redcedar habitat types, TSHE is western hemlock habitat types, and ABLA is 

subalpine fir habitat types. Road site preparation includes plots that occurred on road cuts, road fills, and unmaintained 

road beds.

Variable PP WL LP ES DF WP GF WH AF RC

ß0 -1.7936 -0.8617 -1.0935 -2.5216 -2.1325 -1.2269 -1.8619 -1.8742 -2.0991 -1.3326

ln(age) 1.3737 1.3093 1.3836 1.3595 1.3167 1.2842 1.2260 1.5824 1.1671 1.0819

ba -0.0052 -0.0038 -0.0070 -0.0030 -0.0031 -0.0034 -0.0038 -0.0033 -0.0021

elev -0.0136 -0.0099 -0.0182 -0.0048 -0.0173 -0.0118

slo -0.6632 -0.2329

Habitat type series

PSME -0.0852 -0.1708 0.1665* -0.0137 N.D. N.D. N.D. * N.D.

ABGR 0.0885 0.1289 0.1665 0.1287 0.0 N.D. *

THPL 0.1364 0.1889 0.1522 0.2820 0.1525 *

TSHE 0.1364* 0.1059 0.2160 0.2284 0.0

ABLA 0.0 0.0 0.0 0.0 0.0 * *

National Forest

Bitterroot -0.2393 -0.0249 0.1759 -.3367* -0.4759 N.D. -.0734* N.D. -0.2277 N.D.

Boise -0.2857 N.D. -0.1365 -0.2387 -0.2399 N.D. -0.4095 N.D. -.1756* N.D.

Clearwater 0.0 0.0915 0.1759 -0.1386 0.0085 -0.0368 N.D. -0.1756

Colville 0.0* 0.0 -0.1365 0.0* -0.1247 * -0.1171 * 0.0*

Deerlodge -.2393* -0.0249 -0.0658 -.3367* -0.3972 N.D. N.D. N.D. -.2277* N.D.

Flathead N.D. -0.1683 0.0594 -.3367* -0.2223 * -0.0734 N.D. 0.1866* N.D.

Gallatin N.D. N.D. 0.0594 -.3367* -0.6311 N.D. N.D. N.D. -.2277* N.D.

Helena N.D. N.D. 0.0594 N.D. -0.6311 N.D. N.D. N.D. 0.1866 N.D.

Kootenai -0.2393 0.2030 -0.1905 0.0248 -0.0725 -0.0734 0.1866

Lolo -0.3803 -0.0770 -0.0658 -0.3367 -0.4539 * -0.0734 * -0.2277

Nez Perce -0.2092 0.0773 0.1759 0.0872 0.0193 N.D. -0.1389 N.D. -0.1756 *

Payette -0.4394 0.0773* -0.2332 -0.2387 -0.2851 N.D. -0.4095 N.D. -0.1756 N.D.

Panhandle 0.0* 0.0 0.0 0.0 0.0 0.0 0.0

Site preparation

none 0.0 0.0 0.0 0.0 0.0

mechanical 0.1642 0.1130 0.1365 0.0144 -0.1338

burn 0.1372 0.0405 0.2895 0.1517 0.0239

road 0.1262 0.1875 0.1177 0.0829 0.1557

n 600 540 842 600 1487 355 3100 346 501 453

AIC 778 790 1077 811 2295 464 4443 553 772 748

Residual 0.1187 0.1107 0.1140 0.1334 0.1512 0.1423 0.1637 0.1867 0.1265 0.1643

Log bias 

correction 

factor 1.28 1.27 1.26 1.36 1.31 1.23 1.28 1.41 1.27 1.28

N.D. = no data in the category.

* Fewer than 10 trees in the category; combined with another National Forest or habitat type series.
6 USDA Forest Service RMRS-RP-82WWW. 2010.

Habitat type series was important for species with wider distributions, such as ponderosa pine, lodgepole pine, Engelmann spruce, and Douglas-fir. NF locations were important 

for 7 of the 10 species. Three species with relatively narrow distributions—western white 

pine, western hemlock, and western redcedar—had no location-specific coefficients.

Plot site preparation was a significant predictor of heights for ponderosa pine, lodgepole 

pine, Engelmann spruce, Douglas-fir, and western redcedar. Generally, site preparation 

was associated with taller trees, compared to no site preparation. Coefficients for burn site 

preparation were larger, compared to mechanical site preparation, for Engelmann spruce, 

Douglas-fir, and western redcedar.

Figures 1 through 10 show height-age curves using the equations given in Table 4. These 

figures depict results of exercising the equations for two elevations (35 and 50) and four 

levels of residual basal area (0, 40, 80, and 120 ft2) while holding slope at 0 percent and 

using class variables for habitat type series, NF, and site preparation that have the highest number of observations shown in Table 2. The purpose of the figures is to show how 

height-age curves differ among species, elevations, and basal areas. Some species have 

only one figure because elevation was not significant in the equations, and six species do 

not have a 120 ft2 basal area prediction because of lack of data at high densities. Each figure 

has a horizontal line at 4.5 ft to aid in visually determining age at breast height.

Figure 1. Predicted height-age curves for ponderosa pine with three overstory densities.
USDA Forest Service RMRS-RP-82WWW. 2010. 7

Figure 2. Predicted height-age curves for western larch with three 

overstory densities and two elevations: (a) 35 and (b) 50.

(a)

(b)
8 USDA Forest Service RMRS-RP-82WWW. 2010.

Figure 3. Predicted height-age curves for lodgepole pine with three overstory 

densities and two elevations: (a) 35 and (b) 50.

(a)

(b)
USDA Forest Service RMRS-RP-82WWW. 2010. 9

Figure 4. Predicted height-age curve for Engelmann spruce.

Figure 5. Predicted height-age curves for Douglas-fir with four overstory 

densities.
10 USDA Forest Service RMRS-RP-82WWW. 2010.

Figure 6. Predicted height-age curves for western white pine with three 

overstory densities and two elevations: (a) 35 and (b) 50.

(a)

(b)
USDA Forest Service RMRS-RP-82WWW. 2010. 11

(b)

Figure 7. Predicted height-age curves for grand fir with four overstory 

densities and two elevations: (a) 35 and (b) 50.

(a)
12 USDA Forest Service RMRS-RP-82WWW. 2010.

(a)

(b)

Figure 8. Predicted height-age curves for western hemlock with four 

overstory densities and two elevations: (a) 35 and (b) 50.
USDA Forest Service RMRS-RP-82WWW. 2010. 13

Figure 9. Predicted height-age curves for subalpine fir with three 

overstory densities.
14 USDA Forest Service RMRS-RP-82WWW. 2010.

Figure 10. Predicted height-age curves for western redcedar with four 

overstory densities and two elevations: (a) 35 and (b) 50.

(a)

(b)
USDA Forest Service RMRS-RP-82WWW. 2010. 15

Table 5 shows predicted ages to breast height, by species, for the same two elevations 

and for three to four levels of residual overstory basal area used to develop Figures 1 

through 10. The equations in Table 4 are solved for a 4.5 ft tall tree. With other variables 

held constant, the species that reach 4.5 ft most rapidly are western larch and lodgepole 

pine, while subalpine fir and western redcedar take the longest. Increasing residual overstory density is associated with additional years to reach breast height for all species except 

Engelmann spruce.

The appendix shows examples of how to use the equations. Prior to transformation of 

predicted height to the original units (ft), estimates must be multiplied by a log bias correction factor. These correction factors are species-specific and are shown at the bottom of 

Table 4. The log bias correction is necessary to avoid underestimating heights when transforming log models back to the original units of measurement (Baskerville 1972).

Discussion

Even though western hemlock has the largest coefficient for ln(age) in Table 4, trees are 

taller at a given age for western larch and lodgepole pine (Figures 8, 2, and 3). This occurs 

because the intercept coefficient for western hemlock is a larger negative number than 

the intercept terms for western larch and lodgepole pine. The net effect is that heights of 

western hemlock are initially shorter than western larch and lodgepole pine, but the slope 

of the western hemlock curve is steeper than western larch and lodgepole pine. Even with a 

steeper curve, heights of western hemlock do not reach heights of western larch and lodgepole pine during the 20-yr time period.

An independent variable used in the analyses was the number of years from the disturbance to the germination of the tree (Table 3). This variable, called delay, was never 

significant in the equations that predicted height. Conventional wisdom suggests that any 

delay to germination would leave trees behind competitors that germinated earlier, resulting 

Table 5. Predicted ages to breast height using equations* in Table 4.

Residual basal area (ft2

/acre)

Species Elevation 0 40 80 100

Ponderosa pine n.s. 10.6 12.3 14.3 n/a

Western larch 35 7.7 8.7 9.8 n/a

50 9.0 10.2 11.4 n/a

Lodgepole pine 35 6.9 8.4 10.3 n/a

50 7.6 9.4 11.5 n/a

Engelmann spruce n.s. 12.5 12.5 12.5 n/a

Douglas-fir n.s. 11.7 12.8 14.0 15.4

Western white pine 35 11.7 12.9 14.2 n/a

50 14.5 16.0 17.6 n/a

Grand fir 35 12.9 14.4 16.1 18.0

50 13.7 15.3 17.1 19.1

Western hemlock 35 10.0 11.0 12.1 13.3

50 11.8 12.9 14.2 15.7

Subalpine fir n.s. 17.9 20.0 22.4 n/a

Western redcedar 35 16.0 17.3 18.7 20.3

50 18.9 20.4 22.1 23.9

* Coefficients used for habitat type series, National Forest location, and site preparation 

are for the highest number of trees per species in Table 2, and slope was set at zero 

(flat ground) for these predictions.
16 USDA Forest Service RMRS-RP-82WWW. 2010.

Table 6. Mean number of years to reach breast height.

Means calculated Mean medians from

Species from Table 5 Berglund and others (2008)

Ponderosa pine 12.4 7.7

Western larch 9.5 8.6

Lodgepole pine 9.0 9.5

Engelmann spruce 12.5 17.4

Douglas-fir 13.5 12.4

Western white pine 14.5 9.4

Grand fir 15.8 14.4

Western hemlock 12.6 15.0

Subalpine fir 20.1 22.4

Western redcedar 19.7 15.5

in differentiation of tree sizes over time. The trees chosen for sampling in this study were 

the best (tallest) trees on the plot, so they may not have been negatively affected by competition. Even though there may have been a delay between disturbance and germination for 

best trees, this delay was probably not as long as for other trees of the same species on the 

plot. It should be noted that delay to germination is still detrimental if the goal is prompt 

regeneration of an area; for example, a 5-yr delay means that 5 yr of growth is lost.

Berglund and others (2008) estimated the number of years to breast height for conifers 

in the northern Rocky Mountains. Their sample trees came from stand examination data, 

which included all the conifers shown in Table 1. They had 39,200 trees with heights between 4.0 and 5.0 ft. Their average number of years to breast height was most often longer 

than averages shown in Table 5 because their data came from a wide range of stand ages 

(for example, stands greater than 20 yr old) and disturbance histories. Also, their data 

included ingrowth trees, which are trees that become established beyond the regeneration 

period triggered by a disturbance event.

Despite differences in the design between the two studies, results are similar. Table 6 

shows median number of years to breast height from Berglund and others (2008) versus 

species averages calculated from Table 5. For this comparison, medians (50th percentile) 

reported by Berglund and others (2008) for northern Idaho and western Montana were 

averaged by species so that their averages could be compared to data collected for this 

study. Four of the 10 species agree within 2 yr of each other (western larch, lodgepole pine, 

Douglas-fir, and grand fir), and 6 of the 10 species agree within 3 yr of each other (western 

larch, lodgepole pine, Douglas-fir, grand fir, western hemlock, and subalpine fir). Four species (ponderosa pine, Engelmann spruce, western white pine, and western redcedar) differ 

by 4.2 to 4.9 yr. For ponderosa pine, western white pine, and western redcedar, predicted 

ages at breast height using equations in Table 4 exceeded average medians calculated from 

Berglund and others (2008).

The difference of 4.7 yr for ponderosa pine is due to the inclusion of the coefficient 

for the Payette NF (-0.4394) in the calculation of ages to breast height that is reported in 

Table 4. Berglund and others (2008) do not have data for the Payette NF. When the ponderosa pine equation is re-run for the Nez Perce NF (where Berglund and others [2008] do 

have data), predicted ages to breast height for ponderosa pine are 8.9 yr for 0 ft2

 of basal 

area, 10.4 yr for 40 ft2

 of basal area, and 12.1 yr for 80 ft2 of basal area. The overall average 

is 10.5 yr, which is within 3 yr of the average median value in Berglund and others (2008).
USDA Forest Service RMRS-RP-82WWW. 2010. 17

Berglund and others (2008) reported an average median of 9.4 yr to breast height for 

western white pine, while the average from Table 5 is 14.5 yr. The discrepancy may be due 

to the method for aging trees. In the inventory methods described by Berglund and others 

(2008), field crews either severed the tree at the root collar and counted annual rings or they 

counted the number of whorls. Counting whorls on western white pine can be problematic, 

especially as the trees become taller and it becomes difficult to determine the location of 

whorls near the ground. Haig (1932) reports that dominant white pine take an average of 5 

yr to reach 1 ft tall (4 yr on better sites and 6 yr on poorer sites) in even-age second-growth 

stands. He reports ages at breast height of 9 yr on good sites, 11 yr on average sites, and 14 

yr on poor sites. This range of 9 to 14 yr is in good agreement with predictions for white 

pine in Table 5 that use no overstory density.

The difference in age to breast height for western redcedar is 4.2 yr (19.7 yr versus 15.5 

yr; Table 6). For this species, the discrepancy may be due to difficulties counting the number of whorls. Parker and Johnson (1987) investigated the problem of backdating heights 

on western redcedar. They found that annual terminal increments can be determined for the 

previous 3 to 5 yr. Because western redcedar lack a major whorl of branches at the beginning of each year’s growth, ocular estimates of tree age would tend to underestimate tree 

age. Therefore, aging the tree at groundline should be more accurate than counting whorls.

For Engelmann spruce, Berglund and others (2008) reported an average of 17.4 yr to 

breast height, while the average from Table 5 is 12.5 yr. The difference may be due to our 

inclusion of the coefficient for burn site preparation (0.2895). The average for mechanical 

site preparation would be 13.9 yr and 15.4 yr for no site preparation, which are closer to the 

average reported by Berglund and others (2008).

There was also good agreement between the two studies on which species reached 

breast height quickly or slowly (Table 6). Shade-intolerant ponderosa pine, western larch, 

and lodgepole pine reached breast height relatively quick, while shade-tolerant subalpine 

fir took about twice as long to reach breast height.

Height-age relationships for these data could differ from other disturbance types. Data 

reported here are for operationally harvested and site prepared stands. Height-age relationships might be different for regeneration following wildfires where there is a flush 

of nutrients and where competing vegetation has been burned. Likewise, data from areas 

where overstory trees are killed by bark beetles may differ from data in this study because 

overstory trees continue to cast shade for many years in beetle-killed areas.

Results of this study could also differ from other techniques used to determine heightage relationships in young trees. One technique to determine total tree age from breast 

height age is to sample large trees with either increment cores or by severing the tree at 

groundline and at 4.5 ft. Sampling larger trees could give different answers than sampling 

regeneration-size trees because the larger trees are usually the survivors from denser stands 

that have self-thinned due to natural causes. Large trees could be those that exhibit the best 

early growth or they could be slower growing survivors that were spared from insects, 

diseases, or secondary succession. Conversely, randomly sampling regeneration-size trees 

could result in including many trees that will not become part of the eventual overstory. 

Our technique of sampling the best (tallest) trees meant that trees with the highest likelihood of reaching the overstory were used to develop height-age relationships.

Equations in Table 4 can be used to predict height-age relationships for 10 northern 

Rocky Mountain conifer species when the disturbance event is harvesting. Most of the 

trees in the sample are natural regeneration. Equations can be used for stands up to about 

15 yr old, with various amounts of residual overstory density, 4 site preparation methods, 

and 5 habitat type series. These equations are applicable to pre-climate change conditions, 

and, therefore, are valuable as reference data.
18 USDA Forest Service RMRS-RP-82WWW. 2010.

References

Baskerville, G. L. 1972. Use of logarithmic regression in the estimation of plant biomass. Canadian 

Journal of Forestry. 2:49-53.

Berglund, D.; Bush, R.; Zack, A. 2008. Estimates of years to breast-height for large conifer tree 

species in the Northern Region. Rep. 08-03 v3.0. Missoula, MT: USDA Forest Service, Region 

One. 20 p.

Cooper, S. V.; Neiman, K. E.; Roberts, D. W. 1991. Forest habitat types of northern Idaho: A second 

approximation. Gen. Tech. Rep. INT-236. Ogden, UT: USDA Forest Service, Intermountain 

Research Station. 143 p.

Daubenmire, R. 1959. A canopy-coverage method of vegetation analysis. Northwest Science. 

33:43-64.

Daubenmire, R. 1966. Vegetation: identification of typal communities. Science. 151:291-298.

Ferguson, D. E.; Carlson, C. E. 1993. Predicting regeneration establishment with the Prognosis 

Model. Res. Pap. INT-467. Ogden, UT: USDA Forest Service, Intermountain Research Station. 

54 p.

Ferguson, D. E.; Stage, A. R.; Boyd, R. J. 1986. Predicting regeneration in the grand fir-cedar-hemlock 

ecosystem of the northern Rocky Mountains. Forest Science Monograph 26. Washington, DC: 

Society of American Foresters. 41 p.

Haig, I. T. 1932. Second-growth yield, stand, and volume tables for the western white pine type. 

Tech. Bull. 323. Washington, DC: U.S. Department of Agriculture. 67 p.

Kirk, R. E. 1982. Experimental design, second edition. Brook/Cole Publishing Company, Monterey, 

CA. 911 p.

Littell, R. C.; Milliken, G. A.; Stroup, W. W.; Wolfinger, R. D. 1996. SAS system for mixed models. 

SAS Institute, Cary, NC. 633 p.

Moeur, M. 1985. COVER: A user’s guide to the CANOPY and SHRUBS extension of the Stand 

Prognosis Model. Gen. Tech. Rep. INT-190. Ogden, UT: USDA Forest Service, Intermountain 

Research Station. 49 p.

Parker, T.; Johnson, F. D. 1987. Branching and terminal growth of western redcedar. Northwest 

Science. 61:7-12.

Pfister, R. D.; Kovalchik, B. L.; Arno, S. F.; Presby, R. C. 1977. Forest habitat types of Montana. 

Gen. Tech. Rep. INT-34. Ogden, UT: USDA Forest Service, Intermountain Forest and Range 

Experiment Station. 174 p.

Rehfeldt, G. E.; Ferguson, D. E.; Crookston, N. L. 2008. Quantifying the abundance of co-occurring 

conifers along Inland Northwest (USA) climate gradients. Ecology. 89:2127-2139.

Stage, A. R. 1976. An expression for the effect of aspect, slope, and habitat type on tree growth. 

Forest Science. 22:457-460.

Steele, R.; Pfister, R. D.; Ryker, R. A.; Kittams, J. A. 1981. Forest habitat types of central Idaho. 

Gen. Tech. Rep. INT-114. Ogden, UT: USDA Forest Service, Intermountain Forest and Range 

Experiment Station. 138 p.

Wykoff, W. R.; Crookston, N. L.; Stage, A. R. 1982. User’s guide to the Stand Prognosis Model. 

Gen. Tech. Rep. INT-133. Ogden, UT: USDA Forest Service, Intermountain Forest and Range 

Experiment Station. 112 p.

Wykoff, W. R. 1986. Supplement to the user’s guide for the Stand Prognosis Model–version 5.0. 

Gen. Tech. Rep. INT-208. Ogden, UT: USDA Forest Service, Intermountain Research Station. 

36 p.
USDA Forest Service RMRS-RP-82WWW. 2010. 19

Appendix. Examples of using height-age equations shown 

in Table 4.

Example 1. Predict height of 15-yr-old ponderosa pine on a grand fir habitat type, 

Clearwater NF, no residual overstory, and mechanical site preparation. The value 1.28 

is the log bias correction factor for the ponderosa pine equation.

Height = 1.28 * [ exp (-1.7936 + 1.3737*ln(age) - 0.0052*ba + 0.0885 + 0.1642)]

Height = 11.3 ft

Example 2. Predict the age at which a western larch will reach 4.5 ft, residual overstory 

= 20 ft2

/acre, elev = 35, Lolo NF. The value 1.27 is the log bias correction factor for 

the western larch equation.

Height = 1.27 * [ exp (-0.8617 + 1.3093*ln(age) - 0.0038*ba - 0.0136*elev - 

0.0770) ]

Set Height = 4.5 ft, and solve for age

age = exp [ (ln(4.5/1.27) + 0.8617 + 0.0038*ba + 0.0136*elev + 0.0770)/1.3093 ]

age = 8.2
Federal Recycling Program Printed on Recycled Paper

Rocky

 Mountain

 Research Station

The Rocky Mountain Research Station develops scientific information 

and technology to improve management, protection, and use of the 

forests and rangelands. Research is designed to meet the needs of 

the National Forest managers, Federal and State agencies, public and 

private organizations, academic institutions, industry, and individuals. 

Studies accelerate solutions to problems involving ecosystems, range, 

forests, water, recreation, fire, resource inventory, land reclamation, 

community sustainability, forest engineering technology, multiple use 

economics, wildlife and fish habitat, and forest insects and diseases. 

Studies are conducted cooperatively, and applications may be found 

worldwide.

Station Headquarters

Rocky Mountain Research Station

240 W Prospect Road

Fort Collins, CO 80526

(970) 498-1100

Research Locations

Reno, Nevada

Albuquerque, New Mexico

Rapid City, South Dakota

Logan, Utah

Ogden, Utah

Provo, Utah

The U.S. Department of Agriculture (USDA) prohibits discrimination in all its 

programs and activities on the basis of race, color, national origin, age, disability, 

and where applicable, sex, marital status, familial status, parental status, religion, 

sexual orientation, genetic information, political beliefs, reprisal, or because all 

or part of an individual’s income is derived from any public assistance program. 

(Not all prohibited bases apply to all programs.) Persons with disabilities who 

require alternative means for communication of program information (Braille, 

large print, audiotape, etc.) should contact USDA’s TARGET Center at (202) 

720-2600 (voice and TDD). To file a complaint of discrimination, write to USDA, 

Director, Office of Civil Rights, 1400 Independence Avenue, S.W., Washington, 

DC 20250-9410, or call (800) 795-3272 (voice) or (202) 720-6382 (TDD). USDA 

is an equal opportunity provider and employer.

Flagstaff, Arizona

Fort Collins, Colorado

Boise, Idaho

Moscow, Idaho

Bozeman, Montana

Missoula, Montana