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United States Department of Agriculture

Forest Service

Intermountain Research Station

Research Note INT-359

August 1986

Joyce A) Schlieter’

ABSTRACT

Equations to estimate diameter at breast height outside bark from the stump diameter outside bark are presented for 13 lodgepole pine sites. The data came from three National Forests in Montana. General equations are also given for two varieties of lodgepole pine from data collected across the range of the species in North America. Simple linear regression methods were used. As an application, a procedure for obtaining tree volume is described.

KEYWORDS: diameter at breast height, d.b.h., stump diameter, volume

INTRODUCTION

Utilization researchers needed to predict diameter at breast height (d.b.h.) from stump diameter to reconstruct pretreatment stand tables. This reconstruction was necessary to correct for inadequate plot size in the original sampling scheme. The dominant species was lodgepole pine (Pinus contorta var. latvfolia).

Estimating d.b.h. from stump measurements has other applications, including estimating volume, verifying har- vesting practices following tree removal, determining the history of cutover lands, and assessing damage that results from adverse environmental conditions. In all cases, only the stump diameter is known.

Ziegler (1907) and Alemdag and Honer (1977) presented tabulations of the relationship between breast height and stump diameters for variety latifolia. The data were from Wyoming and Canada, respectively. Faurot (1977) gave an equation relating stump diameter to d.b.h. for lodgepole pine in the Northwest. These studies were neither site specific nor limited to small-diameter stems.

This paper presents equations to estimate d.b.h. from stump diameter for 13 small, overstocked lodgepole pine

The author is mathematical statistician stationed at the Intermountain Research Station’s Forestry Sciences Laboratory, Missoula, MT.

Estimation of Diameter at Breast Height from Stump Diameter for Lodgepole Pine :

3 A ei eet se pe ae he a - ened =

Re eS cea ape i Sere sites in Montana. General equa uations fordatifolia ene rayana representing the range of these lodgepole pibe

varieties in North America arp also giVeR. Nef

DATA COLLE cTION’

For the first study, data were collected from 15 stands on the Deerlodge, Gallatin, and Lewis and Clark National Forests in Montana. Some pretreatment characteristics of the stands are detailed in table 1. These stands are used to evaluate harvesting technology alternatives and to identify those that will result in financially feasible treatment for the existing economically submarginal conditions. This group of stands will also allow long-term evaluations of growth response and regeneration as well as other biological responses.

Original pretreatment stand tables were based on cir- cular fixed plots of 1/300 acre. After harvesting, some stands had few trees remaining, so the plot size was ex- panded to 1/100 acre in order to obtain an adequate post- treatment sample. This enlargement of plot size created statistical problems that could be corrected only by enlarg- ing the pretreatment plot size. Consequently, all stands were reinventoried using either a 1/50-acre or a 1/100-acre plot size.

By the time the reinventory need became apparent, harvesting had been completed on most stands. This re- quired a reinventory procedure that would include both standing residual trees and stumps, and at the same time acquire the data base needed to estimate the d.b.h. of the cut trees. To do this, original 1/300-acre plot centers were located and an enlarged circumference established. Within the plot, both d.b.h. and stump diameter were measured on standing trees to the nearest 0.1 inch at heights of 4.5 feet and 4 inches. For cut trees, stump diameters were taken at 4 inches above the ground or at the highest point on stumps less than 4 inches. These measurements were made outside the bark. Small trees (<3.0 inches d.b.h.) were not well represented in the residual stand because most had been cut. The sample of smaller trees was therefore augmented on five units by adding approxi- mately 40 trees from each control area.

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Table 1—Stand characteristics of 15 lodgepole pine stands in Montana

Eleva- Habitat Stand National Forest Age tion Density Basal area type’ Years Feet Stems/acre Ft */acre Spring Emery Deerlodge 99 6,800 3,168 211 ABLA/LIBO Ballard North Deerlodge 80 6,300 2,997 281 ABLA/LIBO Ballard South Deerlodge 80 6,300 2,249 285 ABLA/LIBO Corduroy East Deerlodge 85 5,900 2,318 206 ABLA/VACA Corduroy West Deerlodge 88 5,900 3,191 196 ABLA/VACA Corduroy North Deerlodge 81 5,900 7,046 202 ABLA/VACA Rattling Gulch Deerlodge 59 5,600 997 139 PSME/VACA Echo Lake Deerlodge 88 6,700 6,159 241 PSME/LIBO South Flat? Gallatin 86 6,800 2,381 171 ABLA/VASC Getcho? Gallatin 96 6,800 1,870 178 ABLA/CARU Reas Pass? Gallatin 88 7,200 1,272 155 ABLA/VASC Dry Fork East Lewis and Clark 57 5,400 4,799 153 PSME/LIBO Dry Fork West Lewis and Clark 50 5,400 5,318 145 PSME/LIBO Currie North Lewis and Clark 54 5,000 2,490 147 PIEN/LIBO Wet Park Lewis and Clark 88 6,800 4,195 247 ABLA/CACA

‘Habitat types from Pfister and others (1977). These three stands were combined in this study.

Table 2—Coefficients and descriptive statistics of equations y = a + bx, where y is d.b.h. in inches outside bark and x is stump diameter in inches outside bark; for 13 lodgepole pine sites in Montana

Sample Range Site Stand a b size of x se R? Inches 1 Spring Emery 0.171 0.806 171 2-8 0.210 0.95 2 Ballard North .428 .728 194 4-12 .247 .96 3 Ballard South .493 .720 255 3-13 .259 .96 4 Corduroy East .155 .193 241 1-11 .210 .98 5 Corduroy West .319 .766 185 2-9 .223 .96 6 Corduroy North .212 ats) 341 1-8 .159 .96 7 Rattling Gulch .237 .758 181 1-13 319 .98 8 Echo Lake .149 774 185 1-8 .197 97 9 South Flat, Getcho, Reas Pass .325 .778 236 2-10 .221 .95 10 Dry Fork East .125 .809 155 2-7 .138 .97 11 Dry Fork West — .027 842 234 1-7 151 .98 12 Currie North — .079 .853 128 2-9 151 .97 13 Wet Park .246 SOUL, 71 2-8 171 97

(8,765 feet) and highest at 37.5 degrees (7,879 feet), with only one longitude per latitude.

Both d.b.h. and stump diameter were recorded in milli- meters but were converted to inches for this report. The stump diameter was measured at 6 inches above the ground. Measurements were made outside the bark.

EQUATIONS

Simple linear regression methods were used to develop stump-d.b.h. equations for the two studies described above. For estimating d.b.h. from stump diameter, these simple models have been shown to be as reliable as more complicated models (Bylin 1982). The form of the equation is y = a + ba, where y is the estimated d.b.h. in inches outside bark and «x is the stump diameter in inches outside bark. The equation coefficients for the Montana study

For the second study on general characteristics, the data were collected as part of a major study on the lodgepole pine resource across the range of the species in North America (Koch 1986). This research involved sampling 243 latifolia trees from latitudes 40 through 60 degrees at 2.5-degree intervals across 10 degrees of longitude. The area sampled reached from central Utah and Colorado north to the Yukon Territory. Trees with d.b.h. of 3, 6, and 9 inches were sampled at low, medium, and high elevations within each latitudinal zone; elevational zone averaged much higher in the south (8,000 to 10,000 feet) than in the north (2,000 to 3,000 feet). In addition, 36 murrayana trees in the same diameter classes were sampled at medium elevation at four latitudes (37.5, 40, 42.5, and 45 degrees) in California and Oregon. Elevations sampled for this variety averaged lowest at 45 degrees

Table 3—Coefficients, descriptive statistics, and general informa- tion for estimating d.b.h. from stump diameter for two lodgepole pine varieties. The equation form is y = a + bx, where y is d.b.h. in inches outside bark and x is stump diameter in inches outside bark

Factor latifolia murrayana a 0.338 0.378 b .790 .802 Sample size 243 36 Range of x (inches) 3-13 3-12 se .402 .344 R? 97 .98 Average age (years) 90 81

sites are given in table 2. More general equations for varieties latifolia and murrayana are shown in table 3.

Statistics given in the tables for each equation are “‘se’”’ and ‘“‘R’. The ‘‘se’”’ stands for the standard error of the estimate and is calculated as the square root of the residual mean square. The ‘‘R®” is the percentage of the variation explained by the regression.

For comparison purposes, the equation developed by Faurot (1977) for lodgepole pine is y = —0.292 + 0.874 x (R? = 0.98 and se = 0.546). In Faurot’s equation y is the estimated d.b.h. in inches outside bark and « is the stump diameter in inches inside bark. The sample of 227 trees was taken from unmanaged second-growth stands in western Montana. Trees were less than 80 years old. Stump diameters were measured at a 1-foot stump height and ranged from 1.4 to 20.7 inches.

USING THE EQUATIONS

The equations, as given in table 2, have most application to small lodgepole pine in western Montana with stump diameters falling within the ranges shown. The specific equation can be chosen by matching site conditions to a stand in table 1. In the absence of this site information, the general equations in table 3 could be used.

Stump heights for all equations were less than the Forest Service standard of 1 foot, which is more common in sawtimber than in post-pole utilization practices. These equations represent relationships between stump diameter and d.b.h. for a 4-inch stump height (6 inches for the general equations). This must be remembered when apply- ing the equations.

A useful application of these results is determining the cubic foot tree volume when only the stump diameter is known. This can be done with the following procedure:

Step 1: estimate d.b.h. from stump diameter Step 2: estimate tree height from d.b.h. Step 3: estimate tree volume using height and d.b.h.

Step 1 is the main topic of this paper; steps 2 and 38 are detailed here.

In addition to the fixed plots described above, variable plot data were collected for the Montana study. The variable plot measurements included tree height and d.b.h. so that equations to predict height for each site could be developed. The form of the relationship is y = ¢ + d log; ) x, where y is tree height in feet and x is d.b.h. in inches outside bark. The equation coefficients for the Mon- tana study sites are given in table 4. Similar equations

Table 4—Coefficients and descriptive statistics of equations y = c + d log,, x, where y is tree height in feet and x is d.b.h. in inches outside bark; for 13 lodgepole pine sites in

Montana

Sample Range Site Stand c d size of x se R?

Inches 1 Spring Emery 12.41 45.82 185 1.6-7.7 3.52 0.76 2 Ballard North 12.51 57.21 263 1.6-9.6 4.07 82 3 Ballard South 7.83 64.49 143 1.8-9.6 4.88 76 4 Corduroy East 17.43 47.61 204 1.9-8.2 3.03 81 5 Corduroy West 16.20 44.01 214 1.0-7.6 3.54 .80 6 Corduroy North 14.34 37.00 92 1.0-5.6 3.47 73 7 Rattling Gulch 14.95 44.10 243 2.1-9.8 4.36 61 8 Echo Lake 16.50 41.56 104 1.0-6.3 3.34 79

9 South Flat, Getcho,

Reas Pass 11.74 48.19 496 1.4-8.5 3.28 .80 10 Dry Fork East 14.38 36.35 160 1.1-5.5 3.18 at As) 11 Dry Fork West 12.46 36.14 175 1.0-5.6 3.17 ath) 12 Currie North 11.65 45.04 Ue 1.5-7.3 3.41 “fal 13 Wet Park 8.62 48.70 133 1.3-9.3 3.59 .83

Table 5—Coefficients and descriptive statistics for estimating tree height from d.b.h. for two lodgepole pine varieties. The equation form is y = c + d log,, x, where y is tree height in feet and x is d.b.h. in inches outside bark

Sample Range Variety c d size of x se R? Inches 1 = J/atifolia — 1.60 68.04 241 2.87-9.41 7.88 0.74 2 = murrayana — 12.60 76.96 36 2.87-9.41 11.41 .65

were developed for varieties latifolia and murrayana using data collected for the general characterization study. These are shown in table 5.

Once the height is estimated from the d.b.h., tree volume can be calculated using an equation derived by James Brickell, formerly with the Intermountain Research Station (Cole 1971):

V = 0.002782 D2H (H°-9488/1)0-0959)

where V is tree volume in cubic feet, D is the d.b-h. in inches outside bark, and H is tree height in feet.

CONCLUSION

The equations here provide a method by which tree diameter, height, and volume can be estimated after harvesting using stump diameter. The equations developed predict quite well and give reasonable estimates across the range of stump diameters in these data bases. They pro- vide new information about the smaller lodgepole pine in the Northern Rocky Mountains specifically, and in general across the North American range of the species.

REFERENCES

Alemdag, I. S.; Honer, T. G. Metric relationships between breast-height and stump diameters for eleven tree species from eastern and central Canada. Information Report FMR-X-49M. Ottawa, ON: Department of the Environment, Canadian Forestry Service, Forest Management Institute; 1977. 62 p.

Bylin, Carl V. Estimating d.b.h. from stump diameter for 15 southern species. Research Note SO-286. New Orleans, LA: U.S. Department of Agriculture, Forest Service, Southern Forest Experiment Station; 1982. 3 p.

Cole, Dennis M. A cubic-foot stand volume equation for lodgepole pine in Montana and Idaho. Research Note INT-150. Ogden, UT: U.S. Department of Agriculture, Forest Service, Intermountain Forest and Range Experi- ment Station; 1971. 8 p.

Faurot, James L. Estimating merchantable volume and stem residue in four timber species: ponderosa pine, lodgepole pine, western larch, Douglas-fir. Research Paper INT-196. Ogden, UT: U.S. Department of Agriculture, Forest Service, Intermountain Forest and Range Experiment Station; 1977. 55 p.

Koch, Peter. Gross characterization of lodgepole pine trees in North America. Missoula, MT: U.S. Department of Agriculture, Forest Service, Intermountain Research Station, Forestry Sciences Laboratory; 1986. 486 p. [Review draft.]

Pfister, Robert D.; Kovalchik, Bernard L.; Arno,

Stephen F.; Presby, Richard C. Forest habitat types of Montana. General Technical Report INT-34. Ogden, UT: U.S. Department of Agriculture, Forest Service, Inter- mountain Forest and Range Experiment Station; 1977. 174 p.

Ziegler, E. A., compiler. Forest tables—lodgepole pine. Circular 126. Washington, DC: U.S. Department of Agriculture, Forest Service; 1907. 24 p.

August 1986 Intermountain Research Station 324 25th Street Ogden, UT 84401