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PNW- 283 December 1976

PREDICTING WOOD VOLUMES FOR PONDEROSA PINE

FROM OUTSIDE BARK MEASUREMENTS .

| P. H. Cochran, Prinetpal Research Soil Scientist

ABSTRACT

Assumption of a constant diameter inside. bark to diameter outside bark Tatio along the bole of ponderosa pine results in an underestimate of wood volume determined from optical dendrometer measurements in the STX program. This ratio gradually increases up the stem to a given diameter outside bark to diameter breast high outside bark ratio that varies with tree size and then decreases to the tip. Equations describing this change in bark thick-

ness can be incorporated into the STX program. Resulting estimates of diameters inside bark, volume segments, and whole tree volumes are closer to true values than estimates derived by the constant ratio assumption.

KEYWORDS: Volume estimation (tree), volume determination methods, bark | thickness, computer programs, STX, ponderosa pine.

DREST SERVICE - U.S. DEPARTMENT OF AGRICULTURE - PORTLAND, OREGON -

INTRODUCTION

Many studies in the Pacific Northwest are concerned wit th the response of sapling-, pole-, and small sawtimber-size ponderosa pine— trees to thinning, fertilization, and treatment of understory vegetation. Assessment of treatment effects on wood production requires conversion of diameter out- side bark (dob) at several points along the bole (usually determined with optical dendrometers) to diameter inside bark (dib) used in calculating wood volumes for standing trees.

In Grosenbaugh's (1964) STX program for processing tree measurements, three options are available) for the dob toidiby conversion) (a) constant: ratio option assuming a uniform dib/dob ratio along the bole; (2) an option assuming that dib/dob increases curvilinearly above diameter breast high (dbh) and decreases curvilinearly below dbh; (3) an option assuming that dib/dob decreases curvilinearly above dbh and increases curvilinearly below dbh. These options use field determinations of dbhib and dbhob.

The constant ratio option (option 1) has been used in the Pacific Northwest for ponderosa pine without evidence to support its use. Wiant and Koch (1974) found that the constant ratio option was most accurate for yellow poplar, red maple, northern red oak, black oak, and scarlet oak. Mesavage (1969) concluded that the second option was best for estimating volumes of loblolly, shortleaf, slash, and longleaf pines.

Grosenbaugh (1964) did arrange his program to receive user supplied options, and the literature indicates that none of the three options describe the change in bark thickness along the bole for some conifers. Saikku (1973, figs. 4 and 5) found that bark thickness of Scots pine decreased with height up the stem below about 6 meters. From between 4 and 6 m to the tip (14 to 20 m), bark thickness remained constant (about 5 m). MacDonald (1973) examined outside and inside bark girths along the bole of Scots pine, Douglas-fir, Sitka spruce, Norway-.spruce, and European larch. He found in general that the ratio

girth outside bark-girth inside bark

girth outside bar nO

decreased with increasing distance above dbh through the lower third of the bole, remained nearly constant from one-third to one-half of the stem, and then increased in the upper one-half of the stem. Brickell (1970) mentioned that the dib/dob ratio may increase, remain nearly constant, then decrease as measurement progresses up the stem. An algebraic rearrangement of Brickell's equation (5) which covers this possibility is

_,.(dbhob-dbhib b-1 arby dope (dbhob-dbnib | (be pre | oc te

Another equation derived in this study, which also describes this pattern of dib/dob along the stem, is

sib/dobe (abhi /adnob) [1 +(dob /apnod)#-PCIP/AERE) aon fapnon) “ACOH / ANCE), METHODS Data for different sites and sizes and ages of trees were collected in

Oregon and Washington to determine patterns of dib/dob variation 29 long stems. For each location, at least 10 trees were felled. Age at 1- foot2 stump and

i Scientific names of trees mentioned are listed on page 8.

2f Metric unit conversion factors are listed on page 8.

(2)

total height to the nearest 0.1 foot were determined. Nails were driven at the 1-foot stump, dbh, and at decile height intervals from dbh to the tip. Diameter ob measurements were taken at these points with a caliper while the inside edge of the graduated portion of the caliper was resting on the nailhead. Then patches of bark were peeled, exposing the wood at 90 and 270 degrees around the bole from the nail, allowing the dib measurements to be made with calipers, again resting on the nail. For each tree, these dob and dib measurements were taken to the nearest 0.05 inch for 11 locations along the bole including stump and dbh.

Diameter ib/dob ratios were calculated for each point on each tree and then plotted as a function of dob/dbhob. Diameter ib/dob ratios gradually increased up the stem to a given dob/dbhob which varied with tree size, then gradually decreased for points progressively farther up the tree. None of the three options in the STX program appeared to describe the resulting pattern. Both equations (1) and (2) resulted in significant fits for points above dbh. Equation (1) could not always be fit significantly to points below dbh. Bark thickness at stump was highly variable for small sawtimber- size trees and not always predictable from dbhib/dbhob. Fortunately, stump bark thickness can be sampled directly in field studies.

Ponderosa pine is a rough-barked species resulting in considerable var- iability in dib/dob. Equations (1) and (2) were rearranged so that factor (dib/dob)/(dbhib-dbhob) for equation (1) and factor (dib/dob) /(dbhib/dbhob) for equation (2) could be fitted as a function of dob/dbhob for groups of at least 10 trees of similar sizes for each sample location. This re- arrangement forces the curves through the point (1, 1) for each tree where dob equals dbhob and produces more homogeneous variances. Fitting by iteration to minimize the sums of squares of the residuals was done as though all data points were independent. Coefficient b in equation (1) and coefficients a, b, c, and d in equation (2) were determined for 10 separate size classes sampled east of the Cascades in Oregon and Washington. Coeffi- cient b in equation (1) and coefficient a in equation (2) varied with tree size. Coefficients b, c, and d in equation (2) did not appear to vary with tree isiize.

Coefficients b (equation 1) and a (equation 2) were functions of the average dbh in inches squared times total height in feet (D4H) for the 10 or more trees used in their derivation. Equations (1) and (2) with their coefficients were then tested with more tree data collected in additional areas of Oregon and Washington. Diameters ib for these test trees were measured directly and also calculated from corresponding dob's using the constant ratio assumption as well as equations (1) and (2) (after shifting the dob term from the left- to the pe eee side) with respective coeffi- cients b and a determined using the D4H for each tree. Volumes for stem segments above dbh were then calculated using actual and estimated dib's with Smalian's formula. Volumes of individual tree segments were summed to obtain whole tree volumes above dbh. These calculations were repeated to include the stump dib's, stump to dbh volume segments, and whole tree volumes above stump.

In a further test 206 trees were sampled on the Deschutes National Forest by the timber management staff. Form class (dib at 16 feet above stump height divided by dbhob) was calculated using actual dib's at 16 feet above stump and the dib's estimated from these 16-foot dob's using option 1 and equations (1) and (2).

Comparisons of dib's, volume segments, and whole tree volumes arising from application of the constant ratio assumption as well as equations (1) and (2) were made from calculations of the root mean square deviation (RMSD):

RMSD = /i(actual value - estimated value) (3) number of estimates

for corresponding sets of data. The lower the root mean square deviation for a set of estimated values the closer those values are to the actual values. Freese's (1960) test of accuracy was also applied to estimated whole tree volumes to separate the bias and lack of precision components of inaccuracy where accuracy was not within defined acceptable limits.

RESULTS AND DISCUSSION

The relationship between coefficient b of equation (1) and D7H for ponderosa pine in the Pacific Northwest is

log, gb=0. 280187646-0.040677437 (log DH) . (4) The relationship between coefficient a of equation (2) and D7H is log, ga=-0.335135683-0.062052639 (log DH). (5)

The r? and F values were 0.73 and 26.42 for regression (4) and 0.65 and 18.67 for regression (5). Coefficients b, c, and d for Northwest ponderosa pine are’ 0.8057,” 0!)2101) and 0))So38).) sAppilacationmotmequiacalons mG) ian @2e) ie

and the constant ratio option to the 114 trees used in defining the coeffi- cients showed that application of equation (1) was superior to equation (2) in predicting dib's, volume segments, and whole tree volumes above dbh. The constant ratio option (option 1 in the STX program) was far inferior to equations (1) and (2), resulting in a 7.03-percent underestimate of total actual volume and much higher root mean square deviations for dib's, volume segments, and whole tree volumes (table 1).

At each of 39 locations east of the Cascades in Oregon and Washington, 5 to 20 additional trees were sampled to test the equations.

Trees were sampled on every National Forest and on the Warm Springs and Spokane Indian Reservations. Site vindiex for the sample locations ranged

from 67 to 138, representing the range found in eastern Oregon and Washington.

Trees in "very smali'' and "small" size classes (tables 2 and 3) were sampled in the same way as the trees used in deriving equations (4) and (5). Trees in the larger size classes were sampled for site index and yield studies conducted by James W: Barrett, research forester, jait the orivicul tune Laboratory in Bend. Diameter ob and dib measurements for these trees were taken on sections cut at 1 foot, dbh, 10 feet, and then at 5- or 10-foot intervals up the stem, depending on tree size. Of these "large" trees, 64 had much greater D¢H's than the largest trees used in defining coefficients in equations (1) and (2) (table 2).

For trees with D?H's larger than 960, the constant ratio option is clearly inferior to both equations (1) and (2) for determining dib's and volumes above dbh (tables 2 and 3). Root mean square deviations were higher for these dib's, and volumes determined by option (1) and total volumes were underestimated. For the "very small" size class, differences between the three methods of determining dib's and volumes are slight; but option 1 was more accurate for a greater number of trees than either equation (table 3). Root mean squares for diameters, volume segments, and whole tree volumes for all but the smallest size class are lower for equation (1) than equation (2) (table 2). Equation’ (1) did a better job of estimating) dibys jand) volume segments for more trees in the two largest size classes than did equation C2 MGeabiley syne

Bi Barrett, James W. Site index curves for managed stands of ponderosa pine. Unpublished data on file at Pacific Northwest Forest and Range Experiment Station, Silviculture Laboratory, Bend, Oreg.

——

Table 1--fotal volwnes above dbh, differences between actual and estimated volwnes above dbh, and root mean square deviations for dib's, volwne segments, and whole tree volwnes above dbh for 114 trees used in defining the coeffictents in equattonsa (1) and (2)

Difference between Root mean square deviations

option option option

Total estimated and actual

actual total volumes Diameters Whole tree volumes volume

(cubic Constant Constant Constant Constant

feet) ratio ratio ratio Eq.(1) | Eq.(2) ratio Eq. (2)

cere Percent ----- ----- Inches ----- ---------- = Cubic feet-----------

1,265.35 -7.03 -0.21 -0.79 0.267 0.150 0.171 0.198 0.077 0.112 1.650 0.559 0.826

Table 2--Total volwnes above dbh, differences between estimated and actual volwnes above dbh, and root mean square deviations for dib's, volwne segments, and whole tree volwnes above dbh

Difference between estimated and total actual volumes

Root mean square deviations

Size,

class— Diameters

Volume segments Whole tree volumes

mcr ee Percent -=--- ----~- Inches -=--- ---------- Cubic feet ----------- Very sma113/ 69 70.51) 1-42 ALE) +1.87 0.092 0.096 0.092 0.007 0.007 0.007 0.057 0.050 0.053 sma14/ 95 216.12 -4.88 -.76 -1.06 171 142 142 025 -015 017 -205 124 144 Medium2/ 200 2,979.16 -5.34 +.69 +.79 282 -169 oliZA:) -212 -110 wee 1.185 -574 -716 Large®/ 64 7,142.60 -6.32 +1.72 +1.43 -638 367 472. 759 419 -513 9.673 4.84) 6.036

ay) Average o°H is the average for the 5 to 20 trees sampled at each location. 2/ Constant ratio option.

ES) Average o*H ranged from 436 to 959 in? ft.

4/ Average D*H ranged from 1,044 to 2,642 in” ft.

5/ Average 0°H ranged from 2,400 to 11,300 in” ft.

5/ Average v*H ranged from 35,000 to 149,000 in? ft.

Table 3--Nunber of test trees by size class and by equations (1) and (2) when these equations produced estimates closer to true values than did the constant ratio option

Equation (1) Equation (2)

Size class Volume Total Volume Total segments | volume segments | volume Very smal1l/ 69 21 25 27 30 27 26 sma112/ 95 67 63 64 67 64 66 Medium?/ 200 162 168 166 160 163 161 Large4/ 64 43 47 46 39 46 49 Total 428 293 303 303 296 300 302

V Average 0H ranged from 436 to 959 in? fit:

cd Average 0H ranged from 1,044 to 2,642 in? ft. 3/ Average 0°H ranged from 2,400 to 11,300 iné ft. 4/ Average 0¢H ranged from 35,000 to 149,000 in? hts

For the 206 trees used to estimate form class, dbh varied from 11.5 to 47.3 inches and heights ranged from 60 to 160 feet. Many of these trees were larger than those used in defining coefficients in equations (1) and (2). Actual form class for these trees was 0.795. Calculated form classes using dib's determined by equations (1) and (2) and the constant ratio option were 0.801, 0.794, and 0.773. RMSD's for calculated dib's at 16 feet were 0.579, 0.620), and 0.811 for equations -(')r (2), and the constant, ~watromopitdonr:

The underestimates of volume above dbh that result when the constant ratio option is used to determine dib's become more serious as tree size increases (table 2). Freese's (1960) test shows that this is not a precision error but a bias error. This bias arises because the bark thickness in the middle of the bole is thinner than predicted by the constant ratio method. This error suggests that, when stump bark thickness is not directly available from past dendrometer measurements, volumes should be recalculated for ongoing studies if a reasonable way to estimate stump dib's is available. Use of equation (1) to predict dib's from dob's larger than dbhob may result in serious error because the ratio dob/dbhob can be very close to the value for the b coefficient which is greater than 1. When this occurs, the factor | (b-dob/dbhob) in equation (1) can be a very small negative or positive number resulting in a calculated dib that can be much too large--the usual case--or small. This leaves equation (2) to determine all dib's or equation (1) or (2) to estimate dib's above dbh combined with the constant ratio option to estimate stump dib's from dbhob and dbhib. Each of these methods produces reasonable results (table 4), but the errors resulting from application of equation (1) alone are quite evident. Except for the ‘very small” size class; the lowest root mean square deviations were produced when equation (1) was used for dib's above dbh in combination with the constant ratio option for stump dib's (table 4). It should be pointed out that it is possible to have errors for dib's above dbh when equation (1) is applied in the case of un- usual stems with swelling of the bole above dbh.

Table 4--Total actual volumes, differences between estimated and actual volwnes above stwnp, and root mean square deviations for dib's, volwne segments, and whole tree volumes for the test trees

Root mean square deviations

Volume segments

Difference between estimated and total actual volumes

Size

class Whole tree volumes

Diameters

fectae n= - Po Percent ---- -----= Inches - ---- ---------- Cubic feet - ---------- Very sma113/ 101.10 0.44 -2.14 +1.67 0.122 0.499 0.096 0.011 0.026 0.007 0.057 0.070 0.055 +3.05 +2.85 -124 22 -010 -010 .068 . 068 sma114/ 264.11 -2.82 -2.13 -0.65 .200 - 932 149 -027 - 169 -018 -185 .571 -145 +0.56 +0.31 -179 .178 .020 -022 -126 - 144 Med ium2/ 3,531.97 -4.48 +427.64 -.16 .288 37.48 -327 -214 260.23 154 1.191 674.93 .673 +.62 +.70 -201 .208 115 - 136 -576 .720 Large®/ 7,764.92 -5.68 +32.78 +1.02 -599 13.98 -521 oP il tey/ -529 9.456 224.862 6.042 +1.73 1.46 -412 -498 «433 -524 5.077 6.300

y The first row for each size class presents values determined by using the constant ratio option or equations (1) and (2) to

calculate all dib's. The second row for each size class presents values where stump dib's were determined with the constant ratio option in every case.

2/ Constant ratio option.

a Average D¢H ranged from 436 to 959 in” ft.

4/ Average p¢H ranged from 1,044 to 2,642 in?

fite 5/ Average D¢H ranged from 2,400 to 11,300 in? fits

§/ average D°H ranged from 35,000 to 149,000 iné ft.

Setting required accuracy equal to 10 percent of the volume of the aver- age size tree within each size class in table 4 (0.14, 0.30, 1.8, and 12 cubic feet for the ''very small" to "large" size classes. Freese's (1960) test can be applied to the whole tree volumes estimated by each method. Resulting chi-square values (table 5) show that the constant ratio method is biased for all but the smallest size.class. Use of equations (1) and (2) for dib's above dbh. combined with the constant ratio for stump dib's produces estimated values for individual trees within the required limits unless a 1-to-20 chance has occurred.

Table 5--Chi-square values for Freese's (1960) test of accuracy comparing

measurements of whole tree volwnes ubove stump! with true values

Constant ratio é Equation (1) Equation (2)

Size class— Constant ratio

option-bias

Very smal13/ 43.904* 62.525* 62.525* 43.342* smal 14/ 138.783 64.378* 84.085* 118.859* Medium2/ 336.373 78.676* 122.931* 166.170" Large®/ 152.667 44.009* 67.766* 71.590*

Y determined by the constant ratio option and equations (1) and (2) for dib above dbh and by the constant ratio option for stump dib. Asterisks indicate that accuracy standards were met at the 5-percent level of probability.

2/ Accepted standards were that each tree would fall within 0.14, 0.30, 1.8, or 12 cubic feet of the true value for the smallest to the largest size class unless a ]-in-20 chance occurred.

3/ Average 0°H ranged from 436 to 959 in? fits

a/ Average 0¢H ranged from 1,044 to 2,642 in? ft.

2 2 Ft.

8/ average D°H ranged from 35,000 to 149,000 in® ft.

5/ Average D“H ranged from 2,400 to 11,300 in

CONCLUSIONS

None of the three options in Grosenbaugh's, (1964) STX program appear to describe the variation in dib/dob along the boles of ponderosa pine east of the Cascades in Oregon and Washington. The two equations presented here produce lower root mean square deviations for dib than did the constant ratio option which was formerly used. Equation (1) was originally presented by Brickell (1970) without recognition that coefficient b varied with tree size and results in lower root mean square deviations than equation (2) for dib's above dbh for all but "very small" trees. Equation (1) may produce errors for dib's estimated from dob's oad ed than dbhob. Both equations have one coefficient which varies with D4H since dib's are predicted at various points along boles of trees with varying heights and forms from a dib and dob measurement at a fixed location. Use of the constant ratio option results in biased estimates of wood volumes which are low for all but "very small" trees. Thus, growth increments in past ponderosa pine studies probably have been slightly underestimated.

Preliminary investigation indicates these equations work with lodgepole pine in Oregon (where equation (2) appears superior to equation (1)) and ponderosa pine from the Black Hills, although the coefficients are different. Since the STX program is widely used, usually with one of the three listed options, investigators elsewhere should be aware that perhaps other equations May more accurately describe dib/dob variation along boles of the species they work with.

METRIC CONVERSIONS

1 inch = 2.54 centimeters 1 foot = 0.3048 meter 1 DH (in” ft) = 1.9664 cm“ m

When D7H is expressed in cm? m rather than in? ft, equations (4) and G) Parnes cespectaveliys

log b = 0.280187646 - 0.04677437 (log (0.5085 D-H)), and log a = -0.335135683 - 0.062052639 (log: (0.5085 D°H)).

COMMON AND SCIENTIFIC NAMES OF TREES

ponderosa pine Pinus ponderosa Laws. yellow-poplar Lirtodendron tultptfera L. red maple Acer rubrum L. northern red oak Quercus rubra L. black oak Quereus velutitna Lam. scarlet oak Quereus cocetnea Muenchh. loblolly pine Pinus taeda L. i shortleaf pine Pinus echinata Mill. slash pine . Pinus etitottte Engelm. longleaf pine Pinus palustris Mill. Scots pine Pinus stlvestrts L. Sitka spruce Picea sitehensts (Bong.) Carr. Norway spruce Picea abtes (L.) Karst. European larch Lartx dectdua Mill. Douglas-fir Pseudotsuga menztestt (Mirb.) Franco lodgepole pine Pinus contorta Dougl. :

LITERATURE CITED :

Brickell James Ee 1970. Test of an equation for predicting bark thickness of western Montana species. USDA For. (Sery. Rese Note INT 1075 7 pia 1 euisl nite anita For. and Range Exp. Stn., Ogden, Utah.

POSSE, Io UIVJOWs WeESswesnyy aeecusceeyo Or, Sil, Oils ls,

Grosenbaugh, L. R. 1964. STX-FORTRAN 4 program for estimates of tree populations from 3P sample-tree-measurements. USDA For. Serv. Res. Pap. PSW-13, 49 p. Pace southwest) Fon. jand Range Exp oitninn BemiKerlcyaunGaletetae

MacDonald, James. 1973. The fonmsof the stem any coniferous) trees.) hore stryaw/eal2 ele Oe

Mesavage, Clement. 1969. Converting dendrometer estimates of outside-bark stem diameters to wood diameters on major southern pines. USDA For. Serv. Res. Note SO-93, 4p. south. For. and Range Exp. Stn., New Orleans, La.

Saikku, Olavi. 1973. Lannoituhsen Vaikutuksesta Mannyn Kuoren Maaraan Kangasmaalla (the effect of fertilization on the amount of the bark of Scotch pine forest land). Folia For. 184:3-15.

Wateinies Islkweamy Wo, dics, ehnel (ClucdStenen 15. Kkoeli. 1974. Predicting diameters inside bark from outside bark measurements of some Appalachian hardwoods. J. For. 12:775.

8 GPO 997-705