Sim 11DmriBIIIm IIBirll IGIBI 11111!11&-IIDJIII NIB'IDIB

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1 . t ' Sim 11DmriBIIIm IIBirll IGIBI 11111!11&-IIDJIII NIB'IDIB ' PNW-97 May 1977 ESTIMATING D.B.H. FROM STUMP DIAMETERS IN SECOND-GROWTH DO UGLAS-FIR by Robert 0. Curtis, Principal Mensurationist and James D. Arney,!! Mensurationist ABSTRACT Gives equations for estimating diameters at breast height of second-groth Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco) from measured stump diameters over bark and stump heights, based on measurements at lo'cations in estern Oregon and Washington. KEYWORDS: D.b.h. measurements, stump measurements, (-d.b.h. estimates, Douglas-fir, Pseudotsuga menziesii Centralia,!! James D. Arney is ith Forestry Research Center, Weyerhaeuser Company, Wash.

2 INTRODUCTION In a yield study of coastal Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco), e found that some of our thinned plot records lacked a tally of trees cut in the initial thinning. In some cases there as a record of stump diameters of cut trees or such information could be obtained by field measurements. To reconstruct initial stand conditions, e needed appropriate regressions relating diameter at breast height (d. b.h.) to diameter and height of stump. Similar needs to estimate tree d.b.h. from stump measurements occur in other research and management activities. Several people have developed estimating equations for specific stands or local areas; but e found no such equations (l) hich ere based on a sample distributed over a ide geographic area and a range of site conditions, () hich applied to a ide range of diameters ithin second-groth stands, and (3) hich explicitly included stump height as a variable. Therefore, e have developed such equations from field measurements made by the Pacific Northest Forest and Range Experiment Station's Olympia Laboratory and by Weyerhaeuser Company's Forestry Research Center. THE DATA Measurements ere obtained from field installations in estern Washington and Oregon. Total number of trees measured as 5, ith a range in d.b.h. from to inches. Maximum age as about 0 years; hoever, most trees ere much smaller and younger than the maximum size and age. Field procedure on each individual plot, ithin each installation, as: 1. Select a number (usually four) of normally formed Douglas-fir, across the range of diameters present.. Measure and record to nearest 0.1 inch: a. d.b. h. outside bark. b. d.o.b. (diameter outside bark) at.0 feet above ground level. c. d.o.b. at 1.0 foot above ground level. d. d.o.b. at 0.5 foot above ground level. e. d. o.b. at 0.5 foot above ground level (measurement omitted here root sell made measurement impracticable). All measurements ere made ith diameter tape. 1. Individual installations Regressions of the form ANALYSIS D.b.h. a + b(d.o.b.) + c(d.o.b.) ere fitted to the data from each installation, separately for each height of measurement, H.0, 1.0, 0.5, and 0.5 ft. Usually, the squared term as nonsignificant. When present, curvilinearity as slight.

3 Regressions ere plotted and superimposed. Inspection indicated that (a) lines for a given stump height ere parallel or nearly so, and (b) although there might be small differences in elevation, possibly related to stand conditions, any such differences ere too small to have much effect on practical applications.. Individual heights of measurement All measurements for a given height ere combined and a regression D.b.h. a + b(d.o.b.) + c(d.o.b.) as fitted separately for each stump height. In each regression, the squared term as statistically significant but curvature as slight and apparently due mainly to a fe of the largest trees. 3. All data combined Scatter diagrams, calculated standard errors of estimate, and plots of residuals indicated that variance increased ith diameter outside bark and ith distance of the measurement point from breast height. A eighted stepise conditioned regression as fitted to all measurements combined, of the form: [d.b.h. - d.o.b.] a (.5-H) + a (.5-H) 1 + [d.o.b.] [b (.5-H) b (.5-H) ] 1 + [d.o.b.] [c (.5-H) + + c (.5-H) ] [d.o.b.] [d (.5-H) + + d (.5-H) ] 1!< in hich 1/[(.5-H)(d.o.b.) ], a eighting factor hich provided approximate uniformity of variance; and a, b, c, and d are regression coefficients. here The resulting equation can be ritten as: D. b. h. a + b(d.o.b.) + c(d.o.b.) + d(d.o.b.) 3 ; (1) a b c (H); (H) (H) (H) (H) ; (H) (H) ; and d (H). D.b.h. is diameter outside bark, in inches, at breast height. D.o.b. is diameter outside bark, in inches, at point of stump measurement. 3

4 H is height above ground, in feet, at point of measurement. Standard error of estimate (SEE) of this equation as 0.00; i.e., SEE in inches 0.00 (.5-H) (d.o.b.), d.b.h. Curves corresponding to equation 1 are shon in figure 1. For individual height measurements, equation 1 reduces to: H.0 feet: 3 D.b.h (d.o.b.) (d.o.b.) (d.o.b.). () H 1. 0 foot: 3 D.b.h l (d.o.b.) (d.o.b.) (d.o.b.). (3) H 0. 5 foot: 3 D.b.h (d.o.b.) (d.o.b.) (d.o.b.). () H 0.5 foot: 3 D.b.h l (d.o.b.) (d.o.b.) (d.o.b.). (5) Curves corresponding to the above equations are shon in figures -5, together ith superimposed data points (a fe points over 0 inches omitted). Relationships are virtually straight lines for trees under inches; curvature is slight and is due to the fe trees of larger size. 36 H.0 ft 3 H1.0 ft H0.5 ft H0.5 ft en :c (. 0 :c co Figure 1--curves of d.b.h. over stump d.o.b. and stump height (equation 1).

5 36 3 (f :I u 0 z :I en Q Figure --Data points and curve of d.b.h. over stump d.o.b. at.0 feet above ground (equation ) (f :I u 0 z :I en Q Figure 3--Data points and curve of d.b.h. over stump d.o.b. at 1.0 foot above ground (equation 3). 5

6 36 3 (/ :r u z :r cc ,. :: /'' -L LL-L -L.LiJI-LiJ-Li i-ll IJi-LJi-LIJi-L i-li -L -L i l Figure --Data points and curve of d. b.h foot above ground (equation ). over stump d.o.b. at 36 3 (/ :r u z :r cc Figure Data points and curve of foot above ground (equation d. b. h. 5). over stump d.o. b. at 6

7 If stumps over inches in diameter are excluded, the folloing simple linear regressions give nearly identical estimates: Stum.e height.0 feet: D.b. h (d.o.b.) (6) Sturn.e height 1.0 foot: D.b.h (d.o.b.) (7) Stump height 0.5 foot: D. b. h (d.o.b.) () Sturn.e height 0.5 foot: D.b.h (d.o.b.) (9) Approximating the above by d.b.h./d.o.b. ratios leads to a nearly equivalent equation for stump diameters measured at variable heights: D.b.h. 0.5 (H' 1063 ) (d.o.b.) (10) APPLICATION The relationships given are based on measurements made ith diameter tape, over bark. Therefore, in applications, stump diameter measurements must be made over bark. If bark is partially or holly missing, an appropriate ocular adjustment must be made at the time of measurement or bark thickness factors must be supplied. If stumps are tallied by diameter over bark and height of stump, d.b.h. can be estimated by equation 1. In many situations, hoever, the range in size of stumps present in any one plot or stand is quite limited. It may be more convenient to measure or estimate stump diameters over bark at one of the standard heights used here (.0, 1. 0, 0.5, 0.5 ft) and then to use equations -5 or figure 1 to estimate the corresponding d.b.h. If stumps do not exceed inches in diameter, equations 6-9 ill give nearly identical estimates and are more convenient. And, if measurements are to a variable stump height, equation 10 is only slightly less precise and is simple enough for ready use ith a pocket calculator. METRIC EQUIVALENTS 1.0 inch.5 ern 0.5 ft 7.6 ern 0.50 ft 15. em 1.0 ft 30. ern.0 ft em breast height.5 ft 137. em 7

8 The mission of the PACIFIC NORTHWEST FOREST AND RANGE EXPERIMENT STATION is to provide the knoledge, technology, and alternatives for present and future protection, management, and use of forest, range, and related environments. Within this overall mission, the Station conducts and stimulates research to facilitate and to accelerate progress toard the folloing goals: I. Providing safe and efficient technology for inventory, protection, and use of resources.. Developing and evaluating alternative methods and levels of resource management. 3. Achieving optimum sustained resource productivity consistent ith maintaining a high quality forest environment. The area of research encompasses Oregon, Washington, Alaska, and, in some cases, California, Haaii, the Western States, and the Nation. Results of the research are made available promptly. Project headquarters are at: Fairbanks, Alaska Juneau, Alaska Bend, Oregon Corvallis, Oregon La Grande, Oregon Portland, Oregon Olympia, Washington Seattle, Washington Wenatchee, Washington Mailing address: Pacific Northest Forest and Range Experiment Station P.O. Box 311 Portland, Oregon 970 GPO