Historic, archived document Do not assume content reflects current scientific knowledge, policies, or practices. United States ¥\ Department of 5; Agriculture Forest Service Cubic-Foot Tree Volume Equations and Tables Pacific Northwest Forest and Range Experiment Station for Western Juniper Research Note PNW-420 December 1984 ports SUMcy UAS Ta Merenitfester and Colin D. MacLean Ta ENT OF ASS Ey? z ao : STATION LI | Abstract This note presents cubic-foot volume equations and tables for western juniper (Juniperus occidentalis Hook.). Total cubic- foot volume (ground to tip, excluding all branches (CVTS)) is expressed as a function of d.b.h. and total height. Utilizable cubic-foot volume (top of 12-inch stump to a 4-inch top, excluding all branches (CV4)) is expressed as a function of CVTS and d.b.h. Keywords: Cubic-foot volume tables, western juniper, Juniperus occidentalis. Rising costs of energy have stimulated an interest in western juniper as a potential source of energy. In response to this interest, the Forest Inventory and Analysis Work Unit of the Pacific Northwest Forest and Range Experiment Station in Portland, Oregon, is expanding its inventory program! / to include an assessment for western juniper (Juniperus occidentalis Hook.) wood supply. But no volume equations or tables have been available. Introduction J/Regional forest inventories are conducted nationwide by the U.S. Department of Agriculture, Forest Service. The Pacific Northwest Forest and Range Experiment Station conducts surveys in Alaska, California, Hawaii, Oregon, and Washington. JUDITH M. CHITTESTER is a mathematical statistician and COLIN D. MACLEAN is a principal mensurationist, Pacific Northwest Forest and Range Experiment Station, P. 0. Box 3890, Portland, Oregon 97208. The Basic Data We have developed an equation for estimating the total volume (CVTS) of western juniper trees, expressed as a function of two independent variables: diameter at breast height (d.b.h.) and total height. A second equation is presented to convert total volume to utilizable cubic volume (CV4). We needed a volume equation suitable for use on western juniper trees throughout eastern Oregon and northeastern California. Although we would have preferred using measurements from a large sample of trees representing the complete range of forest conditions found in the region, time and funding restrictions limited us to using available tree measurement data plus a smal] sample for testing the results from our original data set. Available data were limited to measurements from 52 trees that were felled and sectioned for a western juniper site index study (Sauerwein 1982). The data were gathered in central, southern, and southeastern Oregon and from one plot in northeastern California. The trees are believed to sample all site indexes throughout the range of western juniper--southwestern Idaho, eastern Oregon, northeastern California, and western Nevada. Juniper trees at higher altitudes in the Sierra Nevada are not represented. Although the trees selected were all dominants, western juniper grows in such open stands that the relative social position of individual trees is not well defined. We are, therefore, assuming that these data are representative of the population and are usable for developing western juniper volume equations. Second-growth stands were selected representing well-stocked sites free from cutting, excessive grazing, and fire. The three tallest trees per one-fifth acre were cut and measured. Data were recorded on the felled trees at ground line, 1 foot, 4.5 feet, and every 3 feet thereafter to the tip. Inside and outside bark diameters were taken to tenths of inches and heights to tenths of feet. The STX program (Grosenbaugh 1967) was used to calculate CVTS and CV4 for each of the sample trees. The test set consisted of 24 trees from the area around Madras and Sisters in central Oregon. Trees were selected to bracket the range of diameters and heights common to the species. Only a few trees were found, nowever, with diameters over 20 inches. Table 1 shows the distribution of both data sets by 4-inch diameter class. Developing the Equations Table 1-—Number of western juniper trees used to develop volume equation, by 4-inch diameter class Diameter Site index Test class study 1/ sample 2/ Total Inches 5.0-8.9 10 6 16 9.0-12.9 26 9 35 13.0-16.9 9 5 14 17.0-20.9 4 1 5 21.0-24.9 -- 1 1 25.0-28.9 -- -- = 29.0-32.9 -- 2 2 Total 49 24 fe} \/From central, southern, and southeastern Oregon, and from northeastern California. 2/From Madras and Sisters areas, central Oregon. An important assumption of least squares regression is homogeneity of variance. To satisfy this condition, cubic volume was transformed with the method used by Bruce and DeMars (1974). The dependent variable chosen was form factor (F), obtained by dividing total cubic volume including stump by the volume of a cylinder with a basal area and height equal to that of the sample tree (F=CVTS/(BA*H)). This model had been successfully used in developing volume equations for California species (MacLean and Berger 1970). Least squares regressions were fit using independent variables of total height and d.b.h. outside bark, their powers, and crossproducts. A problem was encountered in fitting short Squat trees. Tnree trees under 18 feet in height were dropped from the data set when the transformation failed. Their omission had negligible effect on our ability to estimate their volumes. After consultation with Bruce ,¢/ we added a further transformation: the basal area of all trees (BA) was multiplied by (H/(H - 4.5) )©, thereby improving the fit for short trees. After the final model was selected using 49 trees, we ran a covariance analysis to see if the 49 trees and the test sample of 24 trees could be combined to obtain a final equation by least squares regression. The covariance analysis showed no significant difference between the slopes, so the sets were combined to obtain the final equation. To convert CVTS to CV4, we turned to the tarif system developed by the Department of Natural Resources (DNR), State of Washington. We had CV4 computed by the STX program for 51 of the 52 trees from the site index study. When the most recent CV4/CVTS tarif ratios (Chambers and Foltz 1979) were plotted against the study trees, the results were substantially biased, probably because of the heavy taper typically found in western juniper stumps. To correct this bias, we recalibrated the aaa following the model described by Turnbull and Hoyer 1965). The form factor equation is: IP = 0.307 + 0.00086*H - 0.0037*D*H/(H-4.5). The volume equations are: CVTS = BA*F*H*(H/(H-4.5))@, and CV4 = (CVTS + 3.48)/(1.18052 + 0.32736*e(-9.1*D)) - 2,948; where: D = diameter at breast height outside bark (inches), H = total height including stump and tip (feet), BA = 0.005454154 * Dé (square feet), F = CVTS/(BA*H), CVTS = total cubic volume from ground to tip, excluding all branches (cubic feet), and CV4 = utilizable cubic volume from top of 12-inch stump to a 4-inch top, excluding all branches (cubic feet). The root mean square error for F was 3.8 percent. 2/Personal communication with David Bruce, USDA Forest Service, Pacific Northwest Forest and Range Experiment Station, Portland, OR, December 1982. Discussion and Conclusions Measured volumes were plotted against estimated volumes for CVTS and CV4 (figs. 1, 2). The figures illustrate the lack of bias in the equations as well as the lack of data for large volume trees. Tne small samples and the few number of large trees were major difficulties in the development of these equations. Of the 73 trees used to obtain the final equation, only 3 had a d.b.h. greater than 20 inches. Although the volume tables (tables 2, 3) provide reasonable extrapolations, the user should be Cautious when applying them to trees above 20 inches d.b.h. The study is limited to trees in eastern Oregon and northeastern California. Site index curves developed from these data, however, are suitable for the entire range of western juniper (Sauerwein 1982). We think the equations and volume tables presented here will also be valid for the entire range. Actual volume (CVTS) ¢) 10 20 30 40 50 60 70 Equation volume (CVTS) Figure 1.--Relationship between measured cubic-foot volume (CVTS) of 73 western juniper trees and estimates calculated with the equation. Actual volume (CV4) i) 5 10 15 20 25 30 35 40 Equation volume (CV4) Figure 2.--Relationship between measured utilizable cubic-foot volume (CV4) of 91 western juniper trees and estimates calculated with the equation. Table 2--Cubic-foot volume of western Table 3-—Cubic-foot volume of western juniperL/ 2/ juniper to a 4-inch top Total height (feet) Total height (feet) Diameter at Diameter at breast height breast le" outside bark3/ 10 20 30 40 50 60 70 80 outside bark3/ 10 20) 30 40 50 60 70 | apes. Inches 5 ] 1 5 0 1 6 2 2 6 1 1 7 2 3 7 8 7 1 2 8 3 3 9 11 8 2 2 7 9 4 4 12 14 9 3 3 9 10 4 5 14 16 10 3 4 11 iH 5 6 17 20 i 4 4 13 12 7 20 23 12 5 5 15 13 8 23 27 13 6 18 14 9 ry 31 14 7 21 15 10 30 35 15 8 11 24 16 12 34 39 16 9 12 15 19 23 27 7 13 38 44 7 10 7 21 26 30 18 14 42 48 18 1 15 g é 29 34 19 15 46 53 19 U2 Ge S2iio ize slide 2.37 20 ie 22 29 35 43 50 58 20 13 18 23 29 35 41 21 18 24 31 38 46 55 63 21 15 20 25 31 38 45 22 19 26 3 4 Ad oe 22 16 21 27 34 41 48 23 28 4 23 23 30 37 44 52 24 30-38 58 68 79 24 24-8 9/325 39. 88g 56 25 32 4) 51 62 73 85 25 26 34 42 51 60 26 34 44 54 66 78 9] 26 28 36 45 54 65 27 35 46 58 70 83 96 721] 29 38 48 58 69 628 37 49 6 74 87 102 28 31 40 51 61 73 29 39 51 64 78 92 108 29 33 43 53 65 77 30 4] 54 67 82 97 +114 30 34 45 56 68 81 3) 43 56 71 86 102 119 31 36 47 59 72 85 32 45 59 74 90 107 125 32 37 49 62 75 90 33 46 61 77 94 112 «131 33 39 51 65 79 94 34 48 64 80 98 117 ©1137 34 40 53 67 82 98 35 50 66 Sse eOe 22s 43 35 42 55 70 86 102 36 51 68 87 106 127 149 36 43 57 73 89 106 7 53 71 90 (110) 13) 154 37 45 59 75 SZ iil 38 54 73 93 114 136 160 38 46 61 78 96 115 39 56 75 95 117 141 165 39 47 63 80 99 118 40 57 77 98 121 145 171 40 48 65 BS 102m ize Vapplies to all western juniper except at higher altitudes V/applies to all western juniper except at higher altitudes in the Sierra Nevada. in the Sierra Nevada. 2/Total tree volume including stump and tip (CVTS). Data set 2/stump and top excluded; top diameter = 4 inches; stump is outlined. height = 12 inches. Data set is outlined. 4/Diameter classes are midpoint; for example, the 12-inch 3/Diameter classes are midpoint; for example, the 12-inch Class includes 11.5-12.4 inches. class includes 11.5-12.4 inches. Literature Cited Bruce, David; Dears, Donald J. Volume equations for second- growth Douglas-fir. Res. Note PNW-239. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Forest and Range Experiment Station; 1974. 5 p. Chambers, Charles J., Jr.; Foltz, Bruce W. The tarif system-- revisions and additions. DNR Note No. 27. Olympia, WA: State of Washington, Department of Natural Resources; 1979. 8 p. Grosenbaugh, L. R. STX-FORTRAN-4 program for estimates of tree populations from 3P sample-tree-measurements. Res. Pap. PSW-13, rev. Berkeley, CA: U.S. Department of Agriculture, Forest Service, Pacific Southwest Forest and Range Experiment Station; 1967. 76 p. MacLean, Colin D.; Berger, John M. Softwood tree volume equations for major California species. Res. Note PNW-266. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Forest and Range Experiment Station; 1976. 34 p. Sauerwein, William J. Western juniper site index curves. Woodland Tech. Note No. 14. Portland, OR: U.S. Department of Agriculture, Soil Conservation Service; 1982. 4 p. Turnbull, L. J.; Hoyer, G. E. Construction and analysis of comprehensive tree-volume tarif tables. Resour. Manage. Rep. No. 8. Olympia, WA: State of Washington, Department of Natural Resources; 1965. 58 p.