Historic, archived document Do not assume content reflects current scientific knowledge, policies, or practices. United States beans Equations for Total, Wood, and roe sevice Sa@aw-LOg Volume for Thirteen rei stes. California Hardwoods Research Note PNW-414 sure: ides Norman H. Pillsbury and Michael L. Kirkley Li eo | { Abstract Volume equations for thirteen species of California hardwoods were developed from measurements of 766 sample trees from all parts of the state. The species included: bigleaf maple (Acer macrophyllum Pursh), Pacific madrone (Arbutus menziesii Pursh), giant chinkapin (Castanopsis chrysophylla (Dougl.) A. DC.), tanoak (Lithocarpus densiflorus (Hook. & Arn.) Rehd.), coast live oak (Quercus agrifolia Née), canyon live oak (Quercus chrysolepis Liebm.), blue oak (Quercus douglasii Hook. & Arn.), Engelmann oak (Quercus engelmannii Greene), Oregon white oak (Quercus garryana Dougl. ex Hook), California black oak (Quercus kelloggii Newb.), California white oak or valley Oak (Quercus lobata Nee), interior live oak (Quercus wislizeni A. DC.), and California-laurel (Umbellularia californica (Hook. & Arn.) Nutt.). Measurements were taken of standing trees using a Spiegel Reiaskop. English and metric equations for three utilization standards were developed for each species: (1) total tree volume (all stem and branch wood plus stump and bark); (2) wood volume (all wood inside bark from stump to 10 cm (4 in) top outside bark); and (3) saw-log volume for trees 28 cm (11 in) diameter at breast height and larger (straight sections from stump to 23 cm (9 in) top outside bark). Diameter and height were found to be good predictors of total volume and wood volume. An indicator variable representing whether or not the first segment was merchantable, in addition to diameter and height, was found to be a good predictor of saw-log volume for eight of the species. Keywords: Volume equations, volume measurement, hardwoods, California. NORMAN H. PILLSBURY is head of the Department of Natural Resources Management, School of Agriculture and Natural Resources, California Polytechnic State University, San Luis Obispo, 93407. MICHAEL L. KIRKLEY is an instructor in forestry at Modesto Junior College, Modesto, California 95350. At the time the research was done he was a graduate research assistant at California Polytechnic State University, San Luis Obispo. Introduction Background There is a vast hardwood resource in California. It is estimated' that together all hardwood species occupy 5-6 million hectares (12-15 million acres). Hardwood forest types cover 1.1 million hectares (2.8 million acres) of the 6.6 million hectares (16.3 million acres) of commercial forest lands (excluding parks and wilderness areas) in California. In addition, hardwood trees account for 10 percent or more of the stocking on 1.1 million hectares (2.7 million acres) of commercial conifer types (Bolsinger 1979). Inarecent study the gross volume of hardwoods in the hardwood forests and woodlands in four central coast counties alone was estimated at 24.7 million cords or 56 million cubic meters of wood (two billion cubic feet at 80 cubic feet of wood per standard cord) (Pillsbury and Brockhaus 1981). We have estimated that hardwoods amount to about 26 percent of the total wood volume in California's forests (approximately 18 billion cubic feet). In the past, little has been done to manage native California hardwoods because of the limited market for most hardwood products. The selective cutting of conifers in mixed stands has led to a 34-percent increase in cubic-foot volume of oaks and a 29-percent decrease in conifers since 1953 (Bolsinger 1979). With the increasing demand for hardwood for fuel, energy, wood fiber, lumber, and noncohsumptive uses such as wildlife, watershed protection, and aesthetics -(Asher,” Barrett, 1979, Bolsinger 1979, Crail, ?Smith 1981, Tillman 1978, Verner 1979), information on the distribution and volume of California’s hardwoods is needed to manage the resource. Estimates of standing tree volumes are needed to inventory forests for management purposes, forest valuation, and taxation. Only a few volume equations have been published for native California hardwoods and all have been developed for local or regional use. Existing equations have been reported by several authors: Wiant and Berry (1965)—tanoak; Hornibrook and others (1950)—California black oak, Oregon white oak, Pacific madrone, and tanoak; Pillsbury and Stephens (1978)—coast live oak, blue oak, and tanoak; Harrington and others (1979)—California white oak. Local volume equations have been developed by McDonald (1983) for Pacific madrone, tanoak, and California black oak. Pillsbury and Stephens (1978) developed a methodology to estimate volume in standing trees with multiple stems and irregular forms. Reliable volume equations already exist for red alder (A/nus rubra Bong.), acommercial hardwood in California and the Pacific Northwest (Browne 1962, Curtis and others 1968, Johnson and others 1949, Skinner 1959, Turnbull and others 1963). Volume equations for bigleaf maple also exist, but were developed for use in British Columbia (Browne 1962). ' Personal communication, 1982, Charles L. Bolsinger, Pacific Northwest Forest and Range Experiment Station, Portland, Oregon. 2 Presentation at the Hardwood Inventory and Utilization workshop, 1982, “Hardwood utilization and marketing in southern California,” by James E. Asher, Natural Resources Management Department, California Polytechnic State University, San Luis Obispo. 3 Presentation at the Hardwood Inventory and Utilization workshop, 1982. ‘Demand for hardwoods as a raw material for pulping processes,” by Miles Crail, Natural Resources Management Department, California Polytechnic State University, San Luis Obispo. Figure 1.—Geographic range of the thirteen hardwood species in California (after Plumb 1979 and Griffin and Critchfield 1972). 41° 40° 38° Si 36° 35° 34° 150 Miles ) Son | a a | aa | 50 100 150 200 Kilometers 12428 123° 122" UWS 1205 1tSe 1 t8= Lltee 116° None of the equations, except those for red alder, are considered suitable for a statewide forest inventory because of the inconsistency in measurement standards and the possibility that they may be unreliable outside of the area for which they were developed. In this study, volume equations for thirteen major hardwood species were developed (fig. 1) from data collected on sample trees distributed throughout their natural ranges in California. Equations were developed for: (1) total tree volume (all stem and branch wood plus stump and bark); (2) wood volume (wood inside bark from stump to 10 cm (4 in) top outside bark); and (3) saw-log volume for trees 28 cm (11 in) diameter at breast height (d.b.h.) and larger.* * All measurements were taken in metric units. English units shown in the text are rounded to the nearest unit. Methodology Utilization Standards and Measured Variables The species included in this study are: Scientific name/author Acer macrophyllum Pursh Arbutus menziesii Pursh Castanopsis chrysophylla (Dougl.) A. DC. Lithocarpus densiflorus (Hook. & Arn.) Rehd. Quercus agrifolia Née Quercus chrysolepis Liebm. Quercus douglasii Hook. & Arn. Quercus engelmannii Greene Quercus garryana Dougl. ex Hook. Quercus kelloggii Newb. Quercus lobata Née Quercus wislizeni A. DC. Umbellularia californica (Hook. & Arn.) Nutt. Common name Bigleaf maple Pacific madrone Giant chinkapin Tanoak Coast live oak Canyon live oak Blue oak Engelmann oak Oregon white oak California black oak California white oak (valley oak) Interior live oak California-laurel The volume equations developed for each species are expressed in cubic feet and cubic meters for three utilization standards (fig. 2). 1. Total voiume: includes all stem and branch wood plus stump and bark; excludes roots and foliage. 2. Wood volume: computed from stump height (0.3 m (1 ft)) toa 10-cm (4-in) top outside bark; excludes roots, bark, and foliage. 3. Saw-log volume: computed for trees 28 cm (11 in) d.b.h. and larger; volume computed from stump height to a 23-cm (9-in) top outside bark for straight sections 2.5 m (8 ft) long; excludes roots, bark, and foliage. Figure 2.—Tree segments used in volume assessment. OB = outside bark. v TERMINAL BRANCHES UPPER STEM PORTION ole —23cm OB 2.5m or longer SAW-LOG PORTION oe -0.3 m Stump Stem Breaks Into Forks Sample Design Sample Tree Selection Tree and Site Measurements Each species was sampled throughout its natural range in California based on maps developed by Griffin and Critchfield (1972). The state was divided into six geographic regions: northern coast, northern interior, central coast, central interior, southern coast, and southern interior.° The percentage of trees sampled in each region was proportional to the approximate area each species occupies in the region. Trees were sampled in areas of varying site qualities, stand densities, and topography. Trees were not sampled east of the Sierra Nevada and Cascade Range because few hardwoods occur there. Adesirable sample size for each species was 60 trees, for a total of approximately 780 trees to be measured statewide for the 13 species studied. Experience has shown that a sample of this size is normally satisfactory for estimating regression coefficients and testing for adequacy of the model for the three utilization standards. Insample areas, trees were selected to represent a range of diameters, heights, growth forms, stand structures, and topography. Sound trees 12.7 cm (5 in) in diameter, or larger, at breast height were selected. Decadent trees and trees with major defects were avoided. Sample tree variables measured in the field are summarized in table 1. Total height was measured from ground level to the tip of the tree. Habit class ratings developed by Pillsbury and Stephens (1978) were assigned to each tree sampled (fig. 3). Anumerical * Unpublished Master's Thesis, 1982, Michael L. Kirkley, California Polytechnic State University, San Luis Obispo. Table 1—Summary and measurement description of sample tree variables Variable Units Measurement description Diameter at cm Diameter of main stem at 1.37 meters breast height (4.5 ft) measured to the nearest tenth with a D-tape. Stump diameter cm Diameter of main stem at 0.3 meters (1 ft) measured to the nearest tenth with a D-tape. Height m To the terminal-most leader determined by Relaskop on the uphill side to the nearest tenth. Single bark thickness cm Measured to the nearest tenth at breast height (1.37 m) (4.5 ft) witha ruler. Habit class class Defined by branching pattern. 1-5 1 = conifer-like form; 5 = multi-branching form with many forks (fig. 3). Stand density m?/ha Cross-sectional area of trees atd bh measured using a Relaskop (basal area factor of 4). Site quality class H = high;M = medium; L = low \ > [ (1) (2) (3) 1 \ f f | (4) I Figure 3.—Five habit classes were used for evaluating tree form and branching complexity (from Pillsbury and Stephens 1978). rating of one to five was recorded to indicate the complexity of branching: a rating of one indicated an excurrent growth form with one main bole and one or two lateral branches, and a rating of five indicated a deliquescent growth form with complex branching (fig. 3). Stump diameters were measured to compute the volume of the first segment; bark thickness was measured to develop relationships between diameter at inside bark (d.i.b.) and diameter at outside bark (d.o.b.) for computing underbark volume and developing wood and saw-log volume equations. Basal area per hectare and site quality data were recorded to describé the range of stand densities and sites of the sample trees. In areas with recent logging activity basal area was computed by counting both standing trees and stumps to estimate basal area prior to timber harvesting. Site quality was a subjective rating of high, medium, and low. Stand density, associated vegetation, soil depth, and tree form were used as guides to estimate site quality. Tree Volume For volume measurement, the branching pattern was defined on a segment basis. Measurement Segment length and the diameters at each end were measured using a Spiegel Relaskop (Dilworth 1981). Segment length was determined from coordinates measured at both ends of each segment. Each tree was divided into segments based on four criteria: 1. Segments were defined as the distance from fork to fork in trees with very complex branching pattern such as segment 11, figure 4. 2. If a branch had sweep or crook, segments were meaured to obtain a straight log length such as in segments 3 and 5. 3. Segments were defined if abrupt changes in taper were apparent such as in segments 16 and 17. 4. \If a tree had an excurrent growth form the maximum segment length was approximately 3 m (10 ft). aa Figure 4.—Tree volumes were eee Ze calculated from segment lengths and diameters SSS Computation of Sample Tree Data Error and Outlier Analysis Saw-log tree segments had to be at least 2.5 m (8 ft) long, with a small end diameter of 23 cm (9 in). If swelling was present on the stem, diameter measurements were taken slightly above or below the abnormality. Branches not growing vertically were assigned an angle (estimated to the nearest 5 degrees from horizontal) and segment length was calculated. Segments growing less than 30 degrees from horizontal were measured by projecting their length to the ground and measuring with a cloth tape held parallel to the branch angle. Terminal branches were measured from a 10-cm (4-in) diameter to the tip. All terminal branches were tallied and an average length to the nearest 0.5 m (20 in) was recorded. Segment volumes were computed from Relaskop coordinate and diameter measure- ments in cubic meters using Smalian’s formula. Segment volumes were summed to obtain gross volume for each tree up to a 10-cm (4-in) top. Terminal branch volume was computed as a paraboloid. Regression equations estimating d.i.b. from d.o.b. were Geveloped for each species using bark thickness sample data (table 2). With the exception of tanoak, it was assumed that the d.i.b.: d.o.b. ratio remained constant at all heights in upper stem diameters. Previous work by Pillsbury and Stephens (1978) showed that this relationship did not hold with tanoak. A separate study was done to examine how the d.i.b.: d.o.b. ratio changed at increasing heights in tanoak. Asample of 50 trees was measured in Santa Cruz and Monterey Counties. Bark thickness and d.o.b. measurements were made at 0.3 m (1 ft), 1.37 m (4.5 ft), 2.74 m (9 ft), and 5.18 m (17 ft) on standing trees. The results of the study show that the wood tapers more with height than the bark does. A multiple regression equation was developed for tanoak to estimate d.i.b. at any height (DIB,) using DOB,, and its height above ground (H): DIB, = -4.36852 + 0.95354 (DOB,,) + 0.18307 (H) N = 201 height points on 50 trees; R? = 0.962; SE = 1.16. Asimple linear regression model using tree basal area times height (volume of a cylinder) to estimate volume was computed and plotted to analyze the data for linearity and detect any outliers. Also, d.b.h. was plotted against both volume and total height, and total height was plotted against volume to detect possible errors in the data sets. This was necessary to guard against compensation errors (for example, a case where basal area is too small and height too large, but basal area times height appears normal). Extreme values were analyzed using at-test. Lund’s (1975) standardized residuals were computed and compared to tables for an approximate test for outliers. A total of 13 trees out of 779 trees sampled (1.7 percent) was determined to be outliers and were dropped from the analyses. Table 2—Equations for estimating diameter inside bark based on measurea diameter outside bark for 13 California hardwoods N R? BIGLEAF MAPLE DIB = 0.21235 + 0.94782 (DOB) 61 0.995 CALIFORNIA BLACK OAK DIB = -0.68133 + 0.95767 (DOB) 60 997 BLUE OAK DIB = -0.44003 + 0.94403 (DOB) 60 995 CANYON LIVE OAK DIB = -0.48584 + 0.96147 (DOB) 57 996 GIANT CHINKAPIN DIB = 0.39534 + 0.90182 (DOB) 60 986 COAST LIVE OAK DIB = -1.92379 + 0.93475 (DOB) 60 992 ENGLEMANN OAK DIB = -1.99573 + 0.92472 (DOB) 61 992 INTERIOR LIVE OAK DIB = 0.12237 + 0.92953 (DOB) 58 995 CALIFORNIA-LAUREL DIB = -0.32491 + 0.96579 (DOB) 60 998 PACIFIC MADRONE DIB = -0.03425 + 0.98155 (DOB) 60 999 OREGON WHITE OAK DIB = -0.78034 + 0.95956 (DOB) 60 995 CALIFORNIA WHITE OAK DIB = -0.97254 + 0.93545 (DOB) 60 995 TANOAK DIB, = -4.36852 + 0.95354 (DOB,,) + 0.18307 (H) N = 201 height points on 50 trees; R? = 0.962; SE = 1.16 SE = Standard error of estimate in cm. DIB = diameter inside bark (cm). DOB = diameter outside bark (cm). DIB, = diameter inside bark at any height. DOB,, = diameter outside bark at any height. H = "height above ground. Analysis Development of Volume Equations Multiple regression equations were developed for total, wood, and saw-log volume from sample tree variables. Volume equations were developed for the 13 species in units of cubic feet and cubic meters. A log,, transformation of volume and tree variables was used in developing the regression model to linearize the data and equalize the variation about the regression line. Total and wood volume equations.—Tree volume was tested as a function of diameter at breast height, total height, stand density, and habit class. Diameter at breast height and total tree height were found to be the best predictors of total volume and wood volume. Stand density and habit class contributed little to the prediction of total and wood volume and were dropped from the model. Multiple coefficient of determination (R2) values exceeded 0.92 in all total and wood volume equations, indicating a strong relationship (tables 3 and 4). Table 3—English equations for total, wood, and saw4og volumes for California hardwoods Species Equation R? N SE BIGLEAF TVOL = .0101786350 (DBH?-224©7) (HT°:2756") 0.944 61 45.4 MAPLE WVOL = .0034214162 (NBH?°°°%7) (HT° 62585) 924 61 48.4 SVOL. =) .0004236332 (DBH2 '02'°) (HT 2898+) (Ivo 40017) .767 26 53.7 CALIFORNIA TVOL = .0070538108 (DBH'2749”) (HT°-8°°3*) .971 59 43.1 BLACK OAK WVOL = .0036795695 (DBH? '26°) (HT°:89399) .962 60 45.2 SVOL = .0012478663 (DBH?-%°°99) (HT°:42447) (1v9-28385) .929 38 47.7 BLUE TVOL = .0125103008 (DBH?2°°82) (HT°-461°°) .971 60 43.0 OAK WVOL = .0042324071 (DBH2°2°8”) (HT°°°°9") .970 60 44.1 SVOL = .0036912408 (DBH'-’9722) (HT°-89884) (19-1995) 826 32 46.0 CANYON TVOL = .0097438611 (DBH?:2°°?7) (HT?-°"19°) .978 58 41.8 LIVE OAK WVOL = .0031670596 (DBH?225'9) (HT°:74348) .980 58 42.0 SVOL = .0006540144(DBH22449”) (HT°-81358) (1\V°-43887) 884 68 48.4 GIANT TVOL = .0120372263 (DBH?-°2292) (HT°68638) .960 60 44.4 CHINKAPIN WVOL = .0055212937 (DBH?°”2°?) (HT°:77*°7) .958 60 45.0 SVOL = .0018985111 (DBH?2°85) (HT°-771°°) .880 40 46.2 COAST TVOL = .0065261029 (DBH?319°°) (HT°-62528) .968 60 44.1 LIVE OAK WVOL = .0024574847 (DBH2°°28*) (HT°:9°75) .971 59 44.1 SVOL = .0006540144 (DBH?2449”) (HT°-81958) (1v°-49981) 884 68 48.4 ENGELMANN - TVOL = .0191453191 (DBH24°248) (HT°:2805°) .965 61 43.4 OAK WVOL = .0053866353 (DBH?°'26) (HT°:911°9) .966 61 43.9 10 Tavie 3—English equations for total, wood, and saw-log volumes for California hardwoods, continued Species INTERIOR LIVE OAK 7 CALIFORNIA LAUREL PACIFIC MADRONE OREGON WHITE OAK TANOAK CALIFORNIA WHITE OAK 7) < O Las fh ah teal Me TVOL WVOL SVOL TVOL WVOL SVOL TVOL WVOL SVOL TVOL WVOL SVOL TVOL WVOL SVOL TVOL WVOL SVOL Equation | .0136818837 (DBH?°9°9) (HT°°9?97) .0041 192264 (DBH* '49"°) (HT°:77949) .00065401 44 (DBH?:24497) (Figo 21898) (Io 2992") .0057821322 (DBH' ae) (me 22282) 0016380753 (DBH?°°9'°) (HT1:°929) 0007741517 (DBH?:29°P) (HT1-°970°) 0067322665 (DBH' 96628) (HT°:89458) 0025616425 (DBH'-99295) (HT1-°1932) 0006181530 (DBH" 72625) (HT: 26462) (|\y°-37867) 0072695058 (DBH?:"432") (HT°-74220) 0024277027 (DBH?25575) (HT°871°) .0008281647 (DBH2"' 0651 ) (HiF??" 21 >) (IWO82822) 0058870024 (DBH" 476) (HT? 8655) 0005774970 (DBH? 19576) (HT"- 14078) 0002526443 (DBH?9°949) (HT1-21089) 0042870077 (DBH?3°%") (HT°:74872) 0009684363 (DBH?:29°°°) (HT°-28878) 0001880044 (DBH'®7%*®) (HT'-©2449) the standard error of the estimate in cubic feet. total tree volume in cubic feet. wood volume in cubic feet. saw-log volume in cubic feet. diameter at breast height in inches. total height in feet. an indicator variable (1 =non-merchantable first segment; 10=merchantable first segment). Combined equation for sawlog volumes for canyon live oak, interior live oak, and coast live oak. R?2 0.971 .967 .884 .967 399 913 .967 .959 .905 .961 .958 .838 .973 .961 .906 .990 .990 .929 N 58 58 68 60 60 30 60 58 32 60 66 32 60 59 37 59 59 37 Table 4—Metric equations for total, wood, and saw-log volumes for California hardwoods Species Equation R? N SE BIGLEAF TVOL = .0000718042 (DBH?2246) (HT°°7°°') 0.944 61 1.29 MAPLE WVOL = .0000246916 (DBH?25°4”) (HT°£9°2*) 924 61 1837, SVOL = .0000061361 (DBH2 1°91) (HT"-08*) (Iv°40°"7) .767 26 1.52 CALIFORNIA TVOL = .0000870843 (DBH' 9749”) (HT° 89°) .971 59 1.22 BLACK OAK WVOL = .0000386403 (DBH? 1269) (HT°-82929) .962 60 1.28 SVOL = .0000048067 (DBH?58°°2) (HT°42441) (IV°:28985) .929 38 1.35 ‘BLUE TVOL = .0000697541 (DBH?°9°®) (HT° 491°) .971 60 1.22 OAK WVOL = .0000204861 (DBH?5°98”) (HT°°°°9") .970 60 1.25 SVOL = .0000530200 (DBH' 79722) (HT°-228*) (Ivo 19998) 826 32 1.31 CANYON TVOL = .0000730718 (DBH?:2°°2”) (HT°°"'%) .978 58 1.18 LIVE OAK WVOL = .0000248325 (DBH?2257) (HT°-7424°) .980 58 1.19 * SVOL = .0000060095(DBH22437) (HT°-2195%) (IV9-4999") 884 68 1.37 GIANT TVOL = .0001169607 (DBH?°22) (HT° °°?) .960 60 1.26 CHINKAPIN WVOL = .0000568840 (DBH?°72°) (HT°’74°7) .958 60 1.27 SVOL = .0000145764 (DBH?2°285) (HT° 77") .880 40 1.31 COAST TVOL = .0000446992 (DBH?319°°) (HT°°7°**) .968 60 1.25 LIVE OAK WVOL = .0000135114 (DBH?5928) (HT°-°7%) .971 59 1.25 * SVOL = .0000060095 (DBH22443”) (HT°-8"25°) (Iv°- 499°") 884 68 1.37 ENGELMANN TVOL = .0000805935 (DBH?402*®) (HT°- 28°) .965 61 1.23 OAK WVOL = .0000193268 (DBH?°'26) (HT°-3"1°9) 966 61 1.24 Table 4—Metric equations for total, wood, and saw4og volumes for California hardwoods, continued Species INTERIOR LIVE OAK CALIFORNIA LAUREL PACIFIC MADRONE OREGON WHITE OAK TANOAK CALIFORNIA WHITE OAK wn < O lim eT ae Tie al TVOL WVOL SVOL TVOL WVOL SVOL TVOL WVOL SVOL TVOL WVOL SVOL TVOL WVOL SVOL TVOL WVOL SVOL Equation = .0001238312 (DBH2-°7989) (HT°9297) = .0000396716 (DBH? '49'°) (HT°:77843) = .0000060095 (DBH?:24497) (HT°813°8) (IV9:4387) Il 0000763133 (DBH'94953) (HT°88389) 0000237733 (DBH?-°59"°) (HT 195293) = .0000094003 (DBH?:22°?) (HT1:°97°°) II = 0000821921 (DBH" 26628) (Aine 22°) = .0000378129 (DBH' 29295) (HT"-°159) = .0000157319 (DBH' iZeSS) (HT" aoe) (IN 372e75 = .0000674342 (DBH?1422") (HT°.74220) = .0000236325 (DBH?:°5”5) (HT°-871%) 0000097284 (DBH? 1965") (HT°:912"5) (Iv0-92652) = .0000763045 (DBH'24"®) (HT°-86°6?) = .0000081905 (DBH* '9°’°) (HT'-'4°78) = .0000035019 (DBH?:2°9*2) (HT"-21°6?) = .0000334750 (DBH2:3963") (Hir®? 4972) = .0000095166 (DBH2295°°) (HT°-98878) = .0000063968 (DBH' ®”*4*) (HT ©2443) the standard error of the estimate in cubic meters. total tree volume in cubic meters. wood volume in cubic meters. saw-og volume in cubic meters. diameter at breast height in centimeters. total height in meters. an indicator variable (1 = non-merchantable first segment; 10 =merchantable first segment). Combined equation for sawlog volumes for canyon live oak, interior live oak, and coast live oak. R? N SE .967 58 1.24 .884 68 1.37 .967 60 1.24 .959 60 1.30 913 320 1.28 .967 60 1.23 .959 58 1.27 .905 32 1.30 .961 60 1.26 .958 60 1.30 .838 32 1.41 973 60 1.22 .961 59 1.31 ‘906 37 1.36 .290 59 eS -990 59 1.16 929 37 1-38 Test To Combine Regression Lines Verification of Tree Volume 14 Saw-log volume equations.—A qualitative indicator variable was used to break the Saw-log data into two subsets: trees with a merchantable (straight, at least 2.5 m (8 ft) long, and free of defect) first segment, and trees without a merchantable first segment. A code of “1” means the first segment in nonmerchantable and a code of “10” means itis merchantable. The addition of the indicator variable helped reduce the variation in saw-log equations for 8 of the 13 species (tables 3 and 4). This improved the precision of the saw-log volume equation. Species that forked below 2.5 m (8 ft) commonly had sweep, crook, and a multiple branching pattern, resulting in segment lengths shorter than 2.5 m (8 ft) and an overall lower proportion of saw-log volume. Of the eight species where an indicator variable was included in the modei, trees with a merchantable first segment had an average of 2.3 times more volume than trees without a merchantable first segment. The regression model incorporating the indicator variable was not used for tanoak, chinkapin, and California-laurel because these species usually have merchantable first logs. Also it was not used for California white oak because the indicator variable added little to reduce variation in predicting saw-log volume. Saw-log equations were not developed for Engelmann oak, which has a very complex growth form with few straignt sections. Little or no saw-log volume can be expected in unmanaged native stands of this species. Because of the size and irregular form of the live oak species (canyon, coast, and interior), many trees measured did not have any saw-log volume. As a result the sample size for developing saw-log equations for the live oak species was small. These species were observed to have similar growth forms and an F-test supported combining the data sets. The three live oak data sets were therefore combined to produce one equation for saw-log volume (tables 3 and 4). Most of the sample trees were on private property and were not felled at the time of Relaskop measurement. Pillsbury and Stephens’ (1978) method was used to check tree volumes. They cut and measured 61 trees to check the accuracy of the volumes based on Relaskop measurements of standing trees. They developed a simple linear regression equatien (log; transformation) relating standing tree volume to cut tree volume and obtained a multiple coefficient of determination of 0.990 (SE = 1.17). To validate their equation for use in this study, 10 additional sample trees spanning the range of diameters at breast height were measured. Standing tree measurements were made by the techniques previously discussed in this report. Then each tree was felled and measured with tape and caliper. A simple linear regression (log, transformation) was developed relating standing tree volume to cut tree volume and compared to the Pillsbury and Stephens (1978) equation. An F-test supported combining the two data sets as one population at the 0.99 probability level. All standing volumes were corrected using the Pillsbury and Stephens (1978) equation: Corrected Volume (M°) = 1.166 (Standing Volume (M°))°99*7 The standing tree volumes are increased by approximately 15 percent using this equation, indicating that the technique used to measure standing tree volume tends to underestimate tree volume. Reliability of the Equations The average aggregate difference in percent is -2.1 for total volume, -2.8 for wood volume, and -5.8 for saw-log volume. An independent test was made using total volumes of 76 felled trees in three central coast counties. The average aggregate difference for the 76 trees is 17.0 percent. The reliability of the equations can be measured by the relative deviation of individual tree volumes from the regression surface (MacLean and Berger 1976). A measure of this residual variation is the root mean squared error; that is, the root of the mean squared difference between the predicted and actual values. This comparison, expressed as a percent of the mean volume, is shown in table 5. The root mean squared error difference for 76 trees of known volume in three central coast counties is shown in table 6. The root mean squared errors range from about 20 to 55 for the various utilization standards shown in tables 5 and 6. These values are higher than those reported for conifers (MacLean and Berger 1976) and illustrate the greater variability in volume that occurs for a given diameter and height for many hardwoods. Table 5—Root mean squared errors of standard volume equations for total, wood, and saw-log utilization standards Root mean squared error Species Total volume Wood volume Sawlog volume N Percent N_ Percent N_ Percent Bigleaf maple 61 36 61 46 24 31 California black oak 59 50 60 56 38 21 Blue oak 60) = 27 60 30 32 36 Canyon live oak 538 52 5G) 50 —n/a— Giant chinkapin 60 45 60 46 40 20 Coast live oak 60 36 59 39 —n/a— Engelmann oak 61 30 61 34 —n/a— Interior live oak 58 28 58 38 —n/a— California-laurel 60 24 60 26 30 20 Pacific madrone 60 38 58 39 Se 24 Oregon white oak 60 41 60 47 32 36 Tanoak 60 38 59 54 37 27 California white oak 59) 20 59 22 37 22 Combined: Canyon, interior and coast —n/a— —n/a— 85 64 live oaks n/a = not applicable. Table 6—Results of a test of equations for 76 trees of known total volume from Monterey, San Luis Obispo, and Santa Cruz Counties Species Root mean squared error Number of trees Percent Blue oak 26 42 Coast live oak 35 50 Tanoak 15 24 Use of the Equations Volume Tables and Range of Data Literature Cited 16 Following is an example showing calculations in English units of total, wood, and saw-log volumes for a blue oak tree with these dimensions: d.b.h. = 25.5 inches; and total height = 47 feet. It has a merchantable first segment: TVOL = .0125103008 (25.57:39°89) x (479-4610) — 4140 cubic feet; WVOL = .0042324071 (25.57°3987) x (47959591) — 110 cubic feet; and SVOL = .0036912408 (25.5':7979?) x (47983884) x (10°:-15958) — 45 cubic feet. Although other hardwood volume equations are available, most have been developed for regional or local use and incorporate various utilization standards. Volume equations developed for local areas may provide better estimates of tree volumes in those areas than the equations for the entire state. Field checking may be necessary to compare the accuracy of the statewide equations to locai or regional sites if this use is desired. In the appendix are tables showing calculated volumes for selected diameters and heights for each of the 13 hardwood species studied. The range of measurements used to develop the equations is shown on each table. Barrett, Reginald A. Mammals of California oak habitats—management implications. In: Proc., Symp. on Ecology, management and utilization of California oaks; 1979 June 26-28; Claremont, CA. Gen. Tech. Rep. PSW-44. Berkeley, CA: U.S. Department of Agriculture, Forest Service; 1979: 275-291. Bolsinger, Charles L. Oaks in California’s commercial forests—volume, stand structure, and defect characteristics. In: Proc., Symp. on Ecology, management and utilization of California oaks; 1979 June 26-28; Claremont, CA. Gen. Tech. Rep. PSW-44. Berkeley, CA: U.S. Department of Agriculture, Forest Service; 1979: 101-106. Browne, J. Standard cubic foot volume tables for the commercial tree species of British Columbia. Vancouver, B.C: British Columbia Forest Service Forest Surveys and Inventory Division; 1962: 107 p. Curtis, R.; Bruce, D.; Van Coevering, C. Volume and taper tables for red alder. Res. Pap. PNW-56. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Forest and Range Experiment Station; 1968. 35 p. Dilworth, J. Log scaling and timber cruising. Corvallis, OR: O.S.U. Book Stores, Inc.; 1981. 466 p. Griffin, J. R.; Critchfield, W. B. The distribution of forest trees in California. Res. Note PSW-82. Berkeley, CA: U.S. Department of Agriculture, Forest Service, Pacific Southwest Forest and Range Experiment Station; 1972. 114 p. Harrington, Thomas J.; Pillsbury, Norman H; Barrette, Brian. A gross volume table for California white oak in Monterey and San Luis Obispo Counties. State Forest Note No. 77. Sacramento, CA: California Department of Forestry; 1979. 4 p. Hornibrook, E. M.; Larson, R. W.; Van Akkeren, J. J.; Hasel, A. A. Boardfoot and cubic-foot volume tables for some California hardwoods. Res. Note PSW-67. Berkeley, CA: U.S. Department of Agriculture, Forest Service, Pacific Southwest Forest and Range Experiment Station; 1950. 31 p. Johnson, F. A.; Kallander, R. M.; Lauterback, P. G. Volume tables for red alder. Res. Note PNW-55. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Forest and Range Experiment Station; 1949. 10 p. Lund, Richard E. Tables for an approximate test for outliers in linear models. Technometrics. 17(4): November 1975. MacLean, C.; Berger, J. 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. 33 p. McDonald, Phillip M. Local volume tables for Pacific madrone, tanoak, and California black oak in north-central California. Res. Note PSW-362. Berkeley, CA: U.S. Department of Agriculture, Forest Service, Pacific Southwest Forest and Range Experiment Station; 1983. 6 p. Pillsbury, Norman H.; Brockhaus, John A. Hardwood biomass inventory maps for California's central coast. Salinas, CA: Central Coastal Resource Conservation and Development Project and USDA Soil Conservation Service; 1981. 5 maps. Pillsbury, Norman H.; Stephens, Jeffrey A. Hardwood volume and weight tables for California's central coast. Sacramento, CA: California Department of Forestry; 1978. 54 p. Piumb, Timothy R. Response of oaks to fire. In: Proc., Symp. of Ecology, management and utilization of California oaks, 1979 June 26-28, Claremont, CA. Gen. Tech. Rep. PSW-44. Berkeley, CA: U.S. Department of Agriculture, Forest Service, Pacific Southwest Forest and Range Experiment Station; 1979: 202-215. Skinner, E. C. Cubic volume tables for red alder and sitka spruce. Res. Note PNW-170. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Forest and Range Experiment Station; 1959. 4 p. Smith, Nigel. Wood: An ancient fuel with a new future. Worldwatch Pap. No. 42. Washington, DC: Worldwatch Institute; 1981. 48 p. Tillman, David A. Wood as an energy resource. Academic Press: 1978. 252 p. Turnbull, K. J.; Little, G. R.; Hoyer, G. E. Comprehensive tree volume tariff tables. Olympia, WA: State Washington Department of Natural Resources. 1963. 23 p. and tables. Verner, Jared. Birds of California oak habitats—management implications. In: Proc., Symp. on Ecology, management and utilization of California oaks, 1979 June 26-28, Claremont, CA. Gen. Tech. Rep. PSW-44. Berkeley, CA: U.S. Department of Agriculture, Forest Service, Pacific Southwest Forest and Range Experiment Station. 1979: 246-264. Wiant, Harry V. Jr.; Berry, William S. Cubic-foot volume and tariff access tables for tanoak in Humboldt County, California. For. Rep. 2. Arcata, CA: Division of Natural Resources. Humboldt State College. 1965. 10 p. Uz Appendix Tables 7 through 19 are in English measurement; tables 20 through 32 are in metric measurement. Table 7-Total tree, wood, and saw-log volume for giant chinkapin TOTAL HEIGHT (FEET) DIAMETER AT OE ——————e—— ae BREAST HEIGHT INCHESS fog) Base iam) Seley eI are aa canine conan CUBICNRE Ret —e =) it ea 5: TVOL 2 3 4 5 WVOL 2 2 3 3 SVOL 1 1 2 2 7: TVOL 5 6 8 9 10 1 WVOL 3 4 5 6 7 8 SVOL 2 3 3 4 5 5 9: TVOL 8 VW 13 15 W7 19 21 22 WVOL 5 7 9 VW 12 14 16 7 SVOL 4 5 6 7 8 9 10 11 VW: Q TVOL 12 16 19 23 26 28 31 34 36 39 4) WVOL 8 iW 14 16 19 21 24 26 28 30 32 SVOL 6 8 10 12 14 15 W7 18 20 22 23 13: TVOL V7 22 27 32 36 40 44 47 51 54 58 WVOL 11 16 20 23 27 30 33 37 40 43 46 SVOL 9 12 15 7 20 23 25 28 30 32 34 15: TVOL 30 36 42 48 53 58 63 68 72 77 81 86 90 WVOL 21 26 31 36 4) 45 49 53 58 62 66 69 73 SVOL 17 21 25 28 32 35 39 42 45 48 51 54 57 V7: TVOL 38 47 54 62 68 75 81 87 93 99 105 110 115 WVOL 27 34 41 47 53 58 64 69 75 80 85 90 95 SVOL 22 28 33 38 43 48 52 57 61 65 69 73 77 19: TVOL 58 68 77 86 94 102 109 17 124 131 138 145 WVOL 43 51 59 66 73 80 87 94 101 107 113 120 SVOL 36 43 50 56 62 68 74 79 85 90 96 101 21: TVOL 7 83 94 105 115 125 134 143 152 160 169 77 WVOL 53 63 72 81 90 99 107 116 124 132 139 147 SVOL 46 55 63 71 79 86 94 101 108 115 121 128 23: TVOL 86 100 113 126 138 150 161 172 183 193 203 213 WVOL 64 76 87 98 109 120 130 140 149 159 168 178 SVOL 57 68 78 88 98 107 116 125 134 142 151 159 25: TVOL 102 119 134 149 164 177 191 204 216 228 240 252 WVOL 76 90 104 7 130 142 154 166 178 189 200 211 SVOL 70 83 96 108 119 131 142 153 163 174 184 194 27: TVOL 138 157 174 191 207 223 238 253 267 281 294 WVOL 106 122 137 152 167 181 195 208 222 235 248 SVOL 100 115 129 143 157 170 183 196 208 221 233 29: TVOL 160 181 202 221 240 257 275 292 308 324 340 WVOL 123 141 159 176 193 210 226 241 257 272 287 SVOL 118 136 153 170 186 202 217 232 247 262 276 31: TVOL 183 208 231 253 274 295 315 334 353 371 389 WVOL 141 162 183 203 222 241 259 277 295 312 330 NOTE: BLOCK INDICATES RANGE OF DATA. 1/ TVOL = TOTAL ABOVEGROUND VOLUME OF WOOD AND BARK; EXCLUDES FOLIAGE. WYOL VOLUME OF WOOD FROM A 1-FOOT STUMP TO A 4-INCH TOP OUTSIDE BARK; EXCLUDES BARK AND FOLIAGE. SVOL SAW-LOG VOLUME IN STRAIGHT MERCHANTABLE SECTIONS AT LEAST 8 FEET LONG TO A 9-INCH TOP OUTSIDE BARK ABOVE A 1-FOOT STUMP. 18 Table 8--Total tree, wood, and saw-log volume for California-laurel DIAMETER AT TOTAL HEIGHT (FEET) HEIGHT BUTSIDE BARK 1/ 20 30 40 50 60 70 80 90 100 110 120 INCHES 4 TVOL WVOL SVOL TVOL WVOL SVOL TVOL WVOL SVOL ULE TVOL WYOL SVOL 13: TVOL WVOL SVOL 15's TVOL WVOL SVOL TVOL WVOL SVOL 19: TVOL WVOL SVOL 21: TVOL WVOL SVOL 23: TVOL WVOL SVOL 25: TVOL WVOL SVOL 27: TVOL WVOL SVOL 29: TVOL WVOL SVOL 31: TVOL WVOL SVOL 33: TVOL WVOL SVOL 35: TVOL WYOL SVOL 37: TYOL WYOL SVOL 39: TYOL WYOL SVOL 4): TVOL WYOL SVOL NOTE: 1/TVOL WYOL SVOL BLOCK INDICATES RANGE OF DATA. = TOTAL ABOVEGROUND VOLUME OF WOOD AND BARK; EXCLUDES FOLIAGE. = VOLUME OF WOOD FROM A 1-FOOT STUMP TO A 4-INCH TOP OUTSIDE BARK; EXCLUDES BARK AND FOLIAGE. = SAW-LOG VOLUME IN STRAIGHT MERCHANTABLE SECTIONS AT LEAST 8 FEET LONG TO A 9-INCH TOP OUTSIDE BARK ABOVE A 1-FOOT STUMP. Table 9--Total tree, wood, and saw-log volume for tanoak TOTAL HEIGHT (FEET) DIAMETER AT BREAST HEIGHT OUTSIDE BARK 1/ 20 30 40 50 60 70 80 90 100 110 120 WES eseecescoseseacoeaceeaes CUBIGAFEET Sls eo cre none) Seer ae 5: TVOL WVOL SVOL TVOL WVOL SVOL TVOL WVOL SVOL 11: TVOL WVOL SVOL 13: TVOL WVOL SVOL 15: TVOL WVOL SVOL 7: TVOL WYOL SVOL 19: TVOL WVOL SVOL 21: TVOL WVOL SVOL 233 TVOL WVOL SVOL 25: TVOL WVOL SVOL ee TOTAL HEIGHT (FEET) DIAMETER AT ee nn mn Wane OUTSIDE BARK 1/ 20 30 40 50 60 70 80 90 100 110 120 130 140 eee eee ee NCH ES gee em ie tees ene ee te te Be OE ole tte A) ie a eel ye een eg Baie 86 105 157 223 239 255 WVOL 54 70 86 102 119 136 153 171 189 207 225 SVOL 44 58 103 168 185 203 29EF TVOL 99 120 161 181 257 275 293 WVOL 63 81 100 120 139 159 180 200 221 242 264 SVOL 52 69 86 103 121 198 218 239 31: TVOL 137 160 183 206 292 313 334 WVOL 94 116 138 161 184 208 232 256 280 305 SVOL 80 100 120 142 231 255 279 33: TVOL 155 181 207 232 330 353 377 WVOL 108 133 159 185 211 238 266 294 322 350 SVOL 93 115 139 164 267 294 322 35; TVOL 173 203 232 260 370 396 422 WVOL 123 152 181 210 241 271 303 334 366 398 SVOL 106 132 159 187 306 337 369 Se TVOL 193 226 258 290 321 352 412 441 470 WVOL 139 71 204 238 272 307 377 414 450 SVOL 121 150 181 213 246 279 348 383 419 39: TVOL 214 250 286 321 355 389 456 489 521 WVOL 156 192 229 267 305 344 424 464 505 SVOL 136 170 205 240 (4t/T/ 315 393 433 474 41: TVOL 236 276 315 354 392 429 466 503 539 574 WVOL 174 214 256 298 341 384 428 473 518 564 SVOL 153 191 230 270 311 354 “397 44) 486 532 43: TVOL 258 302 346 388 430 471 511 55] 591 630 WVOL 193 238 284 331 378 426 475 525 575 626 SVOL 171 213 256 301 348 395 443 492 542 593 45: TVOL 282 330 378 424 469 514 558 602 645 WVOL 214 263 314 365 418 47] 525 580 636 SVOL 189 236 285 335 386 438 492 547 602 NOTE: BLOCK INDICATES RANGE OF DATA. 1/TVOL = TOTAL ABOVEGROUND VOLUME OF WOOD AND BARK; EXCLUDES FOLIAGE. WVOL = VOLUME OF WOOD FROM A 1-FOOT STUMP TO A 4-INCH TOP OUTSIDE BARK; EXCLUDES BARK AND FOLIAGE. SVOL = SAW-LOG VOLUME IN STRAIGHT MERCHANTABLE SECTIONS AT LEAST 8 FEET LONG TO A 9-INCH TOP OUTSIDE BARK ABOVE A 1-FOOT STUMP. 21 Table 10--Total tree, wood, and saw-log volume for California white oak TOTAL HEIGHT (FEET) DIAMETER AT BREAST HEIGHT OUTSIDE BARK 1/ 20 30 40 50 60 70 80 90 100 110 120 130 INGHES)) Sa aa a a aa aaa CUB CREE ie S)8 TVOL WVOL SVOL ie TVOL WVOL SVOL 9: TVOL WVYOL SVOL 11: TVOL WVOL SVOL 13: TVOL 58 WYOL 47 SVOL 48 Sy TVOL 81 86 92 WVOL 66 72 78 SVOL 62 72 82 U7 TVOL 108 116 123 WVOL 90 98 106 SVOL 79 91 103 19: TVOL 141 150 159 WVOL 117 127 138 SVOL 97 112 127 21: TVOL 178 190 201 WVOL 149 162 175 SVOL 117 135 153 23 TVOL 220 235 249 WVOL 185 201 218 SVOL 138 160 182 25: TVOL 267 285 303 WVOL 226 246 266 SVOL 162 186 212 22 ee TOTAL HEIGHT (FEET) DIAMETER AT REAST HEIGHT OUTSIDE BARK 1/ 20 30 40 50 60 70 80 90 100 110 120 130 ty Re eee eee TN GEES em es Ce me eames rs Ce mee en) Se es eS CUBIC [sli aoe SSeS Sioa SS ae Se Oi: y TVOL 150 177 252 320 341 362 WVOL 100 124 198 27] 296 320 SVOL 36 52 11 187 215 245 y 29: TVOL W7/7/ 209 298 378 403 428 WVOL 118 148 235 322 351 380 SVOL 4] 59 127 214 246 280 sig TVOL 207 245 348 44] 47] 500 WVOL 139 173 276 378 412 446 SVOL 47 67 144 242 279 318 So: a TVOL 283 511 545 579 WVOL 201 439 478 518 SVOL 76 272 314 357 23) TVOL 325 586 626 664 WVYOL 232 505 551 596 SVOL 84 304 350 399 SV/E TVOL 370 667 WN 756 WVOL 265 577 629 681 SVOL 94 337 389 443 39: TVOL 418 755 806 855 WVOL 300 655 714 773 SVOL 103 372 429 489 41: TVOL 470 539 605 668 730 790 848 905 961 WVOL 339 405 472 539 605 672 738 805 871 SVOL 114 153 196 244 295 350 409 47] 537 43: TVOL 525 602 676 747 816 883 948 1012 1074 WVOL 379 454 529 604 679 753 828 902 976 SVOL 124 167 215 267 323 383 447 BE 587 45: TVOL 584 670 752 831 907 982 1054 1125 1195 WVOL 423 507 590 673 757 840 923 1006 1088 SVOL 135 182 234 290 352 417 487 561 639 NOTE: BLOCK INDICATES RANGE OF DATA. 1/TVOL TOTAL ABOVEGROUND VOLUME OF WOOD AND BARK; EXCLUDES FOLIAGE. WVOL = VOLUME OF WOOD FROM A 1-FOOT STUMP TO A 4-INCH TOP OUTSIDE BARK; EXCLUDES BARK AND FOLIAGE. SVOL = SAW-LOG VOLUME IN STRAIGHT MERCHANTABLE SECTIONS AT LEAST 8 FEET LONG TO A 9-INCH TOP OUTSIDE BARK ABOVE A 1-FOOT STUMP. 23 Table 11--Total tree, wood, and saw-log volume for bigleaf maple TOTAL HEIGHT (FEET) DIAMETER AT BREAST HEIGHT OUTSIDE BARK 1/ 20 30 40 50 60 70 80 90 100 110 120/05 1308 SAO eeesTso iu. ee ete pee ee By TYOL 2 WVOL 1 sVOLI 1 SVOLX 0 3 TVOL 4 WVOL 3 SVOLI 2 SVOLX 1 9: TVOL 8 WVOL 5 SVOLI 3 SVOLX 1 Wis TVOL 12 43 WVOL 8 2 SVOLI 4 54 SVOLX 2 oR 13: TVOL 7 pe WVOL 12 a SVOLI 6 = SVOLX 2 a, Ni}: Or 60 63 NYO 49 53 SVOLI re 2S SVOLX ne aC 17: vor 79 83 WVOL 66 11 SVOLI a at SVOLX oh a 19: TVOL 101 107 112 WVOL 86 92 98 SVOLI 77 86 94 SVOLX 31 34 38 21: TVOL We ee = 1 WVOL oo. 124 «131 SVOLI oR) eS NG SVOLX 38 42 46 50 23: TVOL 154 163 171 179 ~—«*187 WVOL 135 144 153 162 171 SVOLI 116 1282141 154 ~—«(167 syott 46 51 56 61 66 25: nor 186 196" 206. «2G je 22m aaaaeas yi Ge (ee Mee oa ae SVOLI 136. 153) 16800 183 oe au Baal SVOLX 55 61 67 723 79 85 24 DIAMETER AT BREAST HEIGHT OUTSIDE BARK 1/ 20 30 40 50 60 TEPES Ce en rhe en es ote mat meas ha Sah (ANS TVOL 130 148 164 WVOL 104 122 138 SVOLI 60 76 93 SVOLX 24 30 37 zo EVOL 152 173 193 WVOL 123 144 163 SVOLI 70 89 108 SVOLX 28 35 43 Sik TVOL 177 201 223 WVOL 144 168 191 SVOLI 80 102 124 SVOLX 32 4) 49 33: TVOL 203 231 257 WVOL 167 195 221 SVOLI 91 116 142 SVOLX 36 46 56 Sos TVOL 232 263 293 WYOL 192 224 254 SVOLI 103) Pie 160 SVOLX 4 52 64 Sik: TVOL 262 298 331 WVOL 219.255 290 SVOLI 116 148 180 SVOLX 46 59 72 39: TVOL 295 335 372 WVOL 247 289 328 SVOLT 130°) 165201 SVOLX 52 66 80 41: TVOL 329375416 WYOL 278 = 325 369 SVOLI 144184 224 SVOLX 57 73 89 43: TVOL 366 «= 416 «462 WVOL 311 364 413 SVOLI 159 203 247 Sate 63 81 98 45: TVOL 405 461 512 WVOL 347 405 460 SVOLI 175 223 272 SVOLX 70 89 108 179 154 110 44 210 182 128 5] 244 213 147 58 280 247 168 67 320 283 190 75 362 323 213 85 407 365 238 95 455 411 265 105 505 460 292 116 559 512 322 128 TOTAL HEIGHT (FEET) 80 194 169 127 51 200 148 59 264 234 170 68 303 271 194 77 345 311 219 87 391 354 246 98 439 401 275 110 49] 45] 306 122 546 504 338 135 604 561 372 148 90 207 183 144 57 243 217 168 67 369 337 249 99 418 384 280 1 470 435 313 125 525 489 348 138 584 548 384 153 646 609 423 168 300 344 247 393 1 444 125 499 140 558 527 390 155 621 589 431 171 687 656 474 189 317 364 109 415 123 469 139 528 155 590 563 432 172 656 630 478 190 725 701 526 209 245 224 197 Us) 287 265 229 91 333 310 264 105 382 359 301 120 436 412 341 136 493 470 383 152 555 532 428 170 620 598 475 189 689 669 525 209 763 744 578 230 130 140 150 256 267 278 237 249 261 215 233 25] 86 93 100 300 314 326 280 295 309 250 271 292 100 108 116 349 364 378 327 345 362 288 312 336 115 124 134 401 418 435 379 399 419 328 356 383 13] 142 153 457 476 496 436 459 48] 372 403 434 148 160 173 517 539 561 497 523 548 418 453 488 166 180 194 581 606 631 562 592 621 466 506 545 186 201 217 649 677 632 666 518 562 206 224 722 753 707 745 573 621 228 247 798 833 787 829 630 683 251 272 NOTE: BLOCK INDICATES RANGE OF DATA. 1/TVOL WYOL SVOLI SVOLX TOTAL ABOVEGROUND VOLUME OF WOOD AND BARK; EXCLUDES FOLIAGE. VOLUME OF WOOD FROM A 1-FOOT STUMP 10 A 4-INCH TOP OUTSIDE BARK; EXCLUDES BARK AND FOLIAGE. SAW-LOG VOLUME IN STRAIGHT MERCHANTABLE SECTIONS AT LEAST 8 FEET LONG TO A 9-INCH TOP OUTSIDE BARK IN TREES WITH A MERCHANTABLE FIRST SECTION ABOVE A 1-FOOT STUMP. SAW-LOG VOLUME IN STRAIGHT MERCHANTABLE SECTIONS AT LEAST 8 FEET LONG TO A 9-INCH TOP OUTSIDE BARK IN TREES WITHOUT A MERCHANTABLE FIRST SECTION ABOVE A 1-FOOT STUMP. 25 Table 12--Total tree, wood, and saw-log volume for California black oak TOTAL HEIGHT (FEET) DIAMETER AT BREAST HEIGHT OUTSIDE BARK 1/ 20 30 40 50 60 70 80 Qe 1 WO i) ie WH Tee WGHES. Oo ee a ate eet 2 ee ee ee cupic IrEET © oe ee es 5: TVOL 2 WVOL 1 SVOLI 1 SVOLX 0 8 TVOL 4 WVOL 3 SVOLI 2 SVOLX 1 9: TVOL 7 27 WVOL 5 18 SVOLI 3 6 SVOLX 2 3 VW: TVOL 10 40 44 WVOL 7 28 30 SVOLI 5 10 11 SVOLX 3 5 6 13: TVOL 14 56 61 65 WVOL 10 40 43 46 SVOLI 8 16 7 18 SVOLX 4 9 9 9 15: TVOL 19 74 81 87 WVOL 14 54 59 63 SVOLI 12 24 25 26 SVOLX 6 13 13 14 V7: TVOL 24 OS 1s WVOL 18 71 76 82 srort W 34 35 36 SVOLX 9 18 18 19 19: TVOL We) kee) TED WVOL 89 97. 104 SVOLI 45 47 49 SVOLX 24 25 26 21: TVOL 144) 5157) e169 or WU I We SVOLI 59 62 64 SVOLX 31 32 33 23: iver We iby Ay ee 1349) 145) SG SVOLI 76 79 82 SERS 39 41 43 25: TVOL 204 221, | 238) 255 yet ae88 Mo 160... 174 | 187) | 4200 2 i2eeaeees SVOLI 95 99) 102) 106) 109m alts SVOLX 49 51 53 55 57 59 26 ooo TOTAL HEIGHT (FEET) DIAMETER AT BREAST HEIGHT OUTSIDE BARK 1/ 20 30 40 50 60 70 80 [rrr nnn nnn ee [EHS ee we eae ee eR RR see CUBIC FEET ma 109 4©132«=6154 «| :«175~—Ss«<196 WVOL 88 106 123 140 157 SVOLI 79 87 94 100 106 SVOLX 41 45 49 52 55 YZ 29: TVOL 125 152 177 202 226 WVOL 102 123 144 163 183 SVOLI 96 105 114 121 128 SVOLX 50 55 59 67 31: TVOL 173 202 WVOL 142 166 SVOLI 126 136 SVOLX 65 71 33: TVOL 196 228 WYOL 162 189 SVOLI 149 161 SVOLX 77 84 35: TVOL 220 256 WVOL 184 214 SVOLI 174 188 SVOLX 91 98 54 /R TVOL 245 286 WYOL 207 241 SVOLI 202 218 SVOLX 105 114 39: TVOL 272 318 WVOL 232 270 SVOLI 233 251 SVOLX 121 131 41: TVOL 300 351 WVOL 258 300 SVOLI 266 287 SVOLX 138 150 43: TVOL WYOL SVOLI SVOLX 45: TVOL 480 538 WYOL 416 465 SVOLI 394 417 SVOLX 205 217 NOTE: BLOCK INDICATES RANGE OF DATA. 1/TVOL = TOTAL ABOVEGROUND VOLUME OF WOOD AND BARK; EXCLUDES FOLIAGE. 217 173 1 58 250 201 135 70 595 513 438 228 WVOL = VOLUME OF WOOD FROM A 1-FOOT STUMP TO A 4-INCH TOP OUTSIDE BARK; EXCLUDES BARK AND FOLIAGE. SVOLI = SAW-LOG VOLUME IN STRAIGHT MERCHANTABLE SECTIONS AT LEAST 8 FEET LONG TO A 9-INCH TOP OUTSIDE BARK IN TREES WITH A MERCHANTABLE FIRST SECTION ABOVE A 1-FOOT STUMP. SVOLX = SAW-LOG VOLUME IN STRAIGHT MERCHANTABLE SECTIONS AT LEAST 8 FEET LONG TO A 9-INCH TOP OUTSIDE BARK IN TREES WITHOUT A MERCHANTABLE FIRST SECTION ABOVE A 1-FOOT STUMP. 498 123 559 144 624 168 692 193 764 644 424 221 839 72 482 251 918 785 544 283 27 Table 13--Total tree and wood volume for Engelmann oak TOTAL HEIGHT (FEET) DIAMETER AT BREAST HEIGHT OUTSIDE BARK V 20 30 40 50 60 70 INCHES 0 9) 88 === = CUBIC FERN — ni Bi TVOL wWYOL 3 TVOL 6 WVOL 3 Ce TVOL 12 WVOL 6 11: TVOL 19 20 WVOL 10 11 13: TVOL 29 30 WVOL 16 16 15: TVOL 40 42 WVOL 23 24 U7/8 TVOL 55 57 WVOL 32 33 19): TVOL 71 74 WVOL 42 44 21: TVOL 91 95 WVOL 55 58 23: TVOL 113 118 WVOL 70 73 25: TVOL 138 144 WVOL 86 91 28 TOTAL HEIGHT (FEET) DIAMETER AT BREAST HEIGHT OUTSIDE BARK 1/ 20 30 40 50 60 70 NCH EST ene oar CUBICSREET =.) —s= =) a 27: TVOL 137 148 158 166 173 WVOL _ 85 93 100 106 11 29: TVOL 162 176 187 197 206 WVOL 103 112 120 127 134 31: TVOL 190 206 220 231 241 WVOL 122 134 143 152 159 33: TVOL 221 240 255 269 281 WVOL 144 157 169 179 187 35: TVOL 255 276 294 309 323 WVOL 168 184 197 208 218 37: TVOL 291 316 336 354 369 WVOL 194 212 227 241 253 39: TVOL 330 358 381 401 9 WVOL 223 244 261 276 -90 41: TVOL 404 430 453 473 WVOL 278 297 315 330 43: TVOL 453 482 507 530 WVOL 314 337 357 374 NOTE: BLOCK INDICATES RANGE OF DATA. 1/TVOL = TOTAL ABOVEGROUND VOLUME OF WOOD AND BARK; EXCLUDES a FOLIAGE. WVOL = VOLUME OF WOOD FROM A 1-FOOT STUMP TO A 4-INCH TOP OUTSIDE BARK; EXCLUDES BARK AND FOLIAGE. Table 14--Total tree, wood, and saw-log volume for biue oak TOTAL HEIGHT (FEET) TOTAL HEIGHT (FEET) DIAMETER AT oa BREAST HEIGHT OUTSIDE BARK 1/ 20 30 40 50 60 70 80 90 100 OUTSIDE BARK 1/ 20 30 40 50 60 70 80 90 100 INCHES INCHES 5: 27: TVOL tbe ie SVOLI SVOLX SVOLX 7: 29: “TVOL TVOL 154 176 195 212 227 242 255 268 wv WVOL 123 142 159 174 188 201 214 225 SVOLI SVOLI 39 50 60 70 80 89 99 108 SVOLX SVOLX 27 35 42 49 55 62 68 75 9: HW: TVOL TVOL 180 205 227 247 265 282 298 n3 wvoL WYOL 145 168 188 206 223 238 253 267 SVOLI SVOLI 44 56 68 79 90 101 m1 122 SVOLX SVOLX 31 39 47 55 62 70 77 84 li: 33: TVOL TVOL 208 237 263 286 307 327 345 362 wot WVOL 170 197 220 242 261 279 297 313 SVOLI SVOLI 50 63 76 89 101 113 125 136 SVOLX SVOLX 34 44 53 61 70 78 86 94 13: S55 TVOL TVOL 238 272 302 328 352 375 396 415 wVOL WVOL 198 228 256 280 303 324 344 363 SYOLI SVOLI 55 70 85 99 112 125 138 15] SVOLX SVOLX 38 49 59 68 78 87 96 105 15: cea) [wna a Ss —won oa = —fNO > on Poo wo a wo rm wo = oO fo) ~s = oO fos) o = S a wo = rm > o = w rm > —womn foal wo —~—wn7o Oo > Pow w = =—no— a Mm — Oo a oe a =_ ~s wo = np @ ™~s — NOTE: 1/TVOL WYOL SVOLI SVOLX BLOCK INDICATES RANGE OF DATA. TOTAL ABOVEGROUND VOLUME OF WOOD AND BARK; EXCLUDES FOLIAGE. VOLUME OF WOOD FROM A 0.3 METER STUMP TO A 10-CENTIMETER TOP OUTSIDE BARK; EXCLUDES BARK AND FOLIAGE. SAW-LOG VOLUME IN STRAIGHT MERCHANTABLE SECTIONS AT LEAST 2.5 METERS LONG TO A 23-CENTIMETER TOP OUTSIDE BARK IN TREES WITH A MERCHANTABLE FIRST SECTION ABOVE A 0.3-METER STUMP. SAW-LOG VOLUME IN STRAIGHT MERCHANTABLE SECTIONS AT LEAST 2.5 METERS LONG TO A 23-CENTIMETER TOP OUTSIDE BARK IN TREES WITHOUT A MERCHANTABLE FIRST SECTION ABOVE A 0.3-METER STUMP. Table 31--Total tree, wood, and saw-log volume for coast live oak TOTAL HEIGHT (METERS) DIAMETER AT REAST HEIGHT OUTSIDE BARK 1/ 3 6 9 12 15 18 21 24 27 CENTIMETERS a imnes fh pow RON = Paes ages Sa 10: TVOL 0.02 WVOL .01 SVOLI .01 SVOLX .00 20: TVOL .09 WYOL -05 SVOLI 03 SVOLX -01 30: TVOL ~24 WYOL a) SVOLI .08 SVOLX -03 40. TvOL WVOL SVOLI SVOLX 50: TVOL WVYOL SVOLI SVOLX 60: TVOL WVOL SVOLI SVOLX 70: TVOL 2.61 3.36 4.03 4.63 5.19 Ss 7/l 6.21 6.69 WYOL 1.89 2.42 2.88 3.30 3.69 4.05 4.39 4.72 SVOLI -97 ess WSvAl 2.04 oe 2.69 3.00 3.30 SVOLX .36 .50 -63 eS) .87 .99 1.10 1.21 80: TVOL 4.58 5.49 6.31 7.07 7.79 8.47 9.11 WYOL 3.39 4.04 4.63 5.17 SVOLI 1.82 2.30 2.76 3.20 SVOLX .67 ~85 1.02 1.18 90: TVOL 6.03 Usc 8.29 9.29 WYOL 4.57 5.45 6.24 6.97 SVOLI 2.37 3.00 3.59 4.17 SVOLX .87 1.10 1.32 1.54 100: TVOL 9221 10759) 87 WVOL 7.11 8.15 9.10 SVOLI 3.80 4.55 5.28 SVOLX 1.40 1.68 1.94 110: TVOL N49 SS 3210 14-80!) 16.30) i572) 119208 WVOL 9206) 10537" 11-59). W272 13580) 14582 SVOLI 4.70 5.64 6.54 7.41 8.26 9.10 SVOLX 73: 2.08 2.41 2.73 3.04 3235) 120: TVOL W406 16216 V8.1 W995 2168 23.34 WYOL 11.29 12.93 14.44 15.86 17.20 18.48 SVOLI 5.72 6.85 ea 9.01 10.05 11.06 SVOLX 2.11 2.52 2.93 3.32 3.70 4.07 130: TVOL NG93 19546 921281) 924.5025 — 26.1) 28510 WYOL 13283 5.84) 7-69) 919243) 21/307 22263 SVOLI 6.84 8.20 STOO Omen esOZenlaones SVOLX 2.52 3.02 3.50 su97) 4.43 4.87 NOTE: BLOCK INDICATES RANGE OF DATA. 1/TVOL WYOL SY0i_I SVOLX TOTAL ABOVEGROUND VOLUME OF WOOD AND BARK; EXCLUDES FOLIAGE. 7.14 5.03 3.59 os 9.73 7.05 4.85 1.79 12.79 9.51 6.32 (25358) 16.33 12.41 8.00 2.95 20.37 15.80 9.91 3.65 24.93 19.70 12.05 4.44 30.02 24.13 14.42 5.31 2.07 29 1.1] -41 3.47 2.27 1.82 -67 5.30 3.61 2.75 1.01 7.58 5.33 3.88 1.43 10.33 7.48 5.24 1.93 13.58 10.07 6.83 2.51 17.34 13.15 8.65 3.18 21.63 16.75 10.71 3.94 26.46 20.88 13.02 4.79 31.86 25.57 15.58 5.74 36 39 42 3.67 3.86 2.40 2.52 1.96 2.09 -72 alli 5.60 5.88 6.16 3.80 3.99 4.18 2.95 3.15 3.34 1.09 1.16 15728! 8.00 8.41 8.8] 5.62 5.90 6.17 4.17 4.45 4.72 1.53 1.64 1.74 10591 «4712-01 7.88 8.27 8.66 5.62 6.00 6.38 2.07 2.21 2.35 14.34 15.07 15.79 10.62 11:15 11.66 Uo 7.82 8.30 2.70 2.88 3.06 18.31 19.25 20.16 13.87 14.56 15.23 9.28 9.90 10.52 3.42 3.65 3.87 22.83 24.01 25.15 17.66 18.54 19.39 ESO 227 lisi203 4.23 4.52 4.80 27.94 29.38 30.77 ZZ Mee Sell ees, Use WESSON MS eit! 5.15 5.49 5.83 S604) SKS S/5 015 26.96 28.30 29.60 16572 17585" ‘118.96 6.16 6.57 6.98 VOLUME OF WOOD FROM A 0.3 METER STUMP TO A 10-CENTIMETER TOP OUTSIDE BARK; EXCLUDES BARK AND FOLIAGE. SAW-LOG VOLUME IN STRAIGHT MERCHANTABLE SECTIONS AT LEAST 2.5 METERS LONG TO A 23-CENTIMETER TOP OUTSIDE BARK IN TREES WITH A MERCHANTABLE FIRST SECTION ABOVE A 0.3-METER STUMP. SAW-LOG VOLUME IN STRAIGHT MERCHANTABLE SECTIONS AT LEAST 2.5 METERS LONG TO A 23-CENTIMETER TOP OUTSIDE BARK IN TREES WITHOUT A MERCHANTABLE FIRST SECTION ABOVE A 0.3-METER STUMP. 51 Table 32--Total tree, wood, and saw-log volume for interior live oak TOTAL HEIGHT (METERS) DIAMETER AT BREAST HEIGHT x OUTSIDE BARK 1/ 3 6 9 12 15 18 21 24 27 30 33 36 39 GAMES 9 asboodhoséeosseaeoss sso GING MES oso t eo see occ ee eee eee. 10: TVOL WYOL SVOLI SVOLX 20: TVOL WVOL SVOLI SVOLX 30: TVOL WVOL SVOLI SVOLX 40: TVOL WVOL SVOLI SVOLX 50: TVOL WVOL SVOLI SVOLX 60: TVOL 4.60 WVOL 4.00 SVOLI 2.75 SVOLX 1.01 70: TVOL 6.29 6.65 6.99 WYOL 5 BOB SVOLI 3.88 4.17 4.45 SVOLX 1.43 N53) 1.64 80: TVOL 8.25 8.72 9.17 WVOL 7.42 7.94 8.45 SVOLI 5.24 5.62 6.00 SVOLX 1.93 2.07 2.21 90: TVOL 10.48 11.07 11.65 WVOL 9.56 10.23 10.89 ~ SVOLI 6.83 7.33 7.82 SVOLX 2.51 2.70 2.88 100: TVOL 12.98 13.71 14.42 WVOL TWD Uo USS SVOLI 6.05 9.28 9.90 SVOLX 3.18 3.42 3.65 110: TVOL 8.30 Ces Wave) Wee ese sats eet} Woz) Gab 7/1) WVOL 6.70 7.97 Oats WOsss Wess ee) GS dey We G74 SVOLI 4.70 5.64 6.54 7.4 8.26 9.10 Qo WO s7Al Uh) Wo 27/ SVOLX 1.73 2.08 2.41 as) 3.04 3.35 3.65 3.94 4.23 4.52 120: TVOL Or les “AZ GsI2 WSs. GSS eG Be) = OE ASE WVOL 8.07 OO) WeOy AGS ss WSs WOs4 Uy BD SVOLI 5.72 6.85 1395 QO] NOKOS) 06) 1/2052 32021359 7eeta 9) SVOLX 2.11 als 2193, 3.32 3.70 4.07 4.44 4.79 5.15 5.49 130: TVOL 66) 13842) 506s 6461p USEOTN 9R4 7 2028 e220} e2oe Someta, WVOL 9659 1041) 9 13/5 1482) 16245 18203) pl957) 2107)" 22255), 124-00 SVOLI 6.84 8.20 Oso} 10s Wate Wsb23 GSE USS Gave Wok SVOLX 2.52 3.02 3.50 3297 4.43 4.87 5.31 5.74 6.16 6.57 NOTE: BLOCK INDICATES RANGE OF DATA. 1/TYOL = TOTAL ABOVEGROUND VOLUME OF WOOD AND BARK; EXCLUDES FOLIAGE. WYOL = VOLUME OF WOOD FROM A 0.3 METER STUMP TO A 10-CENTIMETER TOP OUTSIDE BARK; EXCLUDES BARK AND FOLIAGE. SVOLI = SAW-LOG VOLUME IN STRAIGHT MERCHANTABLE SECTIONS AT LEAST 2.5 METERS LONG TO A 23-CENTIMETER TOP OUTSIDE BARK IN TREES WITH A MERCHANTABLE FIRST SECTION ABOVE A 0.3-METER STUMP. SVOLX = SAW-LOG VOLUME IN STRAIGHT MERCHANTABLE SECTIONS AT LEAST 2.5 METERS LONG TO A 23-CENTIMETER TOP OUTSIDE BARK IN TREES WITHOUT A MERCHANTABLE FIRST SECTION ABOVE A 0.3-METER STUMP. 1p) o7a