UNIVERSITY OF CALIFORNIA COLLEGE OF AGRICULTURE AGRICULTURAL EXPERIMENT STATION BERKELEY, CALIFORNIA YIELD, STAND AND VOLUME TABLES FOR DOUGLAS FIR IN CALIFORNIA FRANCIS X. SCHUMACHER BULLETIN 491 APRIL, 1930 UNIVERSITY OF CALIFORNIA PRINTING OFFICE BERKELEY, CALIFORNIA 1930 YIELD, STAND AND VOLUME TABLES FOR DOUGLAS FIR IN CALIFORNIA FEANCIS X. SCHUMACHER! INTRODUCTION The United States Forest Service has reecntly completed a study of the yields of Douglas fir (Pseudotsuga taxifolia Britt.) for even-aged stands of Oregon and Washington. 2 The work was not extended to stands south of the Willamette-Umqua divide in Oregon because from observation it is believed that this line roughly divides the Douglas fir forest into two types of decided difference in stand characteristics. But the commercial range of the species on the Pacific slope extends into California about as far south as Yosemite National Park in the Sierra and about San Francisco Bay along the coast. To report the yields of well-stocked, even-aged stands of the species in California is the object of this bulletin. That there are significant differences in certain stand character- istics between the two general regions seems established from the work presented herein. GROWTH OF DOUGLAS FIR STANDS IN CALIFORNIA The growth of the species is shown by tables which state the yield of even-aged stands over a period of years. Age, timber productive quality of the area, and stand density are the most important growth- determining factors of a stand. As there is no satisfactory way of expressing stand density in absolute terms, normal-yield tables based on the ideal density which produces maximum volume are presented. Basic Data The normal-yield tables for Douglas fir are based on 159 sample plots scattered through the geographical range of the species in California. i Assistant Professor of Forestry and Assistant Forester in the Experiment Station. 2 McArdle, R. E. Rates of growth of Douglas fir forests. West Coast Lumberman, 54:90-95, 1928. This article summarizes the results of the study. The complete work is to be published soon as a bulletin of the United States Department of Agriculture. 4 University of California — Experiment Station Plot Selection. — Within even-aged stands plots were established so as to enclose a comparatively complete crown canopy by excluding the larger openings which follow failure of reproduction or accident and at the same time to include within boundaries the area equivalent to that which seemed to be used by the enclosed timber. Plots were surveyed with staff compass and chain. Age Determination. — The age of each plot was determined by counting the annual rings on cores extracted (with Swedish increment borers) from near the base of several trees. By the age of the tree is understood the number of rings on the core plus the necessary cor- rection for height growth to the point of boring. The age of the oldest tree was taken as the plot age although the difference between the ages of the youngest and oldest tree examined was seldom more than two or three years. Field Measurements. — Diameter breast high of every tree was measured with diameter tape and tallied by species and crown class (dominant, codominant, intermediate, or suppressed). The heights of fifteen to twenty-five trees were measured with the Forest Service hypsometer, from horizontal distances measured with the Leitz Fardi Range Finder of 20-centimeter base. Heights were plotted over diameter on cross-section paper in the field, the number of measurements necessary being judged at the time by the range of diameters present and their dispersion around the free-hand curve. A short description of physiographic features completed the field work on each plot. Office Computations. — The computational work necessary for each plot is evident from following paragraphs. The yield tables were constructed by correlating dependent growth variables with age and site quality by the method described by Bruce and Reineke, 3 and the stand tables are based on CharlierV method of calculating theoretical frequencies. Normal Yield Tables Tables 1 to 11 and figures 1 to 11 indicate the growth of Douglas fir in fully-stocked stands in California, for age and site index. 5 Site index is herein defined as the height that the average dominant Douglas fir will attain, or has attained at 50 years of age. Average '■> Druce, D., and L. H. Reineke. Multiple curvilinear correlation in forest investigative work. Unpublished contribution of the United States Forest Service. 1927. < Charlier, C. V. L. Die Grundzuge der mathematischen Statistik. p. 3-125. Lutke und Wulff, Hamburg. 1920. : - Before constructing these tables the sample plot data were compared to the yield tables for Douglas fir in Oregon and Washington. See p. 27. Bul, 491] Yield, Stand, and Volume Tables for Douglas Fir TABLE l Height of the Average Dominant Tree* Age, Site index — height of average dominant at 50 years years 60 80 100 120 140 30 feet • 39 feet 54 feet 67 feet 81 feet 95 40 50 68 85 102 120 50 60 80 100 120 140 60 68 89 112 135 156 70 74 98 122 147 170 80 79 104 131 158 182 90 83 110 138 166 192 100 86 114 146 173 201 110 89 118 152 179 209 120 92 122 156 185 216 130 96 125 159 189 220 140 98 128 162 193 224 150 99 130 164 196 228 160 100 132 165 198 232 * The height from average ground level to tip of the dominant tree of average basal area for the dominant class. SO 60 70 80 ^20 /JO /-90 /so Too Fig. 1. — Height of the average dominant tree for age and site index. These curves were used in site classification of the plots. University of California — Experiment Station TABLE 2 Height of Average Tree* Age, Site index — height of average dominant at 50 years years 60 80 100 120 140 30 feet feet 41 feet 58 feet 72 * feet 85 40 58 77 94 110 50 47 71 92 110 131 60 57 81 104 127 148 70 65 89 114 140 163 80 70 96 123 152 176 90 75 102 132 160 187 100 78 107 139 168 196 110 82 112 145 176 120 85 117 149 180 130 88 121 154 184 140 90 124 157 188 150 91 126 159 192 160 92 127 161 194 The height from average ground level to tip of the tree of average basal area. /30 /-K) /5Q Age /r? c/ears Fig- 2. — Height of the average tree for age and site index. Bul. 491] Yield, Stand, and Volume Tables for Douglas Fir TABLE 3 Number of Trees to the Acre* Site index — height of average dominant at 50 years Age, 60 80 100 120 140 years Number of trees to the acre 30 1060 672 485 394 40 780 497 364 297 50 1033 601 386 278 230 60 790 475 302 220 182 70 643 382 241 176 147 80 530 313 200 148 121 90 445 260 168 125 100 100 378 225 143 104 85 110 324 193 122 91 120 282 170 107 80 130 254 152 95 70 140 230 138 87 62 150 212 124 79 58 160 198 113 75 54 The number of trees that have reached a height of at least 4.5 feet (breast height). Fig. 3. — Number of trees to the acre for age and site index. University of California — Experiment Station TABLE 4 Basal, Area to the Acre* Age, Site index— height of average dominant at 50 years years 60 80 100 120 140 30 sq.ft. sq. ft. 198 sq. ft. 217 sq. ft. 230 sq.ft. 243 40 223 243 267 285 50 205 237 264 290 305 60 214 249 281 305 319 70 222 260 295 316 328 80 228 271 305 323 334 90 233 280 313 329 339 100 238 288 318 333 342 110 242 294 322 336 120 245 298 326 338 130 248 302 328 340 140 250 305 330 341 150 251 308 331 342 160 252 309 332 343 The sum of the cross-sectional areas at breast height, in square feet. 60 70 SO 90 Age /n years Fig. 4. — Growth in basal area to the I /20 J30 1 y y 1 /, > s 1" A ^ «5j «? s> 90' J ^ /O 20 30 50 CO 70 60 90 /OO //O /20 /30 tfO (SO /60 Age /n years Fig. 6. — Mean diameter breast high for age and site index — the average of all diameters in the stand. Bul, 491] Yield, Stand, and Volume Tables for Douglas Fir 11 TABLE 7 Cubic Volume to the Acre* Age, Site index — height of average dominant at 50 years years 60 80 100 120 140 cu. ft. cu.ft. cu. ft. cu.ft. cu. ft. 30 3,300 4,900 6,500 7,700 40 2,300 5,000 7,200 9,350 10,900 50 3,650 6,400 9,000 11,700 13,100 60 4,800 7,600 10,500 13,200 14,800 70 5,700 8,550 11,750 14,500 16,200 80 6,400 9,350 12,750 15,500 17,400 90 6,950 10,000 13,550 16,400 18,400 100 7,400 10,500 14,300 17,200 19,200 110 7,700 11,000 14,900 17,950 120 7,950 8,150 11,400 11,700 15,400 15,950 18,600 19,200 130 140 8,350 8,500 12,000 12,300 16,400 16,800 19,800 20,300 150 160 8,600 12,500 17,200 20,800 * The cubic volume of the entire stem of all trees from ground to tip but without limbs or bark. The volume table used is given following p. 22. Fig. 7. — Growth in cubic volume to the acre for age and site index. 12 University of California — Experiment Station TABLE 8 Mean Annual. Growth in Cubic Volume to the Acre* Age, Site index — height of average dominant at 50 years years 60 80 100 120 140 30 cu. ft. cu. ft. 110 cu. ft. 163 cu.ft. 217 cu.ft. 257 40 58 125 180 234 270 50 73 128 180 234 262 60 80 127 175 220 247 70 82 122 168 207 232 80 80 117 159 194 218 90 77 110 151 182 205 100 74 105 143 172 192 110 70 100 135 163 120 66 95 128 155 130 63 90 123 m 140 60 86 117 141 150 57 82 112 135 160 54 78 107 130 The cubic volume on the acre divided by the age 60 70 80 90 Age tn years /OO //O /20 /30 MO /SO /GO Fig. 8. — Mean annual growth in cubic volume to the acre for age and site index. Bui* 491] Yield, Stand, and Volume Tables for Douglas Fir 13 TABLE 9 Number of Trees Eight Inches and Over,, to the Acre Site index — height of average dominant at 50 years Age, 60 80 100 120 140 years Number of trees eight inches and over 30 185 265 258 252 40 252 278 251 230 50 191 279 258 221 198 60 250 277 230 190 170 70 266 260 203 165 143 80 269 234 179 144 118 90 260 210 158 124 98 100 243 190 139 195 85 110 225 174 122 SI 120 210 159 106 80 130 199 146 94 70 140 187 135 85 63 150 178 124 79 58 160 167 114 75 54 O JO 20 30 50 CO 70 80 90 /OO //O /20 /30 /fO /SO /60 Age /n c/eors Fig. 9. — Number of merchantable trees to the acre for age and site index. 14 University of California — Experiment Station TABLE 10 Volume Board Measure to the Acre* Site index — height of average dominant at 50 years Age, years 60 80 100 120 140 bd. ft. bd. ft. bd. ft. bd. ft. bd. ft. 30 7,760 17,050 27,900 37,000 40 16,000 31,700 47,700 59,400 50 8,940 25,200 45,000 64,800 76,200 60 15,060 34,300 56,900 77,400 90,600 70 21,000 42,700 67,300 89,000 103,500 80 26,500 49,650 76,200 98,400 114,800 90 31,400 55,700 83,800 107,400 124,100 100 35,900 60,600 91,000 115,300 131,500 110 39,400 42,200 65,650 68,200 73,200 76,400 97,600 102,700 122,200 120 127,600 130 44,600 46,750 107,800 133 , 700 140 111,800 139,000 150 48,300 79,700 115,700 142,900 160 49,600 82,400 119,000 146,600 * The board foot contents of the trees by the International log rule of J^-inch kerf between a stump of one foot and a top diameter inside bark of 5 inches scaled in 16-foot logs with 0.3-foot trimming allot- ment to each. Gross volumes are presented, no account being taken of cull factors. The volume table used is given following p. 22. MQ/QOL S HO' I30.0OG / /20,OOC ,/ / / /OQOOO / 9QOO0 80.000 70,00C / / eopoo // / / 5O.0OC / It ■9O.000 30.000 20,000 /QOOO O LL ' . f / / ' r / ■2078 480 573 664 735 837 950 ,060 1,10 ,230 ,320 1150 1530 1610 Z 2 2 666 70S 1210 1400 1510 1510 1630 !™ ;™ 27 ■...7 051 inv, ILW 2 28 310 463 598 700 815 918 1010 1150 1270 1390 1500 1620 1870 2000 „ 29 335 482 634 741 860 078 1070 1210 1340 1470 1800 1720 1880 1000 2100 30 355 626 670 702 010 1040 1140 1300 1430 1560 1700 1830 1990 2,00 2200 31 374 553 715 833 967 1090 1200 1380 1510 1650 1800 1030 2000 3230 2380 „ 32 415 613 792 2 z un 1350 1M0 1590 irni ,<«] 2300 16 3 » 2» , 31 437 642 830 975 1130 1280 1100 1000 1760 1910 2100 2160 2130 26,0 2780 36 457 684 878 1020 1,90 1340 1500 1690 1850 2040 2200 2380 2680 2740 2900 „ ,070 37 502 738 955 1110 ,300 1480 1620 1830 2000 2230 MOO 2600 2800 3000 3200 „ 38 525 770 097 ,180 ,380 1530 1700 1910 2100 2320 2530 2710 2930 3160 3310 39 546 810 1939 1220 ,420 1600 1760 2000 2200 2430 2640 2830 3060 3190 3400 o 40 570 836 1080 ,280 ,490 1680 1890 2090 2300 2550 1730 2020 3200 3420 3630 n 11 593 872 1120 1340 ,550 1730 1920 2180 2390 2640 2880 3080 3330 3850 3760 42 617 910 1180 1390 1600 1800 2000 2240 2490 1710 < 3200 3180 j;i«i 3920 " 640 945 1210 1450 1680 1890 2090 2310 1580 2830 310O 3340 3600 3810 4050 14 m ,,:, 1170 1500 1720 1950 2170 2440 2680 2950 3830 3180 3760 3980 1 B„i.. number ol tree, 1 20 19 50 36 j 33 ,6 " 1 11 4 • ■1 • o 215 ■ [i.trri,,,!,.,,,!,! rulf i»,-mrli k TABLE 15 22 i IB — Volume in Board Feet rot Total height in feet nu 110 120 130 140 150 160 170 180 190 200 Basis, Number it ] 1 of trees Volume in board feet sou 30 34 39 45 52 58 66 73 79 87 5 the 47 53 62 69 77 86 96 107 117 126 16 wit 68 79 110 91 125 100 140 113 152 124 167 139 185 150 200 161 216 175 230 10 CaJ 95 19 fol] 128 143 162 181 198 215 * 238 254 274 295 24 155 177 200 220 240 260 286 309 332 353 24 at i 187 220 259 294 212 238 279 261 306 354 287 338 390 448 312 366 427 483 340 400 460 526 368 430 500 570 394 454 535 602 421 493 570 626 14 250 290 330 14 320 367 13 yea 406 11 vigi 332 370 415 460 500 543 595 642 692 735 7 373 415 415 461 463 518 515 575 564 613 680 665 740 718 798 778 860 824 915 5 wid 627 10 458 517 572 634 695 751 817 883 950 1000 8 the Zon birc 505 559 628 700 768 827 900 975 1040 1110 3 550 613 690 764 817 900 980 1070 1140 1210 6 600 662 750 836 907 978 1070 1150 1230 1300 5 the 656 705 718 774 812 880 900 975 985 1060 1080 1150 1240 1240 1340 1320 1420 1410 1520 5 i 1140 8 l: 735 837 950 1060 1140 1230 1320 1450 1530 1640 807 890 1010 1120 1210 1300 1310 1400 1410 1510 1540 1630 1640 1770 1750 1880 3 867 951 1080 1200 2 918 1010 1150 1270 1390 1500 1620 1760 1870 2000 976 1070 1210 1340 1470 1600 1720 1880 2000 2100 1040 1140 1300 1430 1560 1700 1830 1990 2100 2200 1090 1160 1210 1200 1270 1350 1380 1440 1510 1510 1590 1690 1650 1740 1800 1900 1930 2090 2220 2380 2500 2380 2500 2620 2030 2200 2300 1 1850 2000 2150 1280 1400 1600 1750 1920 2100 2260 2430 2610 2780 1340 1500 1690 1850 2040 2200 2380 2580 2740 2900 1400 1560 1760 1920 2130 2300 2500 2680 2890 3040 1 1480 1620 1830 2000 2230 2400 2600 2800 3000 3200 1530 1700 1910 2100 2320 2530 2720 2930 3160 3340 ' 1600 1790 2000 2200 2430 2640 2830 3060 3290 3490 , 1680 1890 2090 2300 2550 2730 2920 3200 3420 3630 1730 1920 2180 2390 2640 2880 3080 3330 3850 3760 1800 2000 2240 2490 2720 3000 3200 3480 3700 3920 1890 2090 2310 2580 2830 3100 3340 3600 3810 4050 i 1950 2170 2440 2690 2950 3330 3480 3750 3980 4200 1 i 33 16 11 9 11 4 2 215 ach< i d. i. b. in top by International rule (H-inch kerf). m-aged stands in Mendocino and Trinity Counties. APPENDIX Bul. 491] Yield, Stand, and Volume Tables for Douglas Fir 25 YIELD AND STAND TABLES Basic Data The sample plots on which the yield and stand tables are based were measured by the Division of Forestry in 1927. Out of the 175 plots originally measured, 16 were discarded (see table 20). The 159 actually used are from the following- watersheds given in table 17. TABLE 17 Distribution of Plots by Principal, Watersheds Region and watershed Number of plots Coast Range: 3 3 2 5 Big River Eel River Van Duzen River 3 38 6 Mad River 12 23 Trinity River 38 Klamath River Sierra Nevada Mountains: 5 14 Yuba River Feather River 5 2 Total 159 The composition of the plots by basal areas of the various species included is shown in table 18. TABLE 18 Composition op Basal Area of the Plots Used Species Douglas fir Western yellow pine Oak, laurel and madrone Redwood White fir Sugar pine Incense cedar Grand fir Total Basal area in percentage of total 94.99 1.48 1 04 98 57 45 37 12 100.00 26 University of California — Experiment Station The distribution of the plots by site and age classes is given in table 19. In this table, site index is defined as the height of the average dominant and codominant at 100 years, as the tables were first constructed on site index so denned for purposes of comparison with yields of Douglas fir in Oregon and Washington. TABLE 19 Distribution of Plots by Site and Age Classes Age in Site index —height in feet of the average dominant and codominant tree at 100 years years 75-84 85-94 95- 104 105- 114 115- 124 125- 134 135- 144 145- 154 155- 161 165- 174 175- 184 185- 194 195- 204 205- 214 Total 25- 34 35- 44 1 1 3 10 5 1 2 8 2 1 4 2 10 2 1 5 6 7 2 2 1 8 8 45- 54 1 1 4 12 55- 64 . 4 1 5 1 7 2 5 2 7 4 5 2 2 59 65- 74 39 75- 84 . 2 85- 94 95-104 1 3 105-114 1 5 6 1 12 115-124 125-134 7 3 1 11 1 135-144 145-154 2 2 155-164 165-174 11 1 1 12 9 4 1 Total 5 6 6 8 24 24 25 24 159 20 30 /OO //O 720 /JO /< **» ^ 1 ®Jf /^3I // t V 7 /' 10 i aa a ■§ .^ J / r A- ? ome fer A y>+s F a / J™ / < < \ r -/ ^az °- 5j r o 8 °°u lo ^Stor ic/aro ' ' c/ev iaf/o/ 7 sy &+ p& p-r* ■O/O 06 ""^5 ~~**35 p < j 1 / i 5 z J 2 f 3 -< j r— J tf o ' <*5 Averoqe dto meter- breast high Fig*. 19. — Relation of mean diameter and standard deviation to average diameter. Bul,. 491] Yield, Stand, and Volume Tables for Douglas Fir 33 1. The plots were sorted into classes according to the squares of their average diameters using class intervals of 50 square inches. 2. For each plot within the respective classes, were tallied the squares of its average diameter, of its mean diameter, and of its standard deviation. Adding the sums of the squares of mean diameter and of standard deviation, and subtracting this total from the sums of squares of average diameter left an aggregate difference of 15 hundredths of one per cent. •hlU r § y 2 ,17. i, • t3+^ -rj>* ">A3 -" *fc* **<& / -+'// > A **?26 Vj^ , 4s 2 ? 6 8/0/2/^/6 /6 20 22 2f- 26 28 30 32 3* 36 36 Fig. 20. — Relation of the coefficient of asymmetry to mean diameter. 3. Within each class interval were plotted the square root of the average of the mean diameters squared, and of the average of the standard deviations squared, over the square root of the average of the average diameters squared (fig. 19). Straight lines were fitted to these points so that M dbt ?+o* = A dbt ? Asymmetry and Excess. — The coefficient of asymmetry (/?..) and the coefficient of excess (/? 4 ) of the plots were correlated with mean diameter (figs. 20 and 21). Starting with average diameter of a site-age class from table 5, its mean diameter and standard deviation were read from figure 19, and, for the indicated mean diameter, its coefficient of asymmetry and 34 University of California — Experiment Station 5" \ y \ —01 \ \ 2 3 ^ 02 /6 ~ ^ 1 \ 1 1 / N / ' . if / V 1 ' 1 //V" ■-la _ +'„ \ 1 1 \ 1 \J v N 1 1 •s / o a -f 6 e to /2 ./# /6 /e ao 22 aT0 J> /o Fc >r A\ f era ge L hamt sfer ->C 20