SSfc^ D i v is Un of A g ricul OF C A L If O R N ! A Empirical Yield Tables for CONTENTS Page THE REDWOOD REGION 5 STAND DEVELOPMENT 7 YIELD STUDIES 11 SAMPLING 11 COMPUTATION OF STAND CHARACTERISTICS 12 SITE INDEX 14 YIELD TABLE CONSTRUCTION 16 YIELDS OF STANDS LARGER THAN 4.5 INCHES IN DIAMETER 16 YIELDS OF STANDS LARGER THAN 10.5 INCHES IN DIAMETER 22 APPLICATION OF YIELD TABLES 28 CONVERSION OF YIELD TABLE BOARD-FOOT VOLUMES TO SPAULDING RULE 31 COMPARISON TO PREVIOUS STUDY 32 APPENDIX 33 Sample Data 33 Site Index 35 Yield Table Checks 38 Volume Tables 38 LITERATURE CITED 46 ACKNOWLEDGMENT 47 James L. Lindquist and Marshall N. Palley Ming-Growth Redwood T |His bulletin presents yield tables, up to age of 100 years, for stands of young- growth coastal redwood and associated species, as these occur in the commercial forest areas of northern California. Tables show expected annual growth and yields at 10-year intervals in terms of basal area, average diameter, number of trees per acre, and volume for portions of these stands exceeding 4.5 inches and 10.5 inches in DBH (diameter at breast height). ^i Growth and yield figures in this bulletin are keyed to stand age and site index. Stand age is measured by counting the annual rings of dominant trees at breast height. Site index is a measure of the expected height of dominant redwood trees ^ < in the stand at the age of 100 years. The tables are recommended for use without adjustment where stand basal areas p are 60 per cent or more of those given in the publication. They are not recommended t. for timber cruising, unless very approximate results are acceptable. Volume growth and yield are given in cubic feet and in board feet, International ^-inch log rule. A graph is provided for converting volumes to the Spaulding log rule. AUGUST, 1963 THE AUTHORS / James L. Lindquist is Assistant Specialist in Forestry in the California Agri- cultural Experiment Station, Berkeley; and Marshall N. Palley is Lecturer in Forestry in the School of Forestry, Berkeley. The study reported in this bulletin was supported in part by funds provided under contract from the California Division of Forestry. LIST OF TABLES AND FIGURES Table No. Page 1. Young-growth redwood dominant heights by age and site index 14 2. Basal area per acre, cubic-foot stand 17 3. Basal area per acre periodic annual increment, cubic-foot stand 18 4. Average diameter, cubic-foot stand 18 5. Number of trees per acre, cubic-foot stand 18 6. Yields of cubic-foot volume per acre 20 7. Cubic-foot volume periodic annual increment 20 8. Cubic-foot volume mean annual increment 21 9. Basal area per acre, board-foot stand 22 10. Basal area per acre periodic annual increment board-foot stand 24 11. Average diameter, board-foot stand 24 12. Number of trees per acre, board-foot stand 25 13. Board-foot/cubic-foot volume ratio 26 14. Yields of board-foot volume per acre 27 15. Board-foot volume periodic annual increment 27 16. Board-foot volume mean annual increment 27 17. Sample problem of table application 29 18. Sample distribution by age and site index 33 19. Sample distribution by age and basal area 34 20. Sample distribution by basal area and site index 34 21. Sample distribution by aspect and site index 35 22. Sample distribution by slope class and site index 35 23. Sample distribution by soil groups and site index 35 24. Redwood site index by dominant heights and age 37 25. Check of yield tables against basic data 38 26. Young-growth redwood cubic-foot volume table 40 27. Young-growth redwood board-foot volume table (International %") 42 28. Young-growth redwood board-foot volume table (Spaulding) 44 Figure No. Page 1. Redwood range 6 2. Young-growth redwood reproduction (1-4 years) 8 3. Young-growth redwood stand (20-30 years) 9 4. Closed stand of young-growth redwood sprouts (80-100 years) 10 5. Site index curves 15 6. Basal area per acre, cubic-foot stand 17 7. Average diameter, cubic-foot stand 19 8. Cubic-foot volume yields 21 9. Basal area per acre, board-foot stand 23 10. Board-foot volume yields 26 11. Conversion of International Rule to Spaulding Rule for young-growth redwood stands 31 12. Redwood site index by dominant heights and age 36 James L. Ltndquist and Marshall N. Palley Empirical Yield Tables for Young Growth Redwood STANDS OF YOUNG-GROWTH redwood (Sequoia semper vir ens [d. Don] Endl.) occupy an increasing portion of the total commercial redwood forest land as the supply of old-growth redwood becomes more restricted through con- tinued harvesting. Stands similar to the virgin redwood forests will never again be produced, on a commercial basis, under existing forest management prac- tices. Thus the permanently established redwood-oriented timber industries of the northern California coast face the ir- replaceable loss of their primary resource base, the virgin redwood. Commercially stocked young-growth stands in 1948 totaled 727,000 acres, approximately 38 per cent of the total redwood acreage, which supported 6.4 billion board feet of living saw-timber (California Forest and Range Exp. Sta., 1953). These figures do not include young-growth redwood in mixed old and young stands. This tremendous source of redwood with great growth potential available now, coupled with the loss of virgin stands, indicates an increased utilization of these young stands in the future. For this reason, the timberland owners and managers need information concerning the growth and yield of this species to arrive at decisions on long range policies concerning physical plant, taxation, marketing, and similar areas of forest management. The yield tables of- 1 Submitted October 30, 1962. fered in this bulletin will aid in making reasonable predictions of long-range stand development. REDWOOD REGION Redwood stands occur from the ex- treme southwestern corner of Oregon south along the Coast Ranges of Cali- fornia to southern Monterey County as a narrow band that seldom extends in- land more than 30 miles (figure 1) (Cali- fornia Forest and Range Exp. Sta., 1953). This belt is not continuous but includes some large gaps, notably in southwestern Humboldt County and around San Francisco Bay. There are isolated stands in Marin and Alameda counties where climatic conditions are favorable for the species. The portion of the range north of Fort Bragg is char- acterized by large relatively unbroken tracts of redwood in association with other conifers. This portion of the range has the greatest remaining amount of old- growth timber. Throughout the southern part of the range redwood is typically found in smaller localized tracts that have environmental conditions favorable to this rather exacting species. There are few stands of commercial virgin redwood remaining south of Fort Bragg; where stands do occur commercially they are of low concentration or difficult of access. Young-growth stands developed sub- sequent to the initiation of logging in the redwood region during the mid-nine- [5] OREGON ESCENT CITY OLD-GROWTH REDWOOD YOUNG-GROWTH REDWOOD PLOT CONCENTRATIONS FORT BRAGG POINT ARENA SANTA CRUZ Hg. 1. Range of old- and young-growth redwood. teenth century. Logging operations at this time were concentrated near the major rivers and bays of the coastal re- gion. As these areas were cut operations spread into the adjacent uplands. The geographical distribution of the young- growth stands indicates major concentra- tions in the southern portion of the range and along the coast and rivers of the northern portion of the range. Changes in the logging operations brought about by the railroad, and later the truck and tractor, have altered the earlier logging patterns and subsequent distribution of the young-growth stands. Figure 1 indi- cates the range of the old- and young- growth redwood stands. Redwood occurs in a region of moist cool climate with relatively high annual precipitation, especially north of San Francisco Bay. Long-range precipitation records of the United States Weather Bu- reau indicate a maximum of nearly 100 inches near the northern range limit dropping to approximately 20 inches near Monterey, with averages varying from 40 to 60 inches throughout the major portion of the range. Precipitation, mostly in the form of winter rain between November and March, is supplemented during the summer by frequent heavy coastal fogs. The high humidity of the fog-belt reduces the amount of water lost by transpiration and evaporation; also, condensation of this fog on the trees is often in such large amounts that the ground is kept damp. The temperature throughout most of the range is moderate with the extremes rarely greater than 100°F or less than 20°F. Frost and snow occur occasionally at the upper elevations over most of the range. The mean tem- perature varies between 50-60°F, with average January temperatures of 44- 48°F, and average July temperatures of 56-64°F (United States Department of Agriculture, 1941). The principal topographic features of the redwood region are the mountain ranges with narrow steep valleys along [6 the coast. Some major drainages of the region are the Smith, Klamath, Mad, Eel, > Noyo, Big, Navarro, Gualala, and Rus- sian rivers. Most of these rivers have nar- I row alluvial flats. Redwood grows at elevations from sea level to nearly 3,000 feet. In the northern, more humid portion of its range it extends up the west slopes of the mountains over the summits to the east side. Further south, ideal condi- tions for growth become more restricted until near its southern limit redwood is found only in sheltered canyons where surface water is available through most of the year and summer fog is common. Topography may influence the distribu- tion of the species by controlling the in- land flow of the fog (Harlow and Harrar, 1950) . An example of this topographic control is the Eel River Valley which per- mits heavy fogs to penetrate well inland behind the much higher coastal ridges of Cape Mendocino where redwood is not found. The principal uplands soils associated with redwood have developed on heavily folded and faulted marine sandstone. These are typified by soils of the Hugo and Goldridge series groups (Storie and Weir, 1953) , which are primarily brown- i ish in color, sandy to clay loam in tex- ture, acidic, and moderately deep even on slopes. These podzolic soils associated with coniferous forest types are rated as high-to-intermediate sites for conifers (Storie and Wieslander, 1952). Alluvial soils adjacent to the major rivers, which represent a small percentage of the range, support the best development of the red- wood type. Young-growth stands are also V found on soils of the sandy marine ter- races of Del Norte and Humboldt coun- ties. Tree species commonly associated with redwood include: Douglas-fir (Pseudo- tsuga menziesii [Mirb.] Franco), Sitka spruce (Picea sitchensis [Bong.] Carr.), grand fir (Abies grandis [Dougl. | Lindl.), western hemlock (Tsuga hetero- phylla [Raf] Sarg.), tanoak (Lithocar- pus densiflorus [Hook, and Arn.] Rehd.) , Pacific Madrone {Arbutus menziesii Bursh), red alder (Alnus rubra Bong.), and California laurel (Umbellularia cali- fornica [Hook, and Arn.] Nutt.) . On the narrow alluvial flats the stands are pure redwood with an occasional laurel or alder. Further up the slopes, on upland soils, the most common associate of red- wood is Douglas-fir. Sitka spruce and western hemlock are found along the northern coastal portions of the range. Near the range limits of redwood, where environmental conditions due to lack of fog, adverse temperatures, and lower rainfall are less favorable for redwood, the less demanding species such as Doug- las-fir, grand fir, oak and tanoak become more prevalent. STAND DEVELOPMENT The initial stage in a young-growth stand following the harvesting of the vir- gin growth is marked by the numerous sprouts which develop on or near the stumps of old-growth trees (figure 2). These clumps of vegetative reproduction provide the earliest and principal means of redwood reoccupancy of a site. During the first years following logging, hard- woods and brush species often become well established in open areas between redwood clumps and provide an effective ground cover. Redwood and other coni- ferous seedlings may become established during these years, however, juvenile growth of seedlings is slow because of the heavy cover of brush. As the stems of the stump sprouts increase in size, quite rapidly during the first few years, mor- tality is simultaneously reducing the number of stems in the clumps quite heavily. However, tree height growth has an effect on the brush, which begins to die out as a result of the outward spread of the sprout clumps' canopy (figure 3). The seedlings which developed in the openings and were retarded by the brush begin their period of rapid growth. Doug- las-fir and grand fir trees which have [7] Fig. 2. Young-growth redwood sprout reproduction (1-4 years). lagged behind sprouted redwood now be- gin to catch up and will surpass redwood in total height. As the stand matures and the canopy closes other conifers maintain their height advantage over redwood for a pe- riod of years despite their apparent younger age when measured at breast- height. Redwoods eventually become the tallest trees of an old stand. Natural prun- ing of redwood branches is slow and dead branches may persist for many years. Within the redwood clumps the portion of the bole toward the center of the clump is often free of branches; most branch development is toward the out- side of the clump. Stems about the old stump may be quite numerous and boles often coalesce as the diameters increase. Because redwood is tolerant of shade in moist conditions many suppressed trees within the clumps continue to live, often resulting in all crown classes being repre- sented within a single clump. Resistance to this competition in the clumps may be due not only to inherent tolerance of the species but also to the use of the massive root system of the old- growth tree. The outreach of the branches of the clumps often effectively closes the canopy when stump spacing is not too wide. Thus these young-growth stands often retard the de- velopment of a second story of younger trees or brush. The more advanced young-growth stands, 80-100 years old, often resemble old- growth stands with [8] Fig. 3. Young-growth redwood stand (20-30 years). their massive wide spread stand elements, a high single crown canopy, and the ground relatively free of brush or ad- vance reproduction to obstruct the view in the stand (figure 4). However, in young- growth the stand elements are not individual trees but groups of trees closely associated with old-growth stumps. The developmental histories of the young-growth stands have been influ- enced to a large degree by the various harvesting methods and topographic con- ditions of the redwood region. There is a close association between these two factors since, with the introduction of heavier more mobile handling and trans- portation equipment, the logging of old- growth redwood progressed into areas formerly inaccessible. Logging tech- niques associated with various types of equipment have fundamental differences in application and effects on the land. This has resulted in redwood re-establish- ment occurring under widely different conditions. Early logging operations were generally restricted to the alluvial river flats where oxen and the rivers provided the principal means of transportation. These logging operations, taking only the best quality trees, moved very slowly up- stream in the narrow valleys leaving some residual trees and adjacent stands on the slopes as a source of seed for restocking the land. Subsequent introduction of heavy equipment and the railroad to the logging operations allowed an expansion [9] Fig. 4. Closed stand of young-growth redwood sprouts (80-100 years) of operations onto the adjacent slopes. Yarding by donkey engines and the high cost of establishing rail lines resulted in a system of clear-cutting whereby most of the timber in a given locality was either harvested or destroyed by the log- ging operations. This resulted in vast areas of open land with few seed trees available. As a result, brush and redwood stump sprout clumps, the only remaining means of redwood regeneration, reoccu- pied the land. The introduction of trac- tors and trucks in the mid-1930's again caused a shift in the harvesting methods. This extremely mobile equipment and concern over the supply of old-growth timber brought about selective cutting methods which do not destroy the resi- dual stands. The oldest existing young-growth stands, 70-100 years old, resulted from the river logging, but constitute a very small percentage of the young-growth acreage. Stands resulting from various types of clear cutting range in age from 30 to 80 years and are by far the most prevalent stands. Stands regenerated fol- lowing selective tractor logging, generally [10 less than 20 years old, do not enter into consideration in this study since they are often uneven-aged mixtures of old- and young-growth trees. YIELD STUDIES Tables of growth and yield express in numerical form the stand development process which has been outlined in the preceding section and illustrated in the photographs. A distinction is made be- tween short-term growth prediction, in which the increment for a period of less than 20 years is the desired result; and yield studies in which the total accumu- lated amounts of volume and other forest stand characteristics are shown at age in- tervals of the active useful life of a stand. This yield study forms part of a larger project which includes prediction of short-term growth as a second main ob- jective. A separate publication will be devoted to short-term growth prediction. A yield table traces the expected devel- opment of forest stands from their origin to some arbitrary age, showing changes in stand basal area, volume, average diameter, and number of trees associated with changes in site index and age. The value of yield table representations of idealized stand development is that they provide a standard against which stands may be compared and a basis for long range projections. Because values shown in yield tables represent an average of existing conditions of a sample of stands, application to actual stands must consider the character of the original sampled stands. The yield tables of young-growth red- wood presented in this study may be de- fined as empirical yield tables, which are tables developed from "average stand conditions as found in nature" (Bruce and Schumacher, 1935) . Sampling car- ried out for compilation of the present tables sought stands that were typical of better stocked conditions occurring within this type. Expressing yields in terms of age and site index is desirable since it incorporates variables important in the management of growing stands. Stocking is not used as a predictive vari- able in these yield tables. Consequently some variability of yield controlled in other yield table methods by either se- lection of normally stocked stands or use of stocking as a predictive variable re- mains unexplained. Construction tech- niques resulted in tables that resemble normal yield tables; however, yield fig- ures represent the average of stands which do not necessarily fully occupy the site. SAMPLING The objective of the data collection was to sample for growth of representative stands in the young- growth concentra- tions occurring throughout the commer- cial range of the type for development of short-term growth predictive equa- tions. Reevaluation of the sample data for yield table presentation resulted in a measure by which long-range assess- ments of productivity could be made. Sampling was carried out in the four North Coast counties of Del Norte, Hum- boldt, Mendocino, and Sonoma with special emphasis on securing a repre- sentative sample of the various sites, ages, and stand densities in each of the major areas visited. The pattern of the logging has influenced the distribution of ages and sites to some extent. Generally, as distance from the coast and elevation increase the site index and age decrease. Geographical distribution of plot concen- trations are shown in figure 1. Sampling was restricted to naturally occurring, essentially even-aged, young- growth stands that originated subsequent to logging of the virgin stands. Samples were not taken in stands that showed evi- dence of recent disturbances due either to logging or excessive windthrow. Also stands that were of two-storied canopy as a result of past cutting history were not sampled. Occasionally, scattered residu- als of the virgin stand occurred in young- [in growth stands selected for sampling. In such cases samples were moved and did not include the residual tree or young- growth trees that might have been influ- enced by the residual. The majority (51 per cent) of the stands sampled were 100 per cent redwood, with 90 per cent of the stands exceeding 50 per cent red- wood by basal area. Species composition of the samples, by basal area, showed the following averages: redwood, 83.7 per cent; other conifers, 13.6 per cent; and hardwoods, 2.7 per cent. On approxi- mately 35 per cent of the sampled stands the trees selected by point sampling were entirely of sprout origin; over-all, the sprouts comprised 65 per cent of the redwood trees included in the samples. The mean basal area per acre of the samples was 374 square feet plus or minus 156 square feet. Relative to basal area stocking density there was an attempt to sample stands that were stocked to such a degree that a manageable and useful crop could be expected. Seriously understocked stands, commonly depicted as brush fields, in- cluding widely scattered clumps of red- wood were not utilized. Distribution of sample plots by site index for age, basal area, major soil groups, slope, and aspect are shown in the appendix. In brief, the stands sampled were even-aged, rela- tively pure, undisturbed representative stands occurring in young-growth red- wood. The point-sampling technique was used for defining the sampling units within the stands. This method proved an efficient way of estimating the stand characteristics needed for yield tables. In particular it was well-suited to select- ing trees for boring for radial growth measurements required for short term growth predicting equations. In the point- sampling method trees are selected with probability proportional to their basal area. Thus, the larger trees which ac- count for nearly all the growth of the stand are sampled more intensively than the smaller trees. The Spiegelrelaskop was used to define the trees to be in- cluded in the sample. Basal area factors of 10, 20, and 40 were used in establish- ing temporary growth sample points of 15 to 25 trees under varying stand con- ditions. At each sample point, diameter at breast-height, past five- and ten-year radial growth, origin (seedling or sprout), and crown class were deter- mined for each living tree over 4.5 inches DBH. Breast-high age and total height were determined on five to eight domi- nant trees of the sampling unit. Dead trees that exceeded 4.5 inches DBH were judged as to probable cause and time of death. Trees dead longer than ten years were not included in the sample. Other information recorded for each sample point included a stem map, verbal stand description, slope class, aspect, soil type, and geographical location. Young-growth stands for sampling were located through the use of Soil and Vegetation Survey Maps, owner type maps where available, and discussions with land owners. A preliminary recon- naissance of an area, using this informa- tion, prior to establishing sample points was helpful in securing a better picture of existing stands of the area. The exact location of sample points within stands was left to the discretion of the crew leader. The principal aim of the point location within the stand was to secure a sample of trees representing uniform stand conditions. Several preliminary estimates of the stand basal area per acre were made, and the point selected was one from which the basal area estimate approximated the average of the prelimi- nary estimates. COMPUTATION OF STAND CHARACTERISTICS Calculation of per-acre estimates of the stand characteristics, number of trees, basal area, volume, and average diameter [12 1 at each sampling location was performed using an original program developed for the University of California IBM 704 computer. These characteristics were computed for the entire stand, defined as all trees over 4.5 inches in diameter, and for the sawtimber stand, those trees over 10.5 inches in diameter. Volumes for the entire stand were expressed in cubic feet and for the sawtimber stand in board- feet in terms of the International ^-inch log rule. For convenience these two por- tions of the stand will be referred to as the cubic-foot and the board-foot stands, respectively. This computer program also developed stand characteristics for five years and for a whole decade earlier us- ing borings and site curves to approxi- mate the earlier states of the stand. However, these results were not used in the preparation of the yield tables, but were utilized instead in studies of short- term growth. The computer program developed stand estimates for each of three species groups, redwood, whitewood (all other conifers) and hardwood, and for all species groups combined. Each tree meas- urement was divided by the square of its diameter (an alternative to dividing by the basal area) and all such weighted tree measurements were accumulated over the plot. The following formulas were applied to the weighted sums to ob- tain per acre figures for basal area, num- ber of trees, and diameter of the tree of average basal area: To compute stand volumes, a separate set of local volume equations was gener- ated for each plot, using the redwood and other conifers whose total height was measured. First, the volume of each of these site trees was computed in cubic feet and in board feet by substituting its diameter and height in tree volume equa- tions for that species and unit of measure- ment. The equations in the appendix (tables 26 and 27) were used for red- wood. For the whitewood tree volumes, equations were fitted to standard Doug- las-fir volume tables (Pacific Northwest Forest and Range Exp. Sta., 1955) . Then, regressions of volume on diameter squared were solved for redwood and for whitewoods, yielding equations of the form volume = a + bD 2 where "a" was the intercept and "b" the slope of the local volume equation. The local volume equations for hardwoods did not vary from plot to plot. Coefficients a and b were computed from U. S. Forest Service local volume tables for tanoak and red alder 2 for both the cubic-foot and board-foot units and these values were used uniformly for all the plots. Once the local volume table coefficients were available, per-acre volumes for each species group and volume measurement unit were computed for each plot by the 2 Data on file with the Pacific Forest and Range Experiment Staton. BASAL AREA PER ACRE BAFX N (1) NUMBER OF TREES PER ACRE = _?AF_ T ± 0.005454 * ^ D 2 -V AVERAGE DIAMETER where : BAF = basal area factor N = number of trees at the sampling point D = diameter at breast height of a tree 0.005454 = constant linking basal area (sq. ft.) to squared diameter (sq. in.) [13] 1 Basal area per acre No . Trees per acre . 005454 c-') (3) following formula (Palley, 1963) : VOLUME PER ACRE = oJHiCaZ^ + bN) (4) SITE INDEX A site index classification was prepared for the various classes of forest land oc- cupied by young- growth redwood in terms of average total height of dominant redwood at a base age of 100 years, ages being determined at breast-height (Lind- quist and Palley, 1961) . Average breast- high stand age and average total height of dominants (Hornibrook, 1942) of data collected in 161 stand samples were graphically curved to develop the site index values represented in table 1 and figure 5. Site indices from 100 to 240 by increments of 20 site units, and ages ranging from 10 to 100 years are in- cluded in these tables. For convenience the site index may be grouped in classes of 20 units that are defined by the curves, i.e., site class I, greater than 201; site class II, 181-200; and so forth to class VI, 101-120. Extension of the site index val- ues to 240 provides an upper limit for the curves, since seldom will stands reach this figure. Values of site index estimated from the curves for the sample plots used in the yield table study ranged from 100 to 232, with but three exceeding 220. Evaluation of the stand site index made from a sub-sample of trees may be accomplished by means of either a fixed area plot or a point sample to define a group of trees representative of a local- ized segment of the stand. Average stand breast-high age and total height are esti- mated from measurements of five to eight dominant redwood included in the group of trees at each location. Application of these averages to the site index curves or tables gives the site index of the plot. As an example, if average breast-high age is 45 years, and the average total height of dominants is 100 feet, by in- terpolation in table 1 or figure 5 a site index of 161 is indicated. Realignment of the site-height data shown in the ap- pendix (table 24 and figure 12) provides Table 1 AVERAGE TOTAL HEIGHTS OF DOMINANT REDWOOD BY BREAST-HIGH AGE AND SITE INDEX Age at b. h. Total height (feet), by site index (years) 100 120 140 160 180 200 220 240 20 30 40 50 60 70 80 90 100 21 34 47 57 67 76 85 93 100 31 48 62 73 84 94 104 113 120 42 62 76 89 102 112 123 132 140 53 76 92 106 119 130 142 152 160 63 89 107 122 136 148 161 171 180 74 103 122 138 154 166 180 190 200 84 117 137 155 171 184 198 210 220 95 131 152 171 188 202 217 229 240 [14 240 200 180 160 140 10 20 90 40 90 60 70 00 SO 100 AVERAGE- BREAST-HIGH AGE OF REDWOOD ( YEARS ) Fig. 5. Site index values of dominant redwood by height and breast-high age class. a more convenient means of estimating site index. Breast-high expression of the average stand age of young-growth redwood is ap- propriate because stump-sprouts show extremely rapid juvenile height growth and often exceed breast-height (4.5 feet) during the first growing season. Sprout- origin trees often develop as the domi- nant trees of the maturing stand. In this way, breast-high and total age are often the same. Restriction of the total height measurement to dominant trees makes es- timates of average stand total height more clearly defined. There is less room for subjective factors to operate when only dominants are used as site-indicator trees. [15] YIELD TABLE CONSTRUCTION Procedures for graphical development of the yield tables and curves followed, in general, recommendations made for the construction of normal yield tables (Bruce and Schumacher, 1935). De- parture from this prescribed plan was necessary for elimination of the abnor- mally stocked stands. Bruce and Schu- macher recommend that elimination of these plots be made on the basis of devia- tions from a curve of the logarithm of number of trees per acre over average stand diameter. Estimates of number of trees per acre made from point sampling procedures have been shown to be more variable than are estimates of the total basal area (Palley and O'Regan, 1961). Consequently estimates of frequency of these stands were assumed to be less reli- able than estimates of basal area. There- fore, rejection of plots was based on the deviations of the actual basal area from the estimate of basal area from prelimi- nary basal area curves (Chapman and Demeritt, 1936) . The basic principle un- derlying the technique for developing these yield tables is the recognition of the variability of stand characteristics that may be associated with stand age. This variability, if inherent in the data, is made apparent through the calculation of the standard deviation and the coeffi- cient of variation for each age class. If curves of these two statistics are depend- ent on age, yield tables which incorporate this technique result in more accurate esti- mates than those made from anamorphic harmonized curves. A further require- ment for the appropriate use of this method is that the independent variables, age and site index, be not correlated. This data reveals no correlation between these two independent variables. The first step in the reduction of the sample data to yield tables is the assign- ment of a site index to each sampled stand. The site index provides a relative measure of the yield capacity of each area and functions as the basis, along with age, for the classification of the sam- ples. Preliminary basal area per acre curves, based on age and site class, were constructed for elimination of the abnor- mally stocked samples. Samples whose total actual basal area per acre differed from the curve estimate by more than two standard errors of estimate, com- puted for each site class, were rejected from consideration in the final set of curves. Seven of the 161 stand samples used in the preparation of site index tables were rejected on this basis, and two samples slightly older than 100 years were also eliminated. Distribution of the stands by basal area and site index are shown in appendix table 20. Yield tables for the portion of the stand 4.5 inches and larger in diameter at breast-height were made by direct graphical curving of the sample plot data. Selection of the minimum tree diameter of 4.5 inches at breast-height as the basis for defining the cubic-foot volume stand was a decision made to restrict the sam- pling and calculation to the more eco- nomically valuable trees. Trees smaller than this diameter limit contribute little to the overall stand volumes and under most circumstances are not of commer- cial importance. Tables relative to the stand larger than 10.5 inches in diameter were constructed through the application of ratio conversions, associated with aver- age diameter, to the table values of the cubic-foot stand. Values of stand char- acteristics represented in the tables are the expected gross per acre yields includ- ing all species, and do not consider loss factors such as decay, defect, and break- age. Adjustments of the gross yields must be made based on individual situations if estimates of net yield are required. YIELDS OF STANDS LARGER THAN 4.5 INCHES IN DIAMETER Basal area per acre (table 2, figure 6) displays a continuing growth throughout [16] Table 2 TOTAL BASAL AREA PER ACRE (SQUARE FEET), TREES OF ALL SPECIES OVER 4.5 INCHES DBH Age Site index (years) 100 120 140 160 180 200 220 240 20 30 40 50 60 70 80 90 100 50 86 127 176 224 264 299 334 364 75 122 169 218 267 307 342 377 407 103 162 217 266 315 355 390 425 455 140 216 280 330 379 419 454 489 519 191 288 365 416 466 506 541 576 606 246 367 458 509 559 599 634 669 699 300 444 549 600 652 692 727 762 792 356 525 644 696 748 788 823 858 888 W X CJ g ^* < X H W O < < H C/3 o w u < w < CD pq 900i i SITE 1 INDEX - 240 - - 220 - jrt 6oo / 180 _ - w w w f A > 160 - en 400 - '/ X' 140 120 - 300 - v / 100 - 200 // - Y& ^ ^ /^ - J ^ i AVERAGE BREAST-HIGH AGE OF REDWOOD (YEARS) Fig. 6. Basal area per acre of young-growth redwood stands, trees of all species more than 4.5 DBH (diameter at breast height). [17] Table 3 BASAL AREA PER ACRE PERIODIC ANNUAL INCREMENT (SQUARE FEET) TREES OF ALL SPECIES OVER 4.5 INCHES DBH Sitei ndex Age period (years) 100 120 140 160 180 200 220 240 20-30 3.6 4.7 5.9 7.6 9.7 12.1 14.4 16.9 39-40 4.1 4.7 5.5 6.4 7.7 9.1 10.5 11.9 40-50 4.9 4.9 4.9 5.0 5.1 5.1 5.1 5.2 50-60 4.8 4.9 4.9 4.9 5.0 5.0 5.2 5.2 60-70 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 70-80 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 80-90 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 90-100 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 Table 4 DIAMETER (INCHES) OF TREE OF AVERAGE BASAL AREA, TREES OF ALL SPECIES OVER 4.5 INCHES DBH Age Site index (years) 100 120 140 160 180 200 220 240 20 7.6 9.6 11.3 12.7 14.1 15.5 16.8 18.1 19.4 8.7 11.1 13.0 14.6 16.2 17.6 18.9 20.2 21.5 9.3 12.4 14.6 16.4 18.0 19.4 20.8 22.2 23.3 10.1 13.7 16.2 18.2 19.9 21.4 22.8 24.1 25.2 10.8 14.8 17.6 19.7 21.6 23.1 24.5 25.8 27.0 11.5 15.8 18.8 21.0 23.0 24.5 26.0 27.3 28.4 12.1 16.7 19.8 22.2 24.2 25.9 27.4 28.7 29.8 12.6 30 40 17.4 20.7 50 23.2 60 70 25.3 27.0 80 . 28.5 90 100 29.8 31.0 Table 5 NUMBER OF TREES PER ACRE OVER 4.5 INCHES DBH, TREES OF ALL SPECIES A.ge Site index (years) 100 120 140 160 180 200 220 240 20 30 40 50 60 70 80 90 100 159 170 182 200 207 202 194 186 177 180 182 184 187 186 182 175 169 162 219 194 186 181 178 173 165 158 153 251 211 195 182 175 168 160 154 149 298 240 216 196 183 174 165 159 152 342 269 238 212 194 183 172 164 159 377 291 257 223 204 189 177 170 164 414 316 275 237 214 198 186 177 169 [18 w o < Q a * 5 h w o > < 35 20 1 — \ — ■T i i — i — - SITE INDEX 240 220 200 — 180 160 140 — ■ 120 <^ **"^ ^^** 100 - Sss %$■ ^> " - A m ^ ^^*+ - J^ ^ w r v 1 » — > i ,. 1 1 10 20 30 40 SO 60 70 80 90 100 AVERAGE BREAST-HIGH AGE OF REDWOOD ( YEARS ) Fig. 7. Diameter of tree of average basal area, trees of all species more than 4.5 inches DBH. the entire age range of these tables. This is in contrast to previous yield-table studies (Bruce, 1923) which show that basal area yield is nearly at a maximum at 60 years of age. The present curves of basal area, for all site-index classes, reach a uniform growth rate at 60 years resulting in parallel yield curves and uniform periodic annual growth rate beyond that age for all site indices (table 3) . Indications from these curves are that redwood stands attain higher basal area per acre yields and sustain a larger growth rate for longer periods of time than formerly believed for young- growth stands. Average diameter for an age-site class (table 4, figure 7) reflects the diameter of the tree of average basal area. Calcula- tion of this stand characteristic depends on estimates of the basal area and num- ber of trees per acre. Because of the variability associated with estimates of number of trees per acre made from point samples, errors in estimates of frequency may be reflected in the estimates of average diameter. The curves are steep up to 20 years of age, due in part to the use of only trees larger than 4.5 inches, the most vigorous trees of a young stand. Between 20 and 30 years the radial growth begins to drop off rapidly in the higher sites. The lower sites sustain a more gradual and uniform reduction in growth rate up to 100 years of age. Numbers of trees per acre exceeding 4.5 inches in diameter (table 5) were developed from the yield tables of total basal area and average diameter. Cal- culation of number of trees for each age- site class in this manner has resulted in these three tables being compatible in that two of the tables will define the third. The configuration of these curves indi- cates that number of trees does not re- spond to age and site as do the other stand characteristics which increase with site and age. This is due to reduction, by mortality, as the age increases, of the large number of stems established initially in [19] the stands. The restriction to a minimum diameter limit introduces ingrowth as an influence on the number of trees occur- ring in the earlier years of the stand de- velopment. Rapid radial growth in the site classes greater than 120 has resulted in most trees exceeding 4.5 inches by 20 years, thus there is a continuing reduction in number of trees for these site classes over the entire age range of the tables. Maxi- mum frequency is not reached in site classes 120 and below until 50 to 60 years, indicating that ingrowth of trees beyond the minimum diameter exceeds the mor- tality on these lower sites. At 100 years the drop in number of trees per acre, as site index increases, is reversed above site index 160 showing number of trees in- creasing with site index. This reversal in trend is undoubtedly due to improve- ment of environmental conditions which allows the suppressed trees to continue in the stand. Yield volumes of cubic-foot volume (table 6 and figure 8) of the stand ex- ceeding 4.5 inches in diameter have a uniform shape, with no abrupt change in slope apparent except for the lower site classes below 40 years of age. This uni- Table 6 CUBIC-FOOT VOLUME PER ACRE YIELDS, TREES OF ALL SPECIES OVER 4.5 INCHES DBH, TO A 4 INCH TOP INSIDE BARK ABOVE A 1.5 FOOT STUMP Age Site index (years) 100 120 140 160 180 200 220 240 20 30 40 50 60 70 80 90 100 200 500 1,000 2,100 3,600 5,200 6,900 8,800 10,600 450 1,050 2,300 3,800 5,820 8,000 10,140 12,260 14,280 1,000 2,500 4,500 6,800 9,220 11,750 14,190 16,580 18,880 2,270 4,400 7,250 10,100 12,960 15,880 18,640 21,340 23,940 3,990 7,040 10,550 14,060 17,450 20,820 23,990 27,050 30,010 5,910 10,000 14,250 18,500 22,480 26,380 29,980 33,450 36,820 7,860 13,000 18,000 23,000 27,580 32,000 36,060 39,940 43,720 9,940 16,200 22,000 27,800 33,020 38,000 42,540 46,860 51,080 Table 7 CUBIC-FOOT PERIODIC ANNUAL INCREMENT, TREES OF ALL SPECIES OVER 4.5 INCHES DBH Age period Site index (years) 100 120 140 160 180 200 220 240 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100 30 50 110 150 160 170 190 180 60 125 150 202 218 214 212 202 150 200 230 242 253 244 239 230 213 285 285 286 292 276 270 260 305 351 351 339 337 317 306 296 409 425 425 398 390 360 347 337 514 500 500 458 442 406 388 378 626 580 580 522 498 454 432 422 [20] 35 i SITE i INDEX 240 - / 220 200 - - / / - - /' / - ■ / '/ 180 160 140 . - / Y/ / - / '/ / " - / // '/ / - - // // ^- 120 100 - A V - & y^ 1 10 20 30 4Q 50 60 70 80 90 100 AVERAGE BREAST-HIGH AGE OF REDWOOD ( YEARS ) Fig. 8. Cubic-foot volume per acre of young-growth redwood stands, trees of all species more than 4.5 inches DBH. Table 8 CUBIC-FOOT MEAN ANNUAL INCREMENT, TREES OF ALL SPECIES OVER 4.5 INCHES DBH Age Site index (years) 100 120 140 160 180 200 220 240 20 30 40 50 60 70 80 90 100 10.0 16.6 25.0 42.0 59.8 74.4 86.2 97.7 106.0 22.5 35.0 57.5 76.0 96.6 114.4 126.8 136.1 142.8 50.0 83.2 112.5 136.0 153.0 168.0 177.4 184.0 188.8 113.5 146.2 181.2 202.0 215.1 227.1 233.0 236.9 239.4 199.5 234.4 263.7 281.2 289.7 297.7 299.9 300.2 300.1 295.5 333.0 356.2 370.0 373.2 377.2 374.8 371.3 368.2 393.0 432.9 450.0 460.0 459.8 457.6 450.8 443.3 437.2 497.0 539.5 550.0 556.0 548.1 543.4 531.8 520.1 510.8 [21] formity of slope, of a given site class, on either side of the age of the culmination of the periodic annual increment indi- cates a broad range of ages from which rotation age could be selected if viewed exclusively from the point of yield and growth. Periodic annual increment (table 7) has culminated for all site classes prior to 100 years, this age occurring earlier as site index increases. Mean annual in- crement (table 8) does not culminate for site indices below 180 until after 100 years; in the higher classes this age varies from approximately 45 years (site 240) to 95 years (site 180) . The period of time until culmination and the flatness of the curves of mean annual increment suggest the possibility of longer rotations for this species if they are desired. YIELDS OF STANDS LARGER THAN 10.5 INCHES IN DIAMETER Tables for the stand 10.5 inches and larger in diameter represent the stand characteristics describing the board-foot stand. Utilization standards dictate an in- terest in the larger trees since they repre- sent the portion of the stands that can be most economically harvested. Develop- ment of this series of tables and curves was based on the tables of the correspond- ing characteristics of the stand larger than 4.5 inches in diameter, the cubic- foot stand, rather than on an independent curving of the plot data using this larger diameter limit. The technique for devel- oping tables of segments of stands (Bruce, 1926) was used to create average diam- eter and basal area tables for the board- foot stand. This procedure utilizes the ratio of the measurements of the board- foot stand to cubic foot stand, expressed as a percentage, plotted over the average diameter of the cubic-foot stand. This curve expresses the percentage by which the smaller diameter values at each age- site class are corrected to give board-foot stand values. The shape of the curves ex- pressing this percentage is usually sig- moid, reaching 100 per cent at the larger diameters where the characteristics of the two stands are the same. This identity was found in the larger average diameter classes when all trees had exceeded the 10.5-inch diameter limit and both stand structures contained the same trees. Yield table values of stand characteristics of the two stand segments became progres- sively closer as the age of the stand increased. Table 9 BASAL AREA PER ACRE (SQUARE FEET), TREES OF ALL SPECIES OVER 10.5 INCHES DBH Age Site index (years) 100 120 140 160 180 200 220 240 20 30 40 50 60 70 80 90 100 11 51 97 148 199 244 283 322 356 31 91 145 198 250 295 333 371 402 57 134 196 250 303 347 384 421 453 90 190 262 318 371 414 451 487 519 135 262 350 407 461 503 540 576 606 192 341 445 503 556 598 634 669 699 243 420 538 595 651 692 727 762 792 299 503 634 692 748 788 823 858 888 [22 W W u g d rH «< E H « w o pes <3 Q fa o w « u «< w fa IOO O ^ E^?" i 20 40 50 eo IOO AVERAGE BREAST-HIGH AGE OF REDWOOD (YEARS) Fig. 10. Board-foot volume per acre of young-growth redwood stands, trees of all species more than 10.5 inches DBH, International % rule. [26] Table 14 BOARD-FOOT VOLUME PER ACRE YIELDS, TREES OF ALL SPECIES OVER 10.5 INCHES DBH (INT. \i" RULE), TO 8 INCH TOP INSIDE BARK ABOVE 1.5 FOOT STUMP Age Site index (feet) (years) 100 120 140 160 180 200 220 240 20 30 40 50 60 70 80 90 100 900 2,800 7,300 14,400 22,800 32,400 44,000 55,760 600 3,100 8,800 16,500 27,400 40,400 53,700 67,400 81,300 2,300 9,500 20,400 33,700 48,900 65,000 81,500 98,300 114,600 7,000 19,600 36,900 55,300 74,500 94,500 114,300 133,800 152,300 14,500 34,500 57,900 82,000 106,100 130,400 153,500 176,400 198,100 23,900 52,300 82,100 112,700 142,100 170,900 198,200 224,100 248,500 35,000 71,600 108,700 146,000 180,900 214,400 244,800 273,600 301,700 46,500 93,200 137,500 181,300 221,900 259,500 293,500 325,700 357,600 Table 15 BOARD-FOOT PERIODIC ANNUAL INCREMENT, TREES OF ALL SPECIES, OVER 10.5 INCHES DBH Age period Site index (years) 100 120 140 160 180 200 220 240 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100 190 450 710 840 960 1,160 1,176 250 570 770 1,090 1,300 1,330 1,370 1,390 720 1,090 1,330 1,520 1,610 1,650 1,680 1,630 1,260 1,730 1,840 1,920 2,000 1,980 1,950 1,850 2,000 2,340 2,410 2,410 2,430 2,310 2,290 2,170 2,840 2,980 3,060 2,940 2,880 2,730 2,590 2,440 3,660 3,710 3,730 3,490 3,350 3,040 2,880 2,819 4,670 4,430 4,380 4,060 3,760 3,400 3,220 3,190 Table 16 BOARD-FOOT MEAN ANNUAL INCREMENT, TREES OF ALL SPECIES OVER 10.5 INCHES DBH Age Site index (years) 100 120 140 160 180 200 220 240 20 30 40 50 60 70 80 90 100 30 70 146 239 326 405 488 556 30 103 220 330 455 578 671 748 813 115 316 510 674 812 929 1,019 1,091 1,146 350 653 922 1,106 1,237 1,351 1,429 1,485 1,523 725 1,149 1,448 1,640 1,761 1,865 1,919 1,958 1,981 1,195 1,742 2,052 2,254 2,359 2,444 2,478 2,487 2,485 1,750 2,384 2,718 2,920 3,003 3,066 3,060 3,037 3,017 2,325 3,104 3,438 3,626 3,684 3,711 3,669 3,615 3,576 [27] growth is not grossly affected by increas- ing age. In addition, because the mean annual and periodic annual growth rates are maintained at a high and relatively uniform level over an extended period of time the selection of rotation age may be exercised over a number of years. This makes consideration of factors other than those strictly associated with volume pro- ductivity of the site more feasible. APPLICATION OF YIELD TABLES Some general observations on these yield tables relative to the prediction of future yields are appropriate for point- ing out important features of their appli- cation to actual stands. Of particular im- portance to bear in mind is that the basis for these tables were undisturbed, even- aged, unmanaged young-growth redwood stands. Consequently these tables are rep- resentative of stands within the range of conditions found in the sample data. It is not deemed appropriate to adjust es- timates of the future yield on the basis of current basal area. Attempts to use the tables on stands which show evidence of disturbance or mixed old- and young- growth might result in errors in esti- mated yields. Estimation of current stand volumes from these tables is not recom- mended as a cruising aid because of the inherent variability of the yields used to make these tables. The tables may be applied to mixed stands provided that redwood comprises more than 50 per cent of the stand by basal area, the user must assume that species composition will remain the same as at present. Yield values for the various stand characteristics, shown by age and site classes in the tables, are to be estimated from actual stand conditions using an es- timate of mean stand site index at a given future age. It is therefore appropriate to consider the estimate of the stand site in- dex in terms of the average of several such stand observations. A single esti- mate within the stand would not likely be an adequate definition of the average stand site index. The stand sample to es- timate site index may be established by means of either fixed boundary plots or point samples, since they are used only as a device to define a group of trees in a localized segment of the stand. Esti- mates of the average stand breast-high age and total height should be made from measurements of five to eight dominant redwood included in each sample plot. The site index estimate is made from the average age and total height observations by application to the site index curves. When using these tables one should bear in mind that the yield values are in terms of average breast-high age of dominant trees, not total age, thus no correction in age is necessary for stump height, also, the tables show per-acre gross yields in- cluding all species. When assessing future productivity of young-growth redwood land it is neces- sary to consider the size and stand com- plexity of the forest property. Sampling units should be distributed in a manner to secure several site index estimates that are representative of the entire property. This may be done by a plan that distrib- utes the sample plots over the property. Where the property acreage is large, or age and site cover a wide variety of con- ditions, total productivity may best be estimated by sampling within several de- fined strata. Delineation of the strata on type maps or aerial photographs is help- ful in planning the sampling system for each stratum and provides necessary es- timates of strata acreages. For example, it may be desirable to base these site in- dex classes on soil and topographic con- ditions, with two or three broad age classes in each site class. Where the acre- age is small, or if the stands of the prop- erty are homogeneous in terms of age and site index, stratification of the property is not necessary. Recommendation of the optimum num- ber of sample plots necessary for an ade- quate representation of the mean site index of an entire property or stratum [28] is difficult because of the variability that occurs within these young-growth stands. However, as a guiding principle the sam- pling should attempt to define the mean population site index with a high degree of precision since site index represents the sole basis for the prediction of the future yields from these tables. Site index is not sensitive to variations in stocking, except in cases of extreme over- or under- stocking, and therefore may function as a unit which combines the stands of vari- ous stocking densities associated within broad site classes. Assuming that the stands of the property have been strati- fied into relatively homogeneous tracts, site index samples within these strata should not define a wide range of values. This sample should be evaluated to de- termine the mean, standard deviation, and coefficient of variation of the ob- served site indices. These provide an esti- mate of the population mean, the disper- sion of the observations about this mean, and the relative value of the standard deviation to the estimated mean. From this analysis it is possible to determine the number of plots necessary to meet re- quirements of a mean site index estimate plus or minus limits of acceptable error at a given level of confidence. The de- pendence on mean site index for the esti- mates of future yield makes it advisable to base the estimates of this value on a sufficient number of site index observa- tions to insure estimates that are within 5 per cent of the population parameter at the 95 per cent level of confidence. An example of the application of the yield tables presented in this bulletin, based on data taken from ten one-fifth acre permanent plots in a relatively homogeneous tract of young-growth red- wood is summarized in table 17. The average breast-high age and average total height of each plot are based on measure- Table 17 EXAMPLE OF PREDICTED PER ACRE STAND YIELDS AT 100 YEARS BREAST-HIGH AGE Age Ave. ht. dom. Site index Predicted plot values at 100 years Plot Basal area Cubic ft volume Ave. dia. Board ft volume 1 2 3 4 5 6 7 8 yrs 37 34 19 17 33 30 20 35 34 35 297 29.7 ft 92 83 43 40 88 92 56 72 86 95 166 160 150 156 170 176 166 143 165 175 sq.ft 545 519 487 506 562 588 545 465 541 584 5,342 534.2 cu.ft 25,761 23,940 21,410 24,446 26,975 28,802 25,761 19,639 25,457 28,497 inches 25.7 25.2 24.7 24.8 26.1 26.6 25.7 23.6 25.6 26.5 int. \-inch 166,040 152,300 133,450 144,600 275,200 188,940 166,040 120,250 9 163,750 10 186,700 Total Average 747 74.7 1,627 162.7 250,688 25,068.8 254.5 25.45 1,597,270 159,727 Values using average site index 163 532 24,850 25.5 159,140 [29 ments of five to eight dominant redwood. Estimates of site index, for each plot, were made by interpolation from either table 1 or figure 5 using average breast- high age and total height. Prediction of yield table values of each stand charac- teristic at 100 years was made under the assumption that site index does not change over the extended growth period. These predictions required only the esti- mate of current site index to interpolate the yield values at the terminal age. Mak- ing predictions on the basis of individual plots requires a considerable amount of interpolation to determine per acre aver- age tract values at the future age. How- ever, prediction of average tract values may be simplified by determining the mean site index of the plots, and apply- ing this estimate to the yield table values at 100 years (see bottom line of table 17) . Comparison of the average stand per acre estimates arrived at by the two proce- dures indicates little difference between the methods. Calculation of the number of site index observations necessary for an estimate within plus or minus 5 per cent of the population mean at the 95 per cent de- gree of confidence from the ten site index values of table 17 indicates that nine plots would have been sufficient to meet these requirements. The coefficient of variation is the percentage ratio of the standard deviation to the mean of the site index observations. These values are de- termined as follows: SD -V E (x-x) 2 N-l 1010.10 10-1 = 10.58 (5) cv = where: 10.58 162.7 X 100.0% = 6.5% (6) X = Site index observations .SD = Standard deviation of site index observations N = Number of observations CV = Coefficient of variation The required number of site observations have been derived from the formula: n (6.5) 2 X(2.2 6) 2 (5) 2 8.63 or 9 plots (7) where: t = the number of standard deviation for 95 per cent confidence and 9 degrees of free- dom (2.26) d = allowable error, as per cent of the mean (5 per cent) n = calculated number of required observa- tions It should be pointed out that the appli- cation of these tables is different from that of normal yield tables. The use of normal yield tables for the prediction of future yields of stands requires an ad- justment of the predicted values, often based on the percentage of the actual to the tabled value of basal area for that age and site index class. The present tables do not require adjustment of the estimates of the future volume yields. They are pre- dicated on the increasingly prevalent idea that well-stocked stands over a fairly wide range of basal area densities produce about the same amount of volume growth (Johnson, 1955; Spurr, 1952). In approximately one-third of the stands of young- growth sampled the red- wood originated entirely from stump sprouts following the logging of the virgin stands. The spatial distribution of the red- wood in these stands is concentrated near the old stumps causing localized areas of dense stocking, while the intervening areas between the stumps are unoccupied. While it is possible to attain very high basal area per acre figures, due to the many trees in these clumps, there is not the equitable distribution of stems that is implied in the definition of a fully stocked stand. For this reason the usual concept of normality does not fully sat- isfy the requirements of the expression of stocking in the undisturbed and un- managed stands of this timber type. As a result it is appropriate to consider the [30] basal area measurements as being repre- sentative of better stocked stands, and the yield table values as the average of those stands expressed in terms of age and site index. The recommended procedure of using a group of site index observations of a homogeneous tract does not require esti- mates of stand basal area. Since adjust- ment of the yield table figures is not war- ranted it is not necessary to compare the actual and table estimates of stand basal area. CONVERSION OF YIELD TABLE BOARD-FOOT VOLUMES TO SPAULDING RULE Measurements of the total board-foot stand volume have been made using vol- ume tables based on the International % inch rule. This formula rule, which allows for taper within a four foot log segment, is most often used for work associated with growth studies. Customarily within the redwood region the board-foot vol- umes are in terms of the Spaulding log rule for young-growth trees or the Hum- boldt rule, which deducts 30 per cent of the Spaulding, for the old-growth timber. Consequently the board-foot volumes of the yield tables will often be converted to the log rules most commonly used in this region. Recent volume tables for young-growth redwood give tree volumes for both the International % rule and the Spaulding rule (appendix tables 27 and 28). These tables indicate that tree volumes by the Spaulding rule are less than by the Inter- national rule. Spaulding tree volumes when expressed as a percentage of the larger volume estimate become propor- tionally larger as the diameter of the tree increases, reaching approximately 100 per cent at a diameter of 50 inches, shown in figure 11. When dealing with stand- volumes, conversions based on this tree- volume curve are not entirely appropriate since stands are composed of trees cover- ing a range of diameters. The effect of diameter distribution oc- curring within a stand structure on the stand volume relationship of the two log rules is shown in figure 11. The curve of stand volume ratio was made from indi- vidual ratios of 27 remeasured permanent plots, whose board-foot volumes were cal- culated using both International and Spaulding volume tables. The average vol- ume ratios of the stands have been plotted over the average diameter of the stand inventory of trees exceeding 10.5 inches. The difference between the stand- and tree-volume ratios which is most apparent in the smaller diameter classes is due to the range of diameters, and consequently tree ratios, within a stand structure. To DIAMETER AT BREAST-HEIGHT OF TREES OVER 10.5 INCHES Fig. 11. Conversion of International % rule volumes to Spaulding rule, volumes for trees and stands. [31] convert board-foot volumes of the yield tables to Spaulding rule it is necessary to determine the future average stand diam- eter of the stand over 10.5 inches. Appli- cation of this future stand diameter to the curve of stand volume ratios will estimate the percentage by which the yield table board-foot volumes must be adjusted. For example, the average diameter of trees over 10.5 inches at 100 years for site index 163 is 25.55 inches This diameter when applied to the stand volume ratio curve indicates that the Spaulding stand volume is approximately 92.7 per cent of the International stand volume. The aver- age volume per acre (Spaulding Rule) at age 100 in the example of table 17 is: (.927) (159,140) = 147,523 board feet. COMPARISON TO PREVIOUS STUDY Reference has been made previously to the yield study of young-growth redwood made by Bruce in 1923 since it represents the only other existing yield investigation of this species. This early work was de- scribed as preliminary because of the limited age range, 60 years, and the lack of data from the poorer site index classes. Yield tables were developed from fully- stocked normal stands as a standard typi- cal of yields that could be expected under management of this species. This manage- ment would include planting, or some other means of securing the full stocking of the stands, and proper care of the stands until maturity. Bruce found that this ideal condition rarely existed except in small restricted stands, and suggested artificial regeneration of the stands to realize maximum utilization of land pro- ductivity. During the intervening years since 1923 very little of the second-growth acreage has been put under any form of management and it is still necessary to deal with unmanaged naturally regener- ated young-growth stands (Fritz, 1959). It is difficult to make comparisons with the Bruce yield tables and draw conclu- sions because of the basic difference in the type of stands utilized as the basis for the studies. Furthermore, there are dif- ferences in the minimum size of tree included, volume tables and log rules, and construction techniques. The most appar- ent and important differences are the trends of yield and growth curves which begin to show at about 50 years of age. These trends indicate, in the Bruce study, that the stands experience a sharp decline in yield and growth, as in the case of basal area per acre which has nearly reached a maximum by 60 years. The trends of the present tables correspond closely with the Bruce results up to age 50, but from that point the present tables indicate a much higher growth rate. This difference in volume yields has impor- tance when considered from the stand- point of culmination of mean annual growth, which often serves as the basis for determining the rotation age. The Bruce curves of mean annual board-foot increment reach their maximum at ap- proximately 45 years. Culmination in this unit for the present study does not occur until at least 70 years of age, and in site index values less than 200 not before 100 years. The range of basal area per acre values between Bruce's site class I and III is narrow relative to the present curves; this is also true for the cubic and board-foot volume yield curves. This would seem to indicate that the differences in yields of these stand characteristics does not de- pend on site index as strongly when deal- ing with fully-stocked stands as is the case with stands of the present study. [32] APPENDIX Sample Data Data for the construction of the empirical yield tables presented in this study were obtained from measurements of the current inventory of 172 temporary point samples of young-growth redwood collected during the summers of 1958 and 1959. The selec- tion of stands to sample was guided by a desire to encompass the conditions that occur in young-growth redwood stands. Not all samples established were utilized for development of the yield tables, 20 of the 172 established samples were rejected. The rejection was accomplished in two stages: the first involved reasons related to the defined stand description; the second based on basal area deviations relative to the standard error of the basal area per acre deviations computed for each of the six site index classes. Basis for plot rejection and number of plots rejected are summarized as follows: NO. OF CAUSE OF REJECTION PLOTS 1. Residual old growth 4 2. Per cent of redwood ( Less than 20% ) 2 3. Missing data 3 4. Older than 100 yrs 4 5. Abnormal stocking 7 TOTAL 20 Frequency distributions of the samples by the principal characteristics of site and stand show the result of the sampling plan and range of conditions encountered. Tables 18, 19, and 20 indicate the frequency distributions of the plots relative to the stand characteristics: basal area, age, and site index. Distribution of the samples by environmental factors of aspect, slope class, and soil parent material by site index classes is shown in tables 21, 22, and 23. Since site index is dependent on a variety of edaphic, climatic, and stand factors it is difficult to understand clearly the function and importance of each set of factors in determining the site index. The distributions in the tables show general trends of sample occurrence within the site index classes. Table 18 FREQUENCY DISTRIBUTION OF SAMPLE POINTS BY BREAST-HIGH AGE AND SITE INDEX Age at b. h. Site index (years) Over 200 181-200 161-180 141-160 121-140 101-120 Total 0-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100 3 7 5 2 2 2 1 1 1 5 • 11 8 11 3 1 1 1 42 3 6 10 15 9 4 4 1 2 6 3 6 4 1 23 2 1 3 2 2 1 11 1 1 2 5 18 35 35 30 16 8 2 3 Total .... 23 51 152 [33] Table 19 FREQUENCY DISTRIBUTION OF SAMPLE POINTS BY AGE CLASS AND BASAL AREA Age class (sq. ft.) 0-10 11-20 21-30 31-40 41-50 51-60 61-70 71-81 81-90 91-100 Total 0-100 101-200 201-300 301-400 401-500 501-600 601-700 701-800 over 800 Total 5 5 1 8 4 3 1 1 18 7 8 12 4 3 1 35 2 3 5 9 9 5 1 1 35 1 3 11 12 2 1 30 1 2 7 3 2 1 16 3 2 2 1 8 1 1 2 1 1 1 3 3 25 22 45 32 15 5 4 1 152 Table 20 FREQUENCY DISTRIBUTION OF SAMPLE POINTS BY BASAL AREA AND SITE INDEX CLASS Basal area Site index class (sq. ft) Over 200 181-200 161-180 141-160 121-140 101-120 Total 0-100 101-200 201-300 301-400 401-500 501-600 601-700 701-800 over 800 1 1 5 3 6 3 3 1 3 7 12 14 4 1 1 2 10 7 17 9 5 1 7 5 6 5 1 3 2 4 1 1 1 3 25 22 45 32 15 5 4 1 Total.... 23 42 51 23 11 2 152 [34 Table 21 FREQUENCY DISTRIBUTION OF SAMPLE PLOTS BY ASPECT (CARDINAL DIRECTION) AND SITE INDEX CLASS Table 22 FREQUENCY DISTRIBUTION OF SAMPLE PLOTS BY SLOPE CLASS AND SITE INDEX CLASS Site Aspect Total Site class Slope class Total class North East South West Level 0-10% 11-30% Over 31% 1 3 1 2 17 23 1 19 2 2 23 2 6 4 11 9 12 42 2 15 17 10 42 3 7 7 14 12 11 51 3 15 14 22 51 4 4 4 6 4 5 23 4 5 6 12 23 5 2 I 6 2 11 5 4 7 11 6 1 1 2 6 1 1 2 Total. 23 16 38 30 45 152 Total. 54 44 54 152 Table 23 FREQUENCY DISTRIBUTION OF SAMPLE PLOTS BY SOIL GROUPS AND SITE INDEX Site class Soil group Total 200 800 900 1 14 7 3 1 25 3 18 25 14 10 1 71 6 17 23 8 1 1 56 23 2 42 3 51 4 23 5 11 6 2 Total 152 Where 200 = Alluvial soils. 800 = Consolidated sandstone. 900 = Weakly consolidated material. Site Index Yield site index curves are designed to display changes of total height with age for selected site index classes which are represented as curved lines. This type of representation is valuable because it shows visually the development of total height and height growth with age. Despite the fact that the nature of this arrangement of the variables is one more appropriately suited for the estimation of height the most common application of these curves is for the estimation of site index from measure- ments of total height and age. Through a realignment of the axes the data shown in table 1 and figure 5 may be displayed in a manner that facilitates direct estimation of site index. The conversion of the data with site index as the dependent variable shows [35] age as straight lines over total height. Interpolation of site index values between the five year age classes shown in table 24 and figure 12 gives the estimate of site index directly. 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Preliminary yield tables for second-growth redwood. University of California Agric. Exp. Sta. Bull. 361:425-67. 1926. A method of preparing timber yield tables. J. of Agric. Res. 32:543-57. Bruce, D. and Schumacher, F. X. 1935. Forest mensuration. 1st edition. New York, McGraw-Hill Co. 376 pp. California Forest and Range Experiment Station 1953. Forest statistics for the redwood-Douglas-fir subregion in California. Forest Survey Release 19, 54 pp. Chapman, H. H. and Demeritt, D. B. 1936. Elements of forest mensuration. 2nd edition. Albany, New York, Williams Press, Inc. 451 pp. Fritz, E. 1959. Characteristics, utilization and management of second-growth redwood. Found, for Amer. Resource Mgmt. 29 pp. Harlow, W. M. and Harrar, E. S. 1950. Textbook of dendrology. 3rd edition. McGraw-Hill Co., New York. 555 pp., illus. Hornibrook, E. M. 1942. Yield of cutover stands of Englemann spruce. J. of Forestry 40:778-81 Johnson, F. A. 1955. Predicting future stand volume for young well-stocked Douglas-fir forests. J. of Forestry 53(4):253-55. Lindquist, J. L. and Palley, M. N. 1961. Site curves for young-growth coastal redwood. Calif. Forestry and Forest Products 29:1-4. Pacific Northwest Forest and Range Experiment Station 1955. Volume tables for Pacific Northwest trees. USDA Handbook 92 Palley, M. N. 1959. Board-foot volume tables for young-growth coastal redwood. Calif. Forestry and Forest Products 11:1-6. 1961. Cubic-foot volume tables for young-growth coastal redwood. Calif. Forestry and Forest Products 28: 1-6. 1963. Plot or point sample values in even-aged stands using a computer. J. of Forestry 61(1) 28- 32. Palley, M. N. and O'Regan, W. 1961. A computer technique for the study of forest sampling methods. Forest Science 7(3) :282- 94. Spurr, S. H. 1952. Forest inventory. New York, The Ronald Press Co. 476 pp. Storie, R. E. and Weir, W. W. 1953. Soil series of California. Associated Students, University of California. 128 pp. Storie, R. E. and Wieslander, A. E. 1952. Dominant soils of the redwood-Douglas-fir region of California. Soil Science Proc, 16(2) : 163-67. United States Department of Agriculture: Yearbook of Agriculture 1941. Climate and Man. 1248 pp., illus. [46] ACKNOWLEDGMENT The authors wish to express thanks to: The many owners and managers of young-growth redwood stands for granting permission to sample their timber lands, and for assistance through detailed informa- tion, maps, and data relative to their stands; J. Drake and D. Denault, former students in the School of Forestry, for their work during establishment of field plots; L. R. Grosenbaugh and E. M. Hornibrook of the United States Forest Service, R. F. Grah and J. A. Zivnuska of the School of Forestry, and members of the Division of Forestry staff at Sacramento for critical suggestions for improving the relevancy and readability of the publication. 7Jm-8,'63(D7238)J.P [47