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Component weights of Douglas fir, western hemlock and western red cedar biomass for simulation of amount… Kurucz, J. 1969

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COMPONENT WEIGHTS OF DOUGLAS FIR, WESTERN HEMLOCK AND WESTERN RED CEDAR BIOMASS FOR SIMULATION OF AMOUNT AND DISTRIBUTION OF FOREST FUELS by J. KURUCZ B.S.F., University of British Columbia, 1961  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF FORESTRY  in the Faculty of FORESTRY  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA September, 1969  In p r e s e n t i n g t h i s  thesis  an advanced degree at  freely available  the requirements f o r  Columbia,  I agree  f o r r e f e r e n c e and  f u r t h e r agree that p e r m i s s i o n f o r e x t e n s i v e copying of  for  this  that  Study. thesis  s c h o l a r l y purposes may be granted by the Head of my Department or  by h i s of  f u l f i l m e n t of  the U n i v e r s i t y of B r i t i s h  the L i b r a r y s h a l l make i t I  in p a r t i a l  representatives.  this  thesis  It  for f i n a n c i a l  is understood that copying or p u b l i c a t i o n gain s h a l l  written permission.  Department The U n i v e r s i t y of B r i t i s h Vancouver 8, Canada  Date  Oc_TOT_eR  K\  Columbia  not be allowed without my  ii ABSTRACT  Potential uses of dry weight information for simulation, and sources of data, f o r simulation of forest fuels were discussed.  Tree and crown com-  ponent dry weights of 23 Douglas f i r , 18 western hemlock, and 23 western red cedar trees expanded to 314 "model" trees were investigated.  Data were c o l -  lected on the University Research Forest near Haney, B r i t i s h Columbia. Multiple regression techniques were used f o r the analysis.  The best four independent  variables are l i s t e d and the p o s s i b i l i t y of retaining a single independent variable, with i t s implications, are discussed.  A l l predicting equations were  conditioned to zero intercept and s t a t i s t i c a l l y tested f o r significance by the F-test. Of the independent variables tested, the combined variable of breast height diameter squared times t o t a l tree height was most c l o s e l y r e lated to tree component dry weights.  The product of diameter and crown width  squared was found to be the best single variable to describe crown component dry weights for Douglas f i r .  The dry weights of western hemlock and western  red cedar crown components were most c l o s e l y associated with breast height diameter times crown length. Reliable estimates of tree component dry weights were obtained. Crown components were highly variable and widely dispersed about the mean which resulted i n less accurate estimates.  iii TABLE OF CONTENTS Page TITLE PAGE ABSTRACT TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES ACKNOWLEDGEMENTS  i i i i i i v viii xi  INTRODUCTION  1  METHODS USED TO DATE  3  METHODS AND DATA COLLECTION Derivation of dry weights  11 17  ANALYSIS OF DATA  30  RESULTS OF ANALYSIS  32  Total-tree, bole-wood and bole-bark relationships A.  TOTAL-TREE DRY WEIGHT  32 36  a. Douglas f i r  36  b. Western hemlock  39  c. Western red cedar  40  B. TOTAL BOLE-WOOD DRY WEIGHT  42  a. Douglas f i r  42  b. Western hemlock  42  c. Western red cedar  43  C. TOTAL BOLE-BARK DRY WEIGHT  46  a. Douglas f i r  46  b. Western hemlock  46  c. Western red cedar  47  iv Page CROWN COMPONENTS  49  Total-crown, needles, fine, medium and large component relationships  49  D. TOTAL-CROWN DRY WEIGHT  52  a. Douglas f i r  52  b. Western hemlock  53  c. Western red cedar  54  LARGE BRANCH COMPONENT  58  E.  F.  a. Douglas f i r  58  b. Western hemlock  59  c. Western red cedar  60  MEDIUM BRANCH COMPONENT  63  a. Douglas f i r  63  b. Western hemlock  64  c. Western red cedar  65  G. FINE BRANCH COMPONENT  68  a. Douglas f i r  68  b. Western hemlock  69  c. Western red cedar  70  H. NEEDLE COMPONENT  73  a. Douglas f i r  73  b. Western hemlock  74  c. Western red cedar  75  DISCUSSION AND CONCLUSION  82  BIBLIOGRAPHY  87  APPENDIX  I  - SCIENTIFIC NAMES OF TREES  APPENDIX II - COMPONENT WEIGHTS PLOTTED OVER VARIOUS INDEPENDENT VARIABLES  91 92  LIST OF TABLES Basic statistics of original measurements for Douglas f i r western hemlock, and western red cedar. Theoretical occurrence of whorls containing from 3-9, 2-7 and 3-7 branches each for Douglas f i r , western hemlock and western red cedar, respectively. Basic statistics for the independent variables. Mean, standard deviation, minimum and maximum dry weights in pounds for the dependent variables. The simple correlation coefficients between total-tree, bole-wood, bole-bark oven dry weights and the independent variables. Relationship of total-tree oven dry weight (pounds) with several independent variable combinations for 112 Douglas f i r trees. Differences between the maximum and conditioned models tested by the F-test for significance. Relationship of total-tree oven dry weight (pounds) with several independent variable combinations for 89 western hemlock trees. Relationship of total-tree oven dry weight (pounds) with several independent variable combinations for 113 western red cedar trees. Relationship of total bole-wood oven dry weight (pounds) with several independent variable combinations for 23 Douglas f i r trees. Relationship of total bole-wood oven dry weight (pounds) with several independent variable combinations for 18 western hemlock trees. Relationship of total bole-wood oven dry weight (pounds) with several independent variable combinations for 23 western red cedar trees. Relationship of total bole-bark oven dry weight (pounds) with several independent variable combinations for 23 Douglas f i r trees. Relationship of total bole-bark oven dry weight (pounds) with several independent variable combinations for 18 western hemlock trees.  vi  15.  16. 17. 18.  19.  20.  21.  22.  23.  24.  25.  26.  27.  Relationship of total bole-bark oven dry weight (pounds) with several independent variable combinations for 23 western red cedar trees.  Page 47  The simple correlation coefficients between oven dry weight crown components and the independent variables.  50  Differences between the maximum and conditioned models tested by the F-test for significance for the crown component functions.  51  Relationship of total-crown oven dry weight (pounds) with several independent variable combinations for 111 Douglas f i r trees.  52  Relationship of total-crown oven dry weight (pounds) with several independent variable combinations for 89 western hemlock trees.  53  Relationship of total-crown oven dry weights (pounds) with several independent variable combinations for 112 western red cedar trees.  54  Relationship of large branch crown component oven dry weight (pounds) with several independent variable combinations for 111 Douglas f i r trees.  58  Relationship of large branch crown component oven dry weight (pounds) with several independent variable combinations for 89 western hemlock trees.  59  Relationship of large branch crown component oven dry weight (pounds) with several independent variable combinations for 112 western red cedar trees.  60  Relationship of medium branch crown component oven dry weight (pounds) with several independent variable combinations for 111 Douglas f i r trees.  63  Relationship of medium branch crown component oven dry weight (pounds) with several independent variable combinations for 89 western hemlock trees.  64  Relationship of medium branch crown component oven dry weight (pounds) with several independent variable combinations for 112 western red cedar trees.  65  Relationship of fine branch crown component oven dry weight (pounds) with several independent variable combinations for 111 Douglas f i r trees.  68  V X 1  28.  29.  30.  31.  32.  33.  34.  35.  Relationship of fine branch crown component oven dry weight (pounds) with several independent variable combinations for 89 western hemlock trees.  Page 69  Relationhip of fine branch crown component oven dry weight (pounds) with several independent variable combinations for 112 western red cedar trees.  70  Relationship of needle crown component oven dry weight (pounds) with several independent variable combinations for 111 Douglas f i r trees.  73  Relationship of needle crown component oven dry weight (pounds) with several independent variable combinations for 89 western hemlock trees.  74  Relationship of needle crown component oven dry weight (pounds) with several independent variable combinations for 112 western red cedar trees.  75  Comparison of simple linear regressions including the most important and most convenient variables for the various predicting equations for oven dry weight.  78  Relative oven dry weights of crown components based on 112 Douglas f i r , 89 western hemlock and 113 western red cedar sample branches.  80  Summary of predicting equations for the various component dry weights.  81  viii LIST OF FIGURES Page 1.  The influence of Douglas f i r branch length on per cent green weight of branch components.  18  The influence of western hemlock branch length on per cent green weight of branch components.  19  The influence of western red cedar branch length on per cent green weight of branch components.  20  The influence of branch length on component dry weight for Douglas f i r .  25  The influence of branch length on component dry weight for western hemlock.  26  The influence of branch length on component dry weight for western red cedar.  27  7.  Example of a theoretical tree-crown construction.  28  8.  Relations between total-tree dry weight and D H for Douglas f i r , western hemlock and western red cedar.  41  Relations between total bole-wood dry weight and D H for Douglas f i r , western hemlock and western red cedar.  45  2. 3. 4. 5. 6.  o  9.  2  o  10.  Relations between total bole-bark dry weight and D^H for Douglas f i r , western hemlock and western red cedar.  48  o  11. 12.  Relations between total-crown oven dry weight and DxCW for Douglas f i r .  56  Relations between total-crown oven dry weight and DxCL + (DxCL) for western hemlock and western red cedar.  57  Relations between large branch crown component oven dry weight and DxCW for Douglas f i r .  61  2  13.  2  14. v"Relations between large branch crown component oven dry weight and DxCL + (DxCL) for western hemlock and western red cedar. 2  15.  Relations between medium branch crown component oven dry weight and DxCW f or Douglas f i r .  66  Relations between medium branch crown component oven dry weight and DxCL + (DxCL) for western hemlock and western red cedar.  67  2  16.  62  2  17.  Relations between fine branch crown component oven dry weight and DxCW for Douglas f i r . 2  71  ix  18.  Relations between fine branch crown component oven dry weight and DxCL + (DxCL) for western hemlock, and western red cedar.  Page  2  19.  72  Relations between needle crown component oven dry weight and DxCW for Douglas f i r .  76  Relations between needle crown component oven dry weight and DxCL + (DxCL) for western hemlock and western red cedar.  77  II-l.  Total-tree dry weight on D H for Douglas f i r .  93  II-2.  Total-tree dry weight on D H for western hemlock.  94  II-3.  Total-tree dry weight on D H for western red cedar.  95  2  20.  2  2  2  2  o  II-4.  Total bole-wood dry weight on D^H and BA for Douglas f i r ;  96  II-5.  Total bole-wood dry weight on D H and BA for western hemlock.  97  II-6.  Total bole-wood dry weight on D H and BA for western red cedar.  98  II-7.  Total bole-bark dry weight on D H and BA for Douglas f i r .  99  II-8.  Total bole-bark dry weight on D H and BA for western hemlock. 2  100  II-9.  Total bole-bark dry weight on D H and BA for western red cedar.  101  2  2  2  2  11-10. Total-crown dry weight on DxCW for Douglas f i r . 11-11. Large branch crown component dry weight on DxCW for Douglas f i r .  102 103  11-12. Medium branch crown component dry weight on DxCW for Douglas f i r .  104  2  11-13. Fine branch crown component dry weight on DxCW for 2  Douglas f i r .  105  11-14. Needle crown component dry weight on DxCW for Douglas f i r .  106  11-15. Total-crown dry weight on DxCL for western hemlock.  107  11-16. Large branch crown component dry weight on DxCL for western hemlock. 11-17. Medium branch crown component dry weight on DxCL for western hemlock.  109  11-18. Fine branch crown component dry weight on DxCL for western hemlock.  110  108  11-19. Needle crown component dry weight on DxGL for western hemlock. 11-20. Total-crown dry weight on DxCL for western red cedar. 11-21. Large branch crown component dry weight on DxCL for western red cedar. 11-22. Medium branch crown component dry weight on DxCL for western red cedar. 11-23. Fine branch crown component dry weight on DxCL for western red cedar. 11-24. Needle crown component dry weight on DxCL for western red cedar.  xi  ACKNOWLEDGMENTS  The writer wishes to express his sincere thanks to Drs. J.H.G. Smith, A. Kozak, and D.D. Munro for their guidance, advice and c r i t i c a l review.  The assistance of Dr. A. Kozak,  Mrs. M. Benmore, and Miss L. Cowdell in programming, and analyzing the data, and the help of Mrs. M. Lambden in drafting are gratefully acknowledged. Data collection during the summers of 1967 and 1968 was financed by the Canada Department of Forestry and Rural Development in the form of an extramural research grant to Dr. Smith. Attendance at the University was facilitated by financial assistance from the Faculty of Forestry, University of British Columbia, in the form of Teaching Assistantships and a University Forest Fellowship. Financial support for the second year of my study was a McMillan Bloedel Fellowship.  1 INTRODUCTION  Wildfire annually destroys valuable timber, well established regeneration, and periodically takes its t o l l of human lives.  Fire is destructive  in uncontrolled form but i f carefully and selectively used on a prescribed basis i t can be a very useful tool for forest managers. Forest managers interested in the application of prescribed burning or in planning for control of wildfires are usually hindered by the lack of quantitative measures of forest fuels. One of the f i r s t things a f i r e control man wants to know about a wildfire is the kind of fuels in which i t is burning. Rate of spread and resistance to control are two major considerations which are v i t a l for a fire control planner.  Resistance to control will vary  directly with volume and/or weight of organic matter on and above the ground evaluated with prevailing topographic conditions.  Fahnestock (1960) reported  that quantity and size of fuel were by far the dominant influence on the rate of spread of experimental slash fires.  It is obvious then that forest fuel  weight and size distributions are two important basic fire behaviour considerations . An objective evaluation of forest fuels in terms of their burning potential and energy release requires that these factors be known to forest managers in planning control of wildfires and in use of prescribed fire for hazard reduction, silvicultural, or other purposes.  With information on the  amount and size distribution of fuels in conjunction with an evaluation of topography and weather conditions the man in charge can plan accordingly for f i r e control, prevention and use.  2  Smith (1968 a) stated "Full knowledge of kind, amount, and horizontal and vertical distribution of fuels may be needed eventually.  However, i t seems  desirable now that forest fire scientists work toward development of comprehensive models of fire behavior in which the fuel elements can be simulated quickly as required."  He also suggested the high desirability of keeping the  field work needed to a minimum and advocated that any fuel system should be quantitive and expressed by functions or tables. Although several studies were made for describing forest fuels in the Pacific Northwest none of them dealt explicitly with a l l three major species of the coast of B.C., cedar.  namely Douglas f i r ^ , western hemlock, and western red  The primary objective of this study is to define fuel component func-  tions for these species.  Once functions are established they can be incorp-  orated with presently known simulation methods to describe and test many fuel problems of interest.  Scientific names of a l l species cited in the test are given in APPENDIX I.  3 METHODS USED TO DATE The literature on green and oven-dry weights of tree and stand components dates back to 1919 when Tufts established correlations between circumference of trunk and weight of top for fruit trees.  Yet, compared to other  fields in forestry research, publications dealing with component weights are relatively few, which is probably the direct result of the time element involved in data collection.  For this reason, Smith (1968 a) suggested that a l l  available data sources should be used fully and shared freely.  Those data  sources presently available will be discussed chronologically in the following sections. In North America the f i r s t comprehensive study on quantitative variations of forest tree foliage was done by Kittridge (1944). Considerable work had been done before him, including that of Burger in Europe, but few investigators correlated component weights with tree stem characteristics. Kittridge studied the amount of foliage of trees and stands of conifers, deciduous, and broadleaved evergreen species representing a wide range of sites and' ages from California to Vermont.  He stated that dry weight of foliage can be  estimated satisfactorily from periodic annual increments of stem wood. To bypass the time-consuming determination of periodic annual growth when growth and yield studies are not readily available, he developed a simpler method of estimation by using  tree diameter at breast height (dbh). He applied logarith-  mic transformation to both the dependent and independent variables. Storey e_t a l. (1955) analysed crowns, crown components, and stems for 211 conifer trees, representing 13 species and 4 sites from four states. Species studied included Douglas f i r , western hemlock, and western red cedar. They found that weights of dry crown, dry branch-wood, and dry foliage were significantly related to stem diameter at base of live crown for each species,  4 provided crown length is taken into account.  This is a very informative  piece of work and provides good background for researchers in this f i e l d . Ovington (1956) discussed the forms, weights, and productivity of tree species, including Douglas f i r , grown in closed stands. Morris (1958) investigated the influence of slash burning on regeneration and hazard reduction in the Douglas f i r region of the Coast and Cascade Ranges in Oregon. Although the fuel component detail of this study is negligable, its interesting finding is that while slash burning will not produce a significant increase or decrease in the number of seedlings as compared to unburned sites i t will reduce the potential fire hazard considerably. Chandler (1960) using the basic data of Storey et a_. (1955) set up slash weight tables based on dbh, and crown length as a percentage of total height for ponderosa pine, sugar pine, Douglas f i r , white f i r , and incense cedar recognizing three components: needles, branches and tops less than 4 inches, and more than 4 inches in diameter. Fahnestock (1960) developed crown weight regression equations for nine northern Rocky Mountain coniferous species including Douglas f i r , western hemlock, and western red cedar.  He found a linear relationship between the loga-  rithm of crown dry weight and the product of dbh and crown length.  The re-  lationship between dbh and crown length showed a linear trend up to 30 inches. With the combination of the two equations he constructed a crown weight table for the species by 2 inch dbh classes. Fahnestock and Dieterich (1962) studied the flammability, rate of fire spread, appearance, and fire intensity for 5-year old slash of nine northern Rocky Mountain conifers. The study indicated that western hemlock, western red cedar, lodgepole pine, and white pine retained large amounts.of fine slash  5  components thus making the flammability s t i l l high 5 years after cutting. Douglas f i r , ponderosa pine, and Engelmann spruce were intermediate while grand f i r and western larch showed very low flammability.  Average rate of fire  spread for a l l species was 23 per cent of that in fresh slash.  The most impor-  tant changes in appearance were an almost total loss of needles by a l l species and compaction of the fuel bed. Brown (1963) determined crown weight and diameter relations in red pine plantations in the Lake States and studied the influence of site and density on the weight of individual crowns. Keen (1963) sampled 900 trees of three softwood species: black spruce, white spruce, and balsam f i r in Quebec and Ontario to analyse: average green weights and centres of gravity, the variation of these parameters between species, season and location, volume and weight of piled slash, and the effect of seasoning on weights of f u l l trees.  To provide a quick reference to tree  dimensions, weights and volumes he summarized the weights and centres of gravity in tables. Young et^ a l. (1964) set up component fresh and dry weight tables for white birch, red spruce, balsam f i r , aspen, hemlock, white pine, and red maple in Maine.  These tables are based on very limited amounts of data obtained in  a small area. Hardy and Weiland (1964) investigated the variation in the weight of stacked wood for spruce, f i r and eight hardwood species in Maine. Rogerson (1964) studied the weight of foliage on loblolly pine trees in a 25-year old North Mississippi plantation.  He applied a logarithmic trans-  formation to estimate foliage weight by tree dbh.  Weetman and Harland (1964) sampling in a pure, 65-year old, unthinned black spruce stand in northern Quebec for foliage and wood production, found that the logarithms of stem volume, crown volume, needle number, surface area, and dry weight per tree a l l showed a linear relationship with the logarithm of  dbh. Muraro (1964) investigated the frequency and weight distribution of  branch l i t t e r under lodgepole pine stands of various ages and heights in south central British Columbia.  He presented a graph from which the surface area of  branch l i t t e r , within specific diameter limits, can be estimated from i t s total weight. Dobie (1964) listed four variables that will influence the green weight of a log of any species. These are: basic density of the wood, the per cent volume of sapwood in the log, the moisture content of the heartwood and sapwood, and the weight of bark on the log. Variation in the density of wood is caused by the variation in per cent latewood, rate of growth, site, location, dominance, age and position within the tree. Brown (1965) described the variation in crown weight due to site quality and stand density for red pine and jack pine in the Lake States.  He  estimated crown weight per tree most precisely with dbh and the product of crown length and dbh, and found tree dbh to be the best single independent variable for crown weight prediction. Magdanz (1965) evaluated the weights and volumes of tree components of western hemlock, interior balsam, and spruce trees.  His analysis was based  on data collected near Terrace, B.C. Baskerville (1965 a) studied dry matter production in natural 40year old balsam f i r , white spruce and white birch stands with varying stand  7  densities in western New Brunswick.  He analyzed 139 trees to determine the  weight and distribution of dry matter among foliage, cones, stem-wood, stembark, branch-wood and branch-bark.  Total dry weight of foliage and branches  was found closely correlated to stem dbh with a well defined relationship of the exponential form. Baskerville (1965 b) presented his findings of (1965 a) for balsam f i r in tabular form and compared the estimates of stand biomass by the following methods: every-tree summation, tree of mean height, tree of mean diameter, tree of mean basal area, stand table, tree of mean volume, and average codominant tree.  He concluded that the average tree approach is useful only  where a rough estimate of total biomass is desired. Young and Chase (1965) investigating the amount of fibre and pulping potential of logging residues in Maine reported that for every 100 tons of dry fibre removed from the forest as merchantable bole 55 tons of dry fibre, including a l l material down to one-quarter inch, is left in the forest in the form of logging residue. Tadaki (1965) described the productivity of a dense naturally regenerated 4-year old green wattle stand by evaluating the data from 8 sample trees in Japan. Tadaki (1966) studied the changes and vertical distribution of leaf biomass.  His results indicated that the leaf biomass per unit ground area in  a closed forest seems to be similar among species, related species, and same plant  formations. Tadaki and Kawasaki (1966) investigated the productivity of suji  trees in very dense plantation.  8 Harada and Sato (1966) discussed the dry matter production of mature wattle trees from seven stands of three regions in Japan. Muraro (1966) analysed 405 lodgepole pine trees from data collected in pure stands southeast of Merritt, British Columbia, for the purpose of predicting slash accumulations resulting from various intensities of utilization. To achieve a straight line relationship between crown weight and dbh he applied a double logarithmic transformation. He found that the proportion of needle weight to branch-wood weight increased towards the tip of the tree, and that surface area per pound of slash was directly proportional to the average dbh of the original stand. Baskerville (1966) using his basic data of (1965 a) evaluated the dry weight distribution of dry roots and vegetation of the forest floor.  He con-  cluded that the total weight of tree roots increases with increasing stand density and that total dry weight of lesser vegetation is insignificant in comparison to the total tree stand. K i i l l (1967 a) presented oven-dry weight tables for live branch-wood and crowns of white spruce and lodgepole pine in west-central Alberta. His results showed that the most precise estimates of fuel weight can be obtained by using dbh and either crown width or crown length.  He used a double loga-  rithmic transformation. His tables were set up by one foot crown width and one inch dbh classes. K i i l l (1967 b) illustrated the effect of stand density on weight and size of aerial and ground fuel components in lodgepole pine stands. Muraro (1967) assessed i n i t i a l (before burning) and residual (after burning) fuel components to demonstrate differences of fire impact due to  9 weather and slash age in the Interior Wet Belt of British Columbia. Dyer (1967) studied fresh and dry weights, nutrient elements and pulping characteristics of northern white cedar in Maine with limited amount of data from a restricted portion of the state. with dbh and total tree height using logarithmic  He estimated component weights transformation.  Johnstone (1967) analysed tree and tree component weights of 63 forest-grown lodgepole pine trees based on data collected in south-western Alberta.  He found that basal area was the best single estimator of component  weights with the exception of bole-bark weight and stem dry weight which were most closely related to tree height and dbh respectively. Johnstone (1968) evaluated the biomass of lodgepole pine trees on two tenth-acre plots near Banff, Alberta. DH 2  He found the combined variable of  (dbh squared times height) most closely associated with component weights  with the exception of branch weight. Van Wagner (1968) demonstrated a simple method of forest fuel sampling which requires only the tally of the pieces intercepted by the sample line. Bella (1968) studied the aerial component weights of 132 young trembling aspen trees in Manitoba and Saskatchewan. D  2  His result showed that  (dbh squared) was the most important single variable for estimating tree  component weights. Osborn (1968) investigated the influence of stocking and density on growth and yield of coastal western hemlock trees and stands.  His biomass  study of 15 trees indicated a linear increase of above-ground tree weight (oven-dry) per unit area with increasing stand density.  10 Smith (1968 a,b,c) stressed the importance of forest fuel d i s t r i bution studies, the need to define explicit objectives, and the development of comprehensive forest fuel simulation models. Kellogg and Keays (1968), working on the complete-tree pulping research at the Vancouver Forest Products Laboratory, determined component weight distribution for three western hemlock trees.  11 METHODS AND DATA COLLECTION The data used in this study were gathered on the University Research Forest near Haney, during the summer months of 1968.  The Forest is  located in the foothills of the Coast Mountains of southern British Columbia. The topography of the whole area is generally rugged with numerous rock outcrops.  The soil is mainly of glacial t i l l origin, and varies in depth from a  few inches to three or more feet. Thirty immature, open-grown and 34 mature, forest-grown trees were sampled; there were 23 Douglas f i r , 23 western red cedar, and 18 western hemlock trees.  Criteria for individual tree selection were fullness of crown,  and representation of species by 2-inch dbh classes from 1 to 48 inches. The latter was achieved for Douglas f i r and western red cedar but size limitations of western hemlock resulted in a 36 inch upper dbh limit for this species. For each individual tree, tree number, species, total height, dbh, total age, live crown length, dead crown length, and crown width were recorded. Five sample branches, representing the f u l l range of live crown, were taken from each tree for determination of branch component weight distributions. Size definitions used in component measurements are: fine-material less than \ inch in diameter outside bark, medium-material less than 3/4 inch and more than \ inch, large-material over 3/4 inch.  For each sample branch, position  in stem from tip, age at butt, total length, and diameter outside and inside bark at butt and midpoint were measured.  Measurements on the three branch  components included: main branch length, and total green weight.  The latter  was determined directly for large and medium components, and indirectly for fine and needle components by sub-sampling.  A specimen sub-section was cut out  at the midpoint of each component length which was used to determine component  12  specific gravity.  For each sub-section, average diameter outside bark (dob),  average diameter inside bark (dib), average length, green weight wood, green weight bark, dry weight wood, and dry weight bark were determined.  A l l sub-  samples were oven-dried to a constant weight in the field laboratory at Haney. Three Thelco model 18 or 28 ovens set to a constant temperature of 105° C were used.  Drying time ranged from 24 to 48 hours.  TABLE 1 shows the basic  statistics for field and laboratory measurements.  Bark samples were taken at one foot and 4.5 feet heights and tenths of total height above breast height using a one-inch diameter plug cutter attached to a hand d r i l l .  Specific gravity for each sample was determined  with the following formula: Sg =  Where:  Dw 12.87 x Th  Sg = Specific gravity Dw = Oven-dry weight of sample (grams) Th = Thickness of sample (inches) 12.87 x Th = Green volume of sample converted to cm  3  (0.5 x 3.1425 x 16.39 x Th) 2  13 TABLE 1.  Basic statistics of original measurements for Douglas F i r , western hemlock, and western red cedar. n ; F i r = 112, Hemlock = 89, Cedar = 113 1  parameter  units  Height  feet  dbh  inches  Age (total)  years  Live crown length  feet  Dead crown length  feet  Crown width  feet  Position in stem from tip Butt age  feet years  Total length  feet  Weight (green )pounds Butt dob  inches  Butt dib  inches  Midpoint dob  inches  Midpoint dib  inches  species  mean  F H C F H C F H C F H C F H C F H C F H C F H C F H C F H C F H C F H C F H C F H . C  117.3 95.4 94.5 25.1 19.1 25.4 93.3 120.0 115.6 72.1 63.6 69.1 5.2 4.9 5.6 27.1 24.3 24.7 42.2 36.0 35.3 32.1 44.4 32.0 14.1 12.1 11.1 24.3 16.5 14.7 2.1 1.9 1.8 1.8 1.6 1.5 1.2 0.9 1.1 1.0 0.7 0.9  standard deviation 66.5 54.7 49.5 14.5 10.9 14.5 65.9 135.9 115.4 30.4 24.9 32.6 5.3 8.3 9.6 8.2 7.5 8.3 27.4 22.4 23.2 24.2 53.3 27.1 6.1 5.5 5.5 26.0 19.5 16.0 1.0 1.1 0.8 0.9 1.0 0.8 0.6 0.5 0.6 0.5 0.4 0.5  minimum  maximum  12.0 14.0 12.0 1.4 1.6 1.3 10.0 18.0 11.0 11.1 14.0 11.0 0.0 0.0 0.0 6.0 8.0 6.0 4.0 3.0 3.0 3.0 3.0 2.0 2.6 2.5 0.8 0.3 0.1 0.2 0.5 0.3 0.4 0.3 0.3 0.2 0.2 0.2 0.2 0.2 0.1 0.1  218.0 176.0 160.0 48.4 36.4 47.1 158.0 398.0 386.0 141.0 98.0 120.0 16.0 30.0 33.0 39.0 36.0 39.0 141.0 93.0 98.0 84.0 195.0 135.0 26.8 27.1 24.4 125.5 99.0 83.9 4.6 5.2 4.0 3.8 4.7 3. 7 2.7 2.2 2.9 2.3 1.9 2.7  continued  14 TABLE 1.  (continued)  parameter  units  Length,fine  feet  Length, medium feet Length,large  feet  Weight, fine (green)  pounds  Weight, medium pounds (green) Weight, large (green)  pounds  Weight,needles pounds Fine dob  inches  Fine dib  inches  Fine length  inches  Weight grams (green fine wood Weight(green) grams fine bark Weight(dry) fine wood  grams  Weight(dry) fine bark  grams  Moisture fine wood  per cent  species F H C F H C F H C ' F H C F H C F H C F H C F H C F H C F H C F H C F H C F ' H C F H C F H G  mean 1.2 2.0 0.9 3.4 3.5 2.4 9.4 6.7 7.8 2.5 1.6 0.7 2.0 1.5 1.6 14.6 10.0 7.6 5.1 3.3 4.7 0.2 0.2 0.2 0.1 0.1 0.1 2.0 2.2 1.4 0.4 0.4 0.3 0.5 0.3 0.3 0.2 0.2 0.2 0.2 0.2 0.1 105.0 96.9 105.7  standard deviation 0.5 0.4 0.4 0.8 1.2 1.0 6.1 5.6 5.8 2.3 1.4 0.6 2.0 1.6 1.9 18.0 15.3 9.8 4.7 2.4 4.2 0.1 0.1 0.1 0.1 0.1 0.1 0.8 0.8 0.5 0.2 0.3 0.2 0.3 0.2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 32.2 26.1 45.5  minimum  maximum  0.3 0.8 0.4 1.7 0.0 0.0 0.0 0.0 0.0 0.1 0.1 0.1 0.1 0.0 0.0 0.0 0.0 0.0 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.8 0.8 0.6 0.1 0.1 0.1 0.2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 50.0 44.4 50.0  3.8 3.3 2.2 5.8 6.3 4.9 22.9 22.7 21.7 13.6 5.9 2.7 10.0 6.7 8.8 93.5 76.9 54.5 20.6 10.2 20.6 0.3 0.2 0.2 0.2 0.2 0.2 3.0 3.0 3.0 1.2 1.7 1.5 1.5 0.8 0.8 0.5 0.8 0.5 0.5 0.4 0.3 235.7 280.0 496.0 continued  15 TABLE 1.  (continued)  parameter  units  Moisture fine bark  per cent  Medium dob  inches  Medium dib  inches  Medium length  inches  Weight(green) grams medium wood Weight(green) grams medium bark Weight (dry) grams medium wood Weight (dry) grams medium bark Moisture medium wood  per cent  Moisture medium bark  per cent  Large dob  inches  Large dib  inches  Large length  inches  Weight(green) grams large wood  species F H C F H C F H C F H C F H C F H C F H C F H C F H C F H C F H C F H C F H C F H C  mean 138.4 123.5 114.1 0.5 0.5 0.5 0.4 0.4 0.4 1.6 1.7 1.4 3.3 3.7 3.6 2.1 1.7 1.6 1.7 2.0 1.7 0.9 0.8 0.7 99.2 87.7 108.8 127.4 132.1 124.4 1.4 1.1 1.2 1.2 1.0 1.1 1.4 1.3 1.4 35.2 26.1 25.8  standard deviation  minimum  45.1 39.6 34.7 • 0.1 0.1 0.1 0.1 0.1 0.1 0.4 0.4 0.5 1.0 1.6 1.5 0.6 0.6 0.6 0.5 0.8 0.7 0.3 0.3 0.2 20.8 19.9 23.3 35.4 32.1 23.6 0.8 0.7 0.6 0.7 0.6 0.6 0.6 0.7 0.6 28.6 22.2 24.4  57.1 21.4 57.1 0.3 0.0 0.0 0.2 0.0 0.0 0.9 0.0 0.0 0.8 0.0 0.0 0.8 0.0 0.0 0.3 0.0 0.0 0.3 0.0 0.0 64.4 0.0 0.0 73.3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0  maximum 283.3 262.5 246.6 0.7 0.7 0.7 0.5 0.5 0.6 3.0 2.1 2.0 6.0 7.9 7.8 3.8 4.1 2.8 3.5 4.0 3.7 1.9 2.6 1.2 166.6 212.7 244.6 271.7 221.8 184.7 3.0 2.6 2.9 2.6 2.2 2.6 2.0 2.2 2.1 123.8 133.5 157.7  continued  16 TABLE 1.  (continued)  parameter S  units  Weight(green) grams large bark Weight (dry) grams large wood Weight (dry) grams large bark  P  M  Moisture large wood  per cent  Moisture large bark  per cent  Per cent large  per cent  Per cent medium  per cent  Per cent fine  per cent  Per cent needles  per cent  Moisture needles sub-sample  per cent  species  mean  F H C F H C F H C F H C F H C F H  11.9 9.1 6.8 19.2 14.5 14.2 6.1 4.5 3.1 72.2 65.0 74.4 90.9 93.3 108.7 44.4 37.4 37.4 13.7 13.1 11.5 15.4 14.7 6.3 26.5 34.8 44.8 113.3 110.7 120.2  G  F H C F H C F H C F H C  standard deviation 9.0 8.2 4.8 15.7 12.1 13.6 5.0 4.4 2.1 30.5 32.7 33.6 45.6 52.9 43.7 22.4 26.3 21.3 11.0 8.5 5.2 8.2 7.2 2.0 9.3 16.4 17.8 18.7 21.4 19.0  minimum 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 4.0 0.0 0.0 4.0 3.0 3.0 13.0 5.0 19.0 75.3 70.6 85.8  maximum 42.2 42.3 28.3 70.0 72.2 82.8 25.1 22.2 11.4 118.1 126.6 251.3 266.8 281.9 174.2 74.0 88.0 66.0 55.0 34.0 35.0 44.0 43.0 14.0 56.0 64.0 86.0 143.9 149.7 221.3  n = number of observations T = Tree measurements, B = Branch measurements, C = Component measurements, S = Sub-section measurements, P = Per cent component figures based on total green weight, and M = Moisture content of needles.  17  Derivation of Dry Weights An indirect determination of green weight components of fine branches and needles was made for individual sample branches. foliage was clipped from the larger branch parts.  The fine component with  The green weight of this  combined-component (fine plus needles) was then determined.  A small, repre-  sentative sub-sample of needles (40-60 grams green) was taken to determine the ratio of dry to green weight of needles. The combined-component and the needle sub-sample were placed in the oven for drying.  After drying (24 to 48  hours), the needles f e l l off easily from the fine branchwood making separation of these two components less time-consuming. determined separately.  The total dry weights were then  Assuming that the ratio of dry weight to green weight  of needles from the sub-sample is the same for the sample branch as a whole, the total green weight of needles was determined by the formula: DWTN = dwtn X gwtn  Where:  o  r  x  =  gwtn dwtn x  D W T N  X = Total green weight of needles (grams) DWTN = Total dry weight of needles (grams) • gwtn = Green weight of needle sub-sample (grams) dwtn = Dry weight of needle sub-sample (grams).  After total green weight of needles is calculated, total green weight of fine component can be determined by simple subtraction: total green weight fine = combined component (green) - X.  The procedure just described  greatly reduces the time required for separating needles from branch-wood. It was not necessary for western red cedar because separation could be carried out directly by clipping, assuming that a l l "green" material was "needles".  18  «Lorge Component (over 3/4" in diameter outside bark) * Medium Component (less than 3/4" and more than 1/4") + Fine Component (less than 1/4") -•Needles Number of Samples for each Point 3  5  IO  -  Z  4  6  2.  4  3  7  3  Total Branch Length in Feet The Influence of Douglas f i r branch length on per cent green weight of branch components.  X  19 80  •  • Large Component (over 3/4" in diameter outside bark)  *  *Medium Component (less than 3/4"and more than 1/4")  +  +Fine Component (less than — o  70  1/4")  Needles  Number of Samples for each Point 4 \ B  O  8  5  3  6  2  6  4  3  Z  5  60  to (A O  o c o  50  w Q)  0_ (A C 0>  40  c o  Q.  E o o  u c o  30  CD  o Q>  20  C  io  B  12.  Total Branch Length in Feet FIGURE 2.  ife  The influence of western hemlock branch length on per cent green weight of branch components.  * L a r g e Component (over 3/4" diameter o-b)  Total Branch Length in Feet  FIGURE 3.  The influence of western red cedar branch ,length on per cent green weight of branch components.  21 For the 30 immature trees, 10 of each species, additional  information  about crown width, and total green weight of branches by one-meter long bole sections was utilized to derive total dry crown component weights.  For each  sample branch green weight component percentages, based on total green weight, were calculated.  Branches were sorted by length and species into length  classes and average percentages were derived for each class.  This was based  on preliminary studies in 1967 which indicated that branch length was the most important determinant of branch weight.  Figures 1, 2, and 3 show the green  weight branch component percentages by length classes.  Half of section crown  width was used as a representative branch length for each section and appropriate percentages were applied to total section green weight to arrive at total component green weight.  Assuming that the ratio of component dry weight  weight to component green weight of the sample branch is the same for the section as a whole, total dry weight for individual sections was calculated by the following formula: dwt = gwt Where:  X GWT  O R  X  _ Q^J,  dwt gwt  X = Total component dry weight of section GWT = Total component green weight of section dwt = Total component dry weight of sample branch gwt = Total component green weight of sample branch.  From dob and dib measurements wood and bark volumes were calculated for each section using Smalian's formula. Dry weight of bole-wood for each tree was derived by multiplying the volumes with specific gravity of wood obtained from Kennedy (1965).  He listed 0.45, 0.409, and 0.312 specific gravity  figures for Douglas f i r , western hemlock, and western red cedar respectively with standard deviations of 0.05 for f i r , 0.04 for hemlock and 0.03 for cedar.  22 Use of actual tree specific gravities would have introduced  a further com-  ponent of variation averaging about 12 per cent into a l l bole weight calculations . Dry weight of bole-bark was determined in the same manner.  Section  barkvolume was calculated from differences between section dob and dib measurements and summed for each tree.  Total bark volumes were then multi-  plied by average specific gravities of 0.43, 0.44 and 0.31 for f i r , hemlock and cedar respectively.  The standard deviation of these mean values were:  0.07 for f i r , 0.04 for hemlock and 0.03 for cedar (Smith and Kurucz 1969). Use of actual bark specific gravity for each tree would have introduced a further component of variation into the estimation process. However, variations in bole and bark specific gravity are small in relation to the other sources of variation studied. Data on sample branch position within the live crown facilitated the expansion of the 64 trees sampled to 314 "model" trees.  Grown components  were calculated for as many crown lengths as there were branches sampled for component weights for each tree.  A tree of a given dbh and height, therefore,  was used with five estimates of crown weight to provide a wide range of crown characteristics for regression analysis. Total component determinations for the 34 mature trees were based on the same principles but required different approaches.  Since green weight  measurements of a l l branches for these trees would be highly impractical, very time-consuming, and a rather d i f f i c u l t task physically, hypothetical crowns were constructed for each tree.  Section crown lengths within a tree were  established from sample branch position.  The average length of two consecu-  tive sample branches was used to represent the average branch.  Sample branch  23 age at butt was utilized to determine number of whorls in the live crown. Data on range and average number of branches per whorl of Smith e_t al^. (1961), substantiated with additional observations, were used.  Standard deviations  for number of branches per whorl were derived with the aid of table 2.2.2 from Snedecor (1956).  The relative frequency of whorls including the whole  range of branches were calculated for each species by the following formula: Z =  x  Where:  -f Sd  Z = Normal deviate X = Class midpoint X = Average number of branches per whorl Sd = Standard deviation  Results are presented in Table 2.  Percentage figures of Table 2 were expressed in number of whorls, and allocated randomly within the crown for each tree.  Multiplying the  number of branches with the observed frequencies and summing these for individ ual sections gave the total number of branches for each section. Sample branches were sorted by length and species into length classes and average component dry weights were derived for each class.  Figures 4, 5, and 6 i l l u s -  trate the influence of total branch length on component dry weight.  Total  number of branches multiplied by corresponding component dry weight values gave total component dry weights for the respective sections. hypothetical crown for tree No. 33 is shown in Figure 7.  An example of a  24 TABLE 2.  Theoretical occurrence of whorls containing from 3 to 9, 2-7, and 3-7 branches each for Douglas f i r , western hemlock and western red cedar, respectively.  Douglas f i r No. of observations Average No. of branches per whorl Range Ratio from Snedecor Standard deviation  36 5.2 6 0.239  0.239 x 6 = 1.4  western hemlock  western red cedar  33 4.8 5 0.241 0.241 x 5 = 1.2  15 4.7 4 0.289 0.289 x 4 = 1.1  Theoretical occurrence as per cent of total whorls No. of branches in a whorl: 2 3 4 5 6 7 8 9  8.6 22.2 27.5 24.1 12.6 4.2 .8  1  2.4 11.3 26.1 32.3 20.8 7.1  Means, that 8.6% of the total number of whorls for a Douglas f i r tree w i l l have 3 branches theoretically.  5.6 19.3 34.5 29.1 11.5  25  • + + + + +  30 •  •  -—Large Component (over 3/4" in diameter outside bark) Medium Component (less than 3/4"and more than 1/4") 'Fine Component (less than 1/4") •Needles  28  26  Number of Samples for each Point 24  5  1  1  4  3  7  4  ^  7  8  6  21  in  TJ c  20  O  o_ c  is  ie o  c a> c  o  a.  \z  E o °  10  lo  IS  20  Total Branch Length in Feet FIGURE 4.  The influence of branch length on component dry weight for Douglas f i r .  25  26  18  -Large Component (over 3/4" in diameter outsid^ bark) "Medium Component (less than 3/4" and more/than 1/4") ' F i n e Component (le"ss than 1/4") •Needles  ••*- + + + + ++ + +  — 16-  Number of Samples for Each Point  14-  8  6  2  .  4  5  5  4  4  2  iz-  c  ion  3 O  0_  O  c a> c o CL  E o o  4  2  0  0  10  5  15  20  2.5  Total Branch Length in Feet FIGURE 5.  The influence of branch length on component dry weight for western hemlock.  27  • , t t + + v ++ + + + ,  30  • •  'Large Component (over 3/4" in diameter outside bark) M e d i u m Component (less than 3/4"and more than 1/4") 'Fine Component (less than 1/4") 'Needles  28  26  Number of Samples for each Point 24-  8  1Z  6  8  8  5  8  5  5  5  22 IO T3 C  20  o Q.  —  18  16  >»  «- 14  q>  12  O  o. E o  10  o  »*• + *• + +--»• -v.  .^-"^  *.+***2i.*-*— ti-+-i — £ 10  •  *  15  Total Branch Length in Feet FIGURE 6.  20  25  The influence of branch length on component dry weight for western red cedar.  28  Tree no» 33 - western red cedar No-of branches Whorl frequency c in a observed o whorl theoretical 3  2  2  4  8  8  5  15  14  6  13  I 5  7  5  4  W  6  No- of branches in a whorl 3 Observed . frequency Sum of branches +  4  1  2  3  5 6  TJ  •£ • $ o» Z  c aj  (rt  i_ O  O  £ <» 2 ^  c o 6 c c o o a>  c c o - J j * ° c —  4-  3  CO  0_  co  i/>  6 7 8  8+30 +  g  a> •0-  0  48  to  —sq  c 3  4  I  5.6  1 2  I  7  4  14  2  3 + 4 + 1 o + 24+l 4 — 5 5 65 3  4  O  5  3  O  12+  ?  I 6 +  5  6  7  o  I  4  I  o  0  6  4  6  5  1  2  4 +Io+  Example  o o a> >  s  12 —  o o  IV 12  —-30 7 1  6  III  1 4 — 3 2  4  4 + 20+  19.4  2  3  3  FIGURE 7.  6  $  V  0  7  -20  of a t h e o r e t i c a l  tree-crown c o n s t r u c t i o n .  29  Dry weight of bole-wood and bole-bark was determined as outlined previously with the exception of 13 cedar trees.  Data on actual bark thick-  ness were not collected for these trees but section dob measurements allowed the calculation of outside bark volumes section by section.  Smith and Kozak  (1967) presented a table for 12 British Columbia tree species in which bark volume is expressed as a per cent of solid wood volume.  Their figure of 14%  for Coastal western red cedar was used to separate outside bark volume from solid wood and bark volumes.  For example; a cedar tree with an outside bark  volume of 228 cubic feet w i l l have 228 114 200 cubic feet of solid wood.  u  =  2  8 cubic feet of bark and  30 ANALYSIS OF DATA The data were analysed using multiple regression techniques. The regression program described by Kozak and Smith (1965) was used for the analysis.  The primary objective was to define dry weight functions, there-  fore determination of green weight equations was not attempted.  Green  weight could be approximated by the use of the percentage moisture contents shown in Table 1.  Tree component weights of large, medium, and fine branches,  needles, bole-wood, bole-bark, total-tree, and total-crown were used as dependent variables a l l measured in pounds, with independent variables tree height in feet (H), crown length in feet (CL), crown width in feet (CW), diameter at breast height in inches (D), and tree basal area outside bark at breast height in square feet (BA). In addition the following combinations of independent variables were generated: the product of diameter squared and height (D H), crown width squared (CW ), gross crown volume (CW x CL), and 2  2  2  the products of diameter with crown length (D x CL), crown width squared (D x CW ) and gross crown volume (D xCW x CL). 2  2  • Component weights were plotted over independent variables to determine general curve-forms.  Linear trends were found for total-tree,  bole-wood, and bole-bark. Crown components plotted over the independent variables showed linear and curvilinear trends for some but for most of the variables indicated no trend at a l l .  General curve-forms are shown in  Appendix II. Each regression equation (maximum model) was conditioned to zero intercept, or in other words the hypothesis that bo = 0 was tested.  The  sum of squared residuals about the maximum model represents the smallest sum of squares that can be obtained by f i t t i n g the model with the least squares  31  procedure.  The hypothetical model, being more restrictive, increases the  sum of squared residuals. The difference between the residuals can be tested for significance with the F-test where the error term is always the residual mean square of the maximum model. An insignificant increase in the sum of squared residuals indicates the validity of the procedure, while a s i g n i f i cant value indicates that the conditioned model should not be accepted. Kozak (1969) discussed the uses and misuses of conditioned regression.  32 RESULTS OF ANALYSIS Total-tree, bole-wood and bole-bark relationships Table 3 presents the means, standard deviations, and minimum and maximum values of the independent variables used in the analysis.  Excluded  from this table are height, dbh, crown length, and crown width which are listed in Table 1. in Table 4.  Basic statistics are shown for the dependent variables  Simple correlation coefficients between total-tree, bole-wood,  bole-bark and the independent variables are listed in Table 5.  A good corre-  lation of height, dbh, basal area and D H with the dependent variables is 2  apparent in Table 5.  Basal area and D H 2  appear to be most closely associ-  ated with total-tree, bole-wood, and bole-bark dry weights. Regression equations, or models, in the following text are assumed to be of linear form, where linearity refers to the parameters.  Each model,  containing the combination of variables that are individually contributing significantly to the overall regression, will be tested for the Null Hypothesis of bo = 0.  If the hypothesis is accepted for the model tested the  y - intercepts, or constant terms, w i l l be zero and will not be listed. The regression program which commences with an equation of a l l variables and then eliminates them one at a time according to the smallest absolute contribution to variance accounted for by the regression equation was used.  Calculation  of the variance ratio of the contribution of each independent variable included in the model incorporated with Miller's (1965) t-prime criterion improves the probability that the most important variables w i l l be retained at a l l stages of analysis.  Only the combinations of variables in which each  contribute significantly to the overall regression will be listed throughout the text.  The possibility of retaining a single independent variable, with  its implications, will be  discussed.  33 TABLE 3.  Basic statistics for the independent variables. n: Fir = 112, Hemlock = 89, Cedar = 113  units  independent variables  species  mean  standard  minimum maximum  BA  square feet  F H C  4.7 2.6 4.7  3.9 2.3 3.9  0.01 0.01 0.01  12.8 7.2 12.1  DH  inch x feet 2  F H C  145578.0 67630.5 112538.0  152823.0 73720.8 107335.0  20.20 35.84 20.30  472726.0 231868.0 334980.0  CW  feet  2  F H C  493.2 358.8 371.1  391.6 304.2 338.0  9.00 4.00 9.00  1521.0 1296.0 1521.0  Gross crown volume (CW x CL)  feet  3  F H C  32023.1 20276.9 22837.7  37222.5 23591.4 30644.5  70.20 26.00 41.40  203604.0 109760.0 158184.0  D x CL  inch x feet  F Hq C  1494.0 907.1 1299.6  1450.6 788.1 1265.6  10.92 10.40 5.98  6627.0 2989.0 5463.6  F H C  14904.6 8432.6 11764.0  15661.3 9474.7 13923.3  12.60 6.40 11.70  67868.0 47174.4 65859.3  F H C  1086490.0 499789.0 796764.0  1623730.0 670941.0 1273320.0  2  2  2  D x CW  o  2  D x Gross crown volume  inch x feet 3 inch x feet  98.28 9569390.0 41.60 2924810.0 53.82 6849360.0  34 TABLE 4.  independent variables  Mean, standard deviation, minimum and maximum oven dry weights in pounds for the dependent variables nl; Fir = 112,Hemlock = 89, Cedar = 113  units  species  mean  standard  minimum  maximum  Total-tree  pounds  F H G  8958.4 4781.1 4281.5  8900.2 5437.9 4109.4  3.8 4.4 2.1  30604.6 19036.7 16537.8  Bole-wood  pounds  F H C  6325.5 3693.8 3136.0  6848.7 4363.2 3207.0  2.0 3.3 1.4  22264.2 13874.8 12028.4  Bole-bark  pounds  F H C  1140.0 531.8 434.3  1219.8 686.3 446.5  0.8 0.8 0.4  3651.3 2337.7 1671.1  Total-crown  pounds  F H C  1211.6 508.2 606.2  1568.4 734.7 878.2  1.0 0.3 0.3  6608.6 2925.2 4044.2  Large  pounds  F H C  701.1 242.7 297.1  1002.4 422.6 502.9  0.0 0.0 0.0  4391.3 1745.0 2285.6  Medium  pounds  F H C  110.5 56.9 62.9  124.3 70.7 89.7  0.3 0.0 0.0  510.7 301.2 449.6  Fine  pounds  F H C  128.6 67.4 34.8  145.9 86.7 44.5  0.3 0.1 0.1  565.5 354.4 193.6  Needles  pounds  F H C  261.0 141.2 211.5  303.2 165.8 247.2  0.4 0.2 0.3  1141.2 650.0 1115.5  Number of observations for bole-wood and bole-bark are 23, 18, and 23 for f i r , hemlock and cedar respectively.  35 TABLE 5.  The simple correlation coefficients between total-tree, bole-wood, bole-bark oven dry weights and the independent variables.  independent variables  units  species  total-tree  bole-wood  bole-bark  Height  feet  F H C  0.920** 0.912 0.868  0.912 0.914 0.860  0.921 0.864 0.859  Crown length  feet  F H C  0.771 0.423 0.635  0.700 0.362 0.499  0.683 0.310 0.498  Crown width  feet  F H C  0.430 0.421 0.431  0.338 0.373 0.311  0.345 0.351 0.309  Diameter  inches  F H C  0.934 0.906 0.902  0.925 0.911 0.900  0.936 0.859 0.898  Basal area  square feet  F H C  0.976 0.972 0.928  0.976 0.978 0.933  0.983 0.937 0.933  DH  inch x feet  F H C  0.982 0.990 0.953  0.991 0.995 0.961  0.992 0.965 0.961  CW  feet'  F H C  0.444 0.438 0.434  0.350 0.389 0.307  0.357 0.375 0.304  Gross crown volume  f eet-  F H C  0.619 0.395 0.509  0.530 0.335 0.363  0.520 0.307 o.361  D x CL  inch x feet  F H C  0.921 0.723 0.799  0.873 0.673 0.692  0.860 0.612 0.692  D x CW  inch x feet'  F H C  0.744 0.685 0.603  0.661 0.641 0.487  0.672 0.627 0.485  D x Gross crown volume  inch x feet"  F H C  0.737 0.582 0.576  0.662 0.522 0.441  0.653 0.493 0.441  2  2  **  A l l coefficients listed are significant at the 0.01 probability level.  36 A. a. TABLE 6.  TOTAL-TREE DRY WEIGHT  Douglas f i r  Relationship of total-tree oven dry weight (pounds) with several independent variable combinations for 112 Douglas f i r trees. independent variables  DH  BA DxCL regression coefficients  2  1.62687 1.62079 1.72610  0.033972 0.035286 0.043364 0.059265  393.592 315.955  SEE (pounds)  or ^2 - 7.50459  0.984 0.984 0.983 0.961  1158 1152 1181 1746  The 4 variables listed in Table 6, with the exception of dbh, form the best combination to describe total-tree dry weight. variable of D H 2  The combined,  is the single most important variable accounting for 96.1%  of the total sum of squares while BA, dbh, and DxCL "explains" 95.2,  87.2,  and 84.8% respectively. Retaining only D^H w i l l result in a negligible loss of information (R 0.984 to r 2  2  0.961), but since 2 significantly contributing vari-  ables were left out (dbh does not contribute significantly to the overall regression) the predicting equation w i l l be less precise.  This shows up  clearly in the standard error of estimate which increases from 1158 pounds (12.9%) to 1746 pounds (19.4%). 2  Although this seems relatively high, i t  compares well with other biomass estimates and appears to be the direct result of the variation inherent in crown components.  Standard error of estimate expressed as a per cent of the mean.  37  o  From the practical point of view D H alone can be used to estimate totaltree dry weight for Douglas f i r with an equation of the form: W = 0.059265 (D H). 2  The hypothesis that the residual sum of squares for the conditioned model is equal to the residual sum of squares for the maximum model was tested for each equation and the results are shown in Table 7.  Q  38 TABLE 7.  equation  Differences between the maximum and conditioned models tested by the F-test for significance.  species  Total-tree  H  model  no. of variables  degrees of freedom  residual mean square  Conditioned Maximum Difference  4 4  108 107 1  1341360 1303290 5414850  4.15*  88 87 1  599924 593061 1197005  2.01 N.S.  109 108 1  990471 993394 674787  0.67 N.S.  21 20 1  883627 927309 9987  0.01 N.S.  Conditioned Maximum Difference Conditioned Maximum Difference  Bole-wood  Conditioned Maximum Difference H  Bole-bark  4 4  F value  Conditioned Maximum Difference  4 4  14 13 1  161433 147406 343784  2.33 N.S.  Conditioned Maximum Difference  4 4  19 18 1  659592 689719 117306  0.17 N.S.  Conditioned Maximum Difference  3 3  20 19 1  23433 24200 8864  0.37 N.S.  Conditioned Maximum Difference  4 4  14 13 1  32998 35048 6344  0.18 N.S.  Conditioned Maximum Difference  4 4  19 18 1  12517 13203 178  0.01 N.S.  * Significant at the 0.05 probability level 1 N.S. = Not Significant The F-value for the total-tree equation (fir) just barely falls into the c r i t i c a l region, and since the differences in R and SEE were very small between the 2 models, the conditioned one was accepted. 2  39 b. TABLE 8.  Western hemlock  Relationship of total-tree oven dry weight (pounds) with several independent variable combinations for 89 western hemlock trees. independent variables  R or r 2  intercept 553.6 646.3 -326.0 -157.0 0.0  DH  D x CL H regression coefficients  2  0.080180 0.082002 0.069904 0.073028 0.071955  0.528911 0.776396 0.418310  -19.5441 -21.9519  D x  CW  2  SEE (pounds)  2  0.024727  0.987 0.986 0.982 0.980 0.980  633 643 736 770 774  Combination of the 4 variables listed in Table 8 describes the best set of independent variables to estimate total-tree dry weight for western 2 hemlock.  The combined variable of D H alone accounts for 98.07. of the total  variation in the dependent variable. The gain in additional information by using a l l 4 variables would only be 0.7/.. Excluding significant variables w i l l result in a slight increase, from 633 pounds (13.37.) to 770 pounds (16.17.), in the standard error of estimate. The conditioned model, when using the same variables shown in Table 8, is significantly different from the maximum model, but when only the most important variable retained (D H) is used the difference between the two models is not significant.  Comparing  the coefficient of determination and the standard error of estimate for the two models (Table 8) shows no change in the r estimate increases only by 4 pounds. combined variable of D H, 2  2  value and the standard error of  Considering the preceding results the  containing two easily obtainable measurements, w i l l  give the best practical estimate of total-tree dry weight in pounds for western hemlock in the form of:  W = 0.071955 (D H). 2  40  c. TABLE 9 .  Western red cedar  Relationship of total-tree oven dry weight (pounds) with several independent variable combinations for 1 1 3 western red cedar trees. independent variables R or r  2  DH 2  DxCL BA regression coefficients  0.071674  0.728502  -1424.440  0.054267  0.770031  -  0.031159  0.596012  D  SEE (pounds)  2  77.1816  636.028  0.037297  0.943  995  0 . 9 3 3  1075  0.922  1155  0.906  1257  Table 9 shows the four variables, each contributing s i g n i f i cantly to the overall regression. The most important single variable again is D H, accounting for the largest portion of the total sum of squares followed by basal area with  8 6 . 1 ,  dbh  8 1 . 3 ,  and DxCL  90.6%,  63.8/o.  Although both basal area and dbh have high simple correlation coefficients, exclusion of these variables w i l l produce only about 4% less informative results. change from  995  On the other hand, standard error of estimate will  pounds  (23.2%)  to  1257  pounds  (29.3%).  The high standard  error of estimate is probably the direct result of butt-swell, a definite characteristic of older cedar trees, coupled with variations in crown component weights.  Given due consideration to the above discussion, for a l l  practical purposes total-tree dry weight in pounds for western red cedar can be estimated with an equation of the form:  W=  0.037297  (D H). 2  Relations between total-tree dry weight and D H are shown in graphical 2  form in Figure 8 .  0  60  120  180  240  300  360  42.0  D^H = Diameter Squared X Total Tree Height ( i n c h * Xfeet) in Thousands FIGURE 8.  Relations between total-tree dry weight and D H for Douglas f i r , western hemlock 2  and western red cedar.  48o  42 B. a. TABLE 10.  TOTAL BOLE-WOOD DRY WEIGHT  Douglas f i r  Relationship of total bole-wood oven dry weight (pounds) with several independent variable combinations for 23 Douglas f i r trees. independent variables R or r 2  H BA regression coefficients 0.046374 0.045649 0.042728 0.044119  3.30050 4.33684 2.34023  - 183.871 - 143.428  D  2  8.16685  A l l four variables but D H 2  0.982 0.982 0.982 0.982  SEE (pounds) 980 958 940 926  in Table 10 contribute insignificantly  to the overall regression. Additional information gained would be n i l by including every variable in the model since R  2  and r  2  are the same. The total  sum of squares attributable to D H alone is 98.2%. The predicting equation 2  w i l l be more precise i f D H 2  is used in a simple regression. The standard  error of estimate will decrease from 980 pounds (15.5%) to 926 pounds (14.6%). Thus, the combined variable of D H will give the best estimate of total bole2  wood dry weight for Douglas f i r with the equation: b.  W = 0.044119 (D H).  Western hemlock  Table 11 presents the independent variable combinations describing total bole-wood dry weight for western hemlock.  D^H again is the most closely  associated variable with total bole-wood dry weight, accounting for 99.0% of the total variation in the dependent variable.  Eliminating basal area im-  proves the standard error of estimate by 28 pounds. No loss of information  43 9  w i l l result from retaining only D^H and the standard error of estimate w i l l increase by a small amount, from 373 pounds (10.1%) to 436 pounds (11.8%). Considering the preceding results, total bole-wood dry weight for western 9  hemlock can be described very well as a function of D^H in the form of: W = 0.056537 (D H). 2  TABLE 11.  Relationship of total bole-wood oven dry weight (pounds) with several independent variable combinations for 18 western hemlock trees. independent variables  DH  H D regression coefficients  2  0.068527 0.061535 0.061246 0.056537  31.8238 27.7986 4.6232  c. TABLE 12.  154.901 114.958  BA - 321.878  v-2  SEE (pounds)  0.993 0.994 0.992 0.990  401 373 401 436  or  Western red cedar  Relationship of total bole-wood oven dry weight (pounds) with several independent variable combinations for 23 western red cedar trees. independent variables R or r 2  DH 2  -  0.067036 0.057651 0.044784 0.028292  BA D regression coefficients - 1396.11 - 1009.02 - 421.27  126.687 56.385  H  2  - 10.8719  0.945 0.944 0.935 0.926  SEE (pounds) 812 795 838 873  44 Table 12 reveals that the variable retained for total bole-wood estimation of western red cedar is D H. 2  Total tree height does not contri-  bute significantly to the overall regression and when this variable is eliminated the standard error of estimate decreases by 17 pounds. The combination of D H,  basal area and dbh forms the best equation with the highest multiple  2  coefficient of determination and the lowest standard error of estimate. Individual contribution of variables to the total sum of squares in receding order are D H 2  (73.9%).  (92.6%), basal area (87.0%), dbh (81.0%) and total tree height  While combination of the four variables accounts for 94.5%, D H, 2  the most closely associated variable, alone accounts for 92.6% of the total sum of squares.  Therefore, only 1.9% loss of information and a small in-  crease (78 pounds) in the standard error of estimate w i l l result i f D^H is used alone for prediction. The higher standard error (873 pounds -' 27.8%) as compared to Douglas f i r (14.6%) and western hemlock (11.8%) is perhaps the result of form differences.  Mature cedar being heavily tapered at the base will yield  a less precise volume estimate thereby indirectly affecting total bole dry weight.  Also, added variation was introduced with the method used for volume  calculations of the 13 cedar trees that were lacking actual data on bark thick2  ness.  For a l l practical purposes D H alone will sufficiently describe total  bole-wood dry weight for western red cedar with an equation of the form: W = 0.028292 (D H) 2  2 Relations between total bole-wood dry weight and D H are shown in graphical form in Figure 9.  D H = Diameter Squared X Total Tree Height (inch* Xfeet) in Thousands 1  FIGURE 9.  Relations between total bole-wood dry weight and D H for Douglas f i r , western 2  hemlock and western red cedar.  ^  46 C. TOTAL BOLE-BARK DRY WEIGHT a. TABLE 13.  Douglas f i r  Relationship of total bole-bark oven dry weight (pounds) with several independent variable combinations for 23 Douglas f i r trees.  independent variables R or r 2  DH 2  0.0044826 0.0066663 0.0065245 0.0079077  BA H regression coefficients 160.90 38.87 48.30  D  2  3.355 0.215  - 24.65  0.987 0.986 0.986 0.984  SEE (pounds) 150 153 149 153  The most important variable for predicting total bole-bark dry  9 weight is the combined vari able of D^H (Table 13) which alone accounts for 98.4% of the total sum of squares.  It appears that there is no advantage in  using multiple regression instead of a simple linear one of total bole-bark dry weight on D H, because gain in information would be minimal and loss in 2  precision would be small.  Then the best practical function describing total  bole-bark dry weight for Douglas f i r w i l l take the form: b.  W = 0.0079077 (D H). 2  Western hemlock  Table 14 l i s t s the independent variables in order of importance for describing total bole-bark dry weight of western hemlock trees. The most closely associated variable is D^H with a simple coefficient of determination of 92.7%. It is apparent from the table that no worthwhile gain would result by using multiple regression and a simple linear regression in2 volving only D H is very satisfactory. Predicting equation for dry weight: W = 0.0084064 (D H). 2  47 TABLE 14.  Relationship of total bole-bark oven dry weight (pounds) with several independent variable combinations for 18 western hemlock trees. independent variables H  DH 2  BA  D  regression coefficients  0.0167035 0.0101088 0.0100794 0.0084064  - 7.792 - 3.999 - 1642  c. TABLE 15.  49.33 11.69  SEE (pounds)  or or r 2  0.942 0.938 0.938 0.927  - 303.00  181 181 176 185  Western red cedar  Relationship of total bole-bark oven dry weight (pounds) with several independent variable combinations for 23 western red cedar trees. independent variables  R or r2 2  BA D regression coefficients  DH 2  - 188.85 - 143.72 - 63.01  0.0092564 0.0081619 0.0063951 0.0039283  15.94 7.74  H  SEE (pounds)  0.946 0.945 0.936 0.926  - 1.269  111 109 115 121  Variables presented in Table 15 with the exclusion of total tree height form the best combination to describe total bole-bark dry weight, o D^H is the single most important variable accounting for 92.6% of the total sum of squares while basal area, dbh, and total tree height "explains" 87, 81, and 74% respectively.  Retaining only D2H w i l l result in a small loss of  information (R 0.946 to r2 0.926) and the increase in the standard error of 2  estimate (12 pounds) w i l l also be small.  It appears that D H alone will give 2  the best practical estimation of bole-bark dry weight for western red cedar in the form of:  W = 0.0039283 (D H). 2  Relations between total bole-bark dry weight and D H are shown in graphical 2  form in Figure 10.  0  60  120  180  2.40  30o  560  420  48o  D2 H = Diameter Squared X Total Tree Height (inch^ X f e e t ) in Thousands FIGURE 10.  Relations between total bole-bark dry weight and D H for Douglas f i r , 2  western hemlock and western red cedar. oo  49 CROWN COMPONENTS Total-crown, needles, fine, medium and large component relationships.  Crown component dry weights plotted over the independent variables showed linear and curvilinear trends. (log 10) and untransformed form.  The data were fitted in transformed  When standard errois of estimate,, result-  ing from the two procedures, were compared logarithmic equations were i n ferior to the linear and curvilinear functions, therefore, contrary to many biomass analyses, transformation was not used. Simple correlation coefficients between crown component dry weights and the independent variables are listed in Table 16. A good, overall corre2 lation of crown length, gross crown volume, D x CL, D x CW  and D x gross  crown volume with the dependent variables is apparent from Table 16. The squared term of D x CL also has a good correlation with crown components for western hemlock and western red cedar.  The highest association (r = 0.906)  is between the large branch component and the squared term of D x CL (hemlock), while the lowest (r = 0.479) is between the large branch component and total tree height (cedar). Crown component equations, like the functions for total-tree, bolewood and bole-bark, were conditioned and the hypothesis that the residual sum of squares for the conditioned model is equal to the residual sum of squares for the maximum model was tested for each equation and the results are in Table 17. The differences between the two models were highly significant for most of the functions when a l l four variables were included in the equations. After each elimination step the new equation was tested again and in a few cases the differences were insignificant.  Table 17 l i s t s the test results  only for the equations with four independent variables.  50 TABLE 16.  independent variables  The simple correlation coefficients between oven dry weight crown components and the independent variables. units  Height  feet  Crown length  feet  Crown width  feet  Diameter  inches  Basal area  feet  DH  inch^ x feet  CW  feet  2  Cross crown volume  feet  3  D x CL  inch x feet  2  2  2  D x CW  inch x feet  2  D x Gross crown volume  inch x feet  3  (D x CL)  inch x feet  2  2  **  2  2  species  total crown  large  branch class medium fine  F H C F H C F H C F H C F H C F H C F H C F H C F H C F H C F H C F H C  0.544** 0.647 0.517 0.740 0.733 0.882 0.653 0.627 0.718 0.543 0.628 0.541 0.518 0.653 0.540 0.488 0.661 0.536 0.665 0.644 0.759 0.727 0.698 0.876 0.701 0.876 0.883 0.767 0.767 0.826 0.717 0.822 0.883 0.599 0.896 0.875  0.527 0.618 0.479 0.725 0.696 0.861 0.631 0.573 0.692 0.528 0.590 0.504 0.510 0.621 0.508 0.482 0.636 0.505 0.647 0.593 0.739 0.724 0.662 0.870 0.702 0.855 0.863 0.762 0.732 0.809 0.724 0.805 0.879 0.609 0.906 0.872  0.586 0.659 0.522 0.776 0.769 0.862 0.681 0.690 0.688 0.586 0.647 0.540 0.560 0.668 0.539 0.530 0.671 0.539 0.684 0.705 0.727 0.743 0.743 0.852 0.743 0.885 0.871 0.789 0.807 0.800 0.734 0.846 0.865 0.626 0.880 0.870  0.555 0.666 0.559 0.761 0.751 0.903 0.694 0.667 0.751 0.557 0.656 0.578 0.522 0.677 0.572 0.486 0.677 0.570 0.696 0.681 0.781 0.729 0.718 0.876 0.708 0.882 0.902 0.769 0.789 0.844 0.698 0.825 0.878 0.579 0.871 0.872  needles 0.563 0.663 0.572 0.745 0.754 0.904 0.681 0.677 0.759 0.552 0.658 0.595 0.515 0.673 0.585 0.482 0.668 0.578 0.683 0.687 0.788 0.711 0.715 0.876 0.693 0.864 0.900 0.758 0.775 0.847 0.680 0.801 0.875 0.551 0.834 0.861  A l l coefficients listed are significant at the 0.01 probability level.  51 TABLE 17.  equation  Differences between the maximum and conditioned model tested by the F-test for significance for the crown component functions. species  Total-crown  F H C  Fine  no. of variables  degrees of freedom  residual mean square  Conditioned Maximum Difference Conditioned Maximum Difference Conditioned Maximum Difference  4 4  107 106 1 85 84 1 108 107 1  900184 821580 9232208 92646 93746 246 119508 112250 896114  107 106 1 85 84 1 108 107 1  386138 355199 3665672 30356 30586 11036 39419 39782 578  107 106 1 85 84 1 108 107 1  4879 4492 45901 784 793 28 1335 1334 1442  107 106 1 85 84 1 108 107 1  7260 6655 71390 1343 1358 83 236 233 557  Conditioned Maximum Difference Conditioned Maximum Difference Conditioned Maximum Difference  Large  Medium  model  F H C  Conditioned Maximum Difference Conditioned Maximum Difference Conditioned Maximum Difference Conditioned Maximum Difference Conditioned Maximum Difference Conditioned Maximum Difference  4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4  F value 11.24** 0.002 N.S, 7.98**  10.32** 0.36 N.S. 0.01 N.S.  10.22** 0.04 N.S. 1.08 N.S.  10.73** 0.06 N.S. 2.39 N.S.  . continued  52 TABLE 17.  (continued)  equation  species  model  no. of variables  degrees of freedom  Needles  F  Conditioned Maximum Difference Conditioned Maximum Difference Conditioned Maximum Difference  4 4  107 106 1 85 84 1 108 107 1  H C  **  4 4 4 4  residual mean square 33346 29771 412296 6062 5938 16478 9543 9553 8473  F value 13.85** 2.78 N.S. 0.89 N.S.  Significant at the 0.01 probability level.  D. TOTAL-CROWN DRY WEIGHT a. Douglas f i r The dependent variables describing total-crown oven dry weight for Douglas f i r are listed in order of importance in Table 18.  The most important  o  single independent variable is D x CW^ which alone accounts for 58.87. of the 2  total sum of squares, while the tree variables, D H and total tree height, only account for 23.8 and 29.67. respectively. TABLE 18.  Relationship of total-crown oven dry weight (pounds) with several independent variable combinations for 111 Douglas f i r trees. independent variables  R or r 2  intercept - 837.5 - 756.5  DxCW  2  0.047575 0.078166 0.071546 0.080017  H DH regression coefficients 2  13.4944 12.9774 1.6220  - 0.00889 - 0.00512  DxCL  2  0.68778  0.678 0.634 0.595 0.588  SEE (pounds) 906 961 1002 1006  53  The last two equations in Table 18, showing insignificant differences between the conditioned and maximum models when tested, were conditioned to zero intercept but highly significant differences prevented application of this procedure to the f i r s t two equations. Retaining only the most important single independent variable w i l l result in approximately 9 per cent loss of information and about 7 per cent decrease in predicting precision.  The best estimating equation would in-  clude a l l four independent variables and possibly an acceptable practical solution to predict total-crown oven dry weight in pounds for Douglas f i r would be in the form of: W = 0.080017 (D x CW ). 2  b. TABLE 19.  Western hemlock  Relationship of total-crown oven dry weight (pounds) with several independent variable combinations for 89 western hemlock trees. independent variables  intercept  - 240.5 - 232.5  DxCL 0.871124 0.900881 0.754453 0.816580 0.165095  DH BA regression <coefficients 2  0.01596 0.01562 0.00095  - 529.712 - 520.126 (DxCL) 0.000255 2  R or r 2  CW  2  2  0.08606  0.834 0.834 0.772 0.767 0.808  SEE (pounds) 304 303 355 356 323  54 The five independent variables in Table 19, with the exception of CW, are a l l contributing significantly to the overall regression. The 2  squared term of DxCL is the most important single variable accounting for the largest portion - 80.3% - of the total sum of squares followed by dbh times crown length 76.7, crown width squared 44.2, D H 43.7 and basal area 42.6%. The best multiple regression would involve the combination DxCL, D2H and basal area. Considering both  9 and standard error of estimate  figures the independent variable DxCL in a curvilinear form gives a better f i t than either DxCL or the squared term of DxCL above.  It seems then that  the best practical solution for estimating total crown oven dry weight for western hemlock w i l l be with an equation involving DxCL in the form of: W = 0.165095 (DxCL) + 0.000255 (DxCL) . 2  c. TABLE 20.  Western red cedar  Relationship of total-crown oven dry weight (pounds) with several independent variable combinations for 112 western red cedar trees. independent variables R or r 2  intercept - 227.8 - 134.4 - 183.1  DxCL 0.505936 0.533041 0.344542 0.610849 0.301496  C. volume BA regression coefficients 0.01015 0.00913 0.01303  - 79.2573 - 55.2776 (DxCL) 0.000072 2  H  2  3.38325  0.860 0.849 0.837 0.779 0.794  SEE (pounds) 335 344 355 414 400  55  Combination of the independent variables listed in Table 20 describes the best set to estimate total-crown oven dry weight for western red cedar.  Crown length times dbh was retained as the best single variable.  Total tree height, basal area, gross crown volume and crown length times dbh account for 86.0% of the total sum of squares and DxCL alone accounts for 77.9%. The two equations listed without intercepts in Table 20 were justified for conditioning. Retaining only DxCL will result in 8.1% loss of information and approximately 80 pounds increase in the standard error of estimate.  Including (DxCL)'' besides crown length times dbh w i l l increase R  by 1.5% and decrease the standard error by 14 pounds.  If higher precision  is desired a multiple regression with the 4 variables should be used, while from the practical point of view DxCL in a curvilinear form w i l l estimate total crown oven dry weight for western red cedar satisfactorily. The predicting equation i s :  W = 0.301496(DxCL) + 0.000072(DxCL) . 2  Relations between total-crown dry weight and the independent variables retained for prediction are shown in graphical forms in Figures 11 and 12.  6600  r  D X C W = Diameter X Crown Width Squared (inch X f e e t ) 2  FIGURE 11.  2  Relations between total-crown oven dry weight and DxCW for Douglas f i r .  4000 Y= 0 . 3 O | 4 q 6 ( D * C L ) + 0. 0 0 0 0 7 2 C D * C L >  3600  3200  C 3 O Q.  Y= OJ65oq5(D*CL)  2800 \  + O. 0 0 0 2 5 5  (DxCL) " 2  2400  o> ^  2000  l_  Q  C 0) >  1600  O ^  1200  o —  o o  I—  800  40O  5oo  IOOO  ISOO  2000  2500  3000  3500  4O0O  D X CL = Diameter X Crown Length (inch X feet) FIGURE 12.  4500  50oo  Relations between total-crown oven dry weight and DxCL + (DxCL) for western hemlock and 2  western red cedar.  5500  58 E.  LARGE BRANCH COMPONENT  a. Douglas f i r TABLE 21.  Relationship of large branch crown component oven dry weight (pounds) with several independent variable combinations for 111 Douglas f i r trees. independent variables  R or r 2  intercept - 527.8 - 475.6  DxCW  2  0.030201 0.049902 0.046353 0.048776  H DH regression coefficients 2  7.5726 7.2397 0.4639  - 0.00533 - 0.00291  DxCL  2  0.44294  0.659 0.615 0.581 0.580  SEE (pounds) 595 630 651 649  Table 21 presents the independent variable combinations describing large branch crown component dry weight for Douglas f i r .  DxCW^ is the most  closely associated variable with large branch component dry weight, accounting for 58.0 per cent of the total variation in the dependent variable. The last two equations (Table 21) were acceptable in conditioned form. The slight disadvantages of retaining only one independent variable in the regression are evident from Table 21, 7.9 per cent loss of information and an increase of 54 pounds in the standard error of estimate. Multiple regression would give better results, but from the practical point of view a satisfactory p  predicting equation w i l l be the one involving only DxCW W = 0.048776 (DxCW ). 2  in the form of:  59  b. Western hemlock TABLE 22.  Relationship of large branch crown component oven dry weight (pounds) with several independent variable combinations for 89 western hemlock trees.  independent variables intercept  - 70.9 - 176.7 - 173.2  DxCL  C. volume DxC. vol. regression coefficients  0.437881 0.300072 0.504422 0.458503 0.052963  0.02171 0.01543 0.00188  0.00087 0.00071  BA 54.900  (DxCL) 0.000203 2  SEE (pounds)  or 0.836 0.814 0.735 0.732 0.821  174 185 220 220 180  The variables listed in Table 22 form the best combination to describe large branch crown component dry weight.  The two most important of  them are DxCL and the squared term of the same variable accounting for 82.1% of the total sum of squares. The equations justified for conditioning were the  f i r s t and last one in Table 22.  The multiple regression equation with  independent variables DxCL, gross crown volumes, Dx gross crown volume and basal area yields the highest R  and the lowest standard error.  Retaining  only DxCL, or the same variable and gross crown volume in a multiple regression form will give the highest standard error of estimate and the lowest coefficient of determination.  Since the last equation (Table 22) practically is the o  same as the f i r s t one with 4 independent variables (comparison based on R and SEE values) the most suitable practical solution for estimating western lemlock large crown component oven dry weight will be the function involving only one independent variable in the form of: W= -0.052963(DxCL) + 0.000203(DxCL) . 2  60  c. Western red cedar TABLE 23.  Relationship of large branch crown component oven dry weight (pounds) with several independent variable combinations for 112 western red cedar trees.  independent variables  R or r 2  intercept  - 73.5 - 115.1  DxCL  C. volume BA regression coefficients  0.256698 0.303818 0.178197 0.342192 0.099398  0.01237 0.00557 0.00802  - 25.2278 - 31.4970  CW  2  2  - 0.53462  (DxCL) 0.000056 2  0.848 0.833 0.815 0.745 0.773  SEE (pounds) 198 208 218 254 240  The variable combinations listed in Table 23 describe the best set of independent variables to estimate large branch crown component dry weight for western red cedar.  The squared term of DxCL accounts for 76% of  the total variation in the dependent variable. mation by using four variables would be 8.8%.  The gain in additional infor Excluding significant variabl  and retaining only DxCL will increase the standard error of estimate by 56 pounds. Conditioned and maximum models were significantly different for 9  variable combinations listed with intercepts.  If (DxCL)  is added to the  function involving only crown length times dbh the coefficient of determination, expressed in per cent, increases by 2.8% and the standard error of estimate decreases by 14 pounds, thereby giving a better practical equation to predict large crown component oven dry weight of western red cedar. The predicting function:  W = 0.099398(DxCL) + 0.000056(DxCL) . 2  Relations between large branch crown component dry weight and th independent variables retained for prediction are shown in Figures 13 and 14  I  loooo  I  20O0O  D X CW 13.  2  3oooo  40000  50000  I  60000  70000  = Diameter X Crown Width Squared (inch X f e e t ) 2  Relations between large branch crown component oven dry weight and DxCW^ for Douglas f i r .  D X CL = Diameter X Crown Length (inch X feet) FIGURE 14.  Relations between large branch crown component oven dry weight and DxCL + (DxCL) for western hemlock and western red cedar.  63 F.  MEDIUM BRANCH COMPONENT  a. Douglas f i r TABLE 24.  Relationship of medium branch crown component oven dry weight (pounds) with several independent variable combinations for 111 Douglas f i r trees. independent variables  intercept - 59.1 - 52.4  DxCW  2  H DH regression coefficients  DxCL  2  0.003604 0.006110 0.005590 0.006931  1.1224 1.0801 0.2567  - 0.00069 - 0.00079  0.05635  SEE (pounds) 0.720 0.673 0.639 0.612  67 72 75 77  Table 24 shows the four variables, each contributing significantly to the overall regression.  The most important single variable is DxCW^,  accounting for the largest portion of the total sum of squares 61.2%, followed by DxCL with 55.2%, total tree height 34.3%, and D H 28.3%. 2  Total tree height  is more important than crown length and i t is the last variable eliminated. The models statistically justified for conditioning to a zero intercept were the ones including DxCW and total tree height. 2  The consequences of retain-  ing only DxCW will be 10.8% decrease in R and 10 pounds increase in SEE. 2  2  For a l l practical purposes medium branch crown component dry weight for Douglas f i r can be estimated with an equation of the form: W = 0.005931(DxCW ). 2  64 b. Western hemlock TABLE 25.  Relationship of medium branch crown component oven dry weight (pounds) with several independnent variable combinations for 89 western hemlock trees.  independent variables intercept  - 15.9 - 15.0  DxCL  DH BA regression coefficients  0.072110 0.085507 0.072905 0.079337 0.039065  CW*  2  0.00138 0.00122 0.00010  - 44.1523 - 39.8467  0.03874  (DxCL) 0.000015 2  or ^2  SEE (pounds)  0.848 0.835 0.789 0.783 0.789  28 28 32 33 31  Crown length times dbh, basal area, crown width squared, D H, and the squared term of DxCL (Table 25) are the independent variables retained to describe medium branch crown component dry weight for western hemlock. Every variable makes significant contributions to the overall regression and dbh times crown length, with a simple coefficient of determination of 0.783, is the variable most closely associated with medium branch component dry weight.  The variable combinations listed without intercepts (Table 25) were  statistically acceptable in conditioned form.  It seems that either the f i r s t  or second set of independent variables would give the best estimate while DxCL alone w i l l produce the lowest r  2  and the highest standard error.  Crown  length times dbh in curvilinear form is comparable to the f i r s t two equations and there would.be no worthwhile gain from using a multiple regression with three or four variables over the one involving DxCL. The predicting equation i s : W = 0.039065(DxCL) + 0.000015(DxCL) . 2  65  c. Western red cedar TABLE 2 6 .  Relationship of medium branch crown component oven dry weight (pounds) with several independent variable combinations for 1 1 2 western red cedar trees. independent variables  R or r^ 2  intercept  -  1 6 . 7  DxCL  BA C. volume regression coefficients  0.048179  -  24.445  0.00115  0.056480  -  5.459  0.00079  0.079273  -  7.998  DH 2  SEE (pounds)  2  0.00077  0.839  36  0.817  38  0.801  40  0.061589  (DxCL)  0.758  44  0.029247  0.000008  0.783  42  2  Table 2 6 presents the independent variables retained in the regression equation after the seventh step in the elimination process. The total sum of squares attributable to DxCL, basal area, gross crown volume and D H is 75.8%.  and the most important single variable, DxCL, accounts for  83.97»,  Conditioning was justified statistically for a l l variable combin-  ations but one.  The systematic reduction of R and the steady increase of 2  the standard error at each step of elimination is evident from Table 2 6 and amounts to  8.l7o  less information and  8  pounds higher standard error i f satis-  factory equation to describe medium branch crown component oven dry weight for western red cedar w i l l be the one involving crown length times dbh in curvilinear form. The predicting equation is: W =  0.029247(DxCL)  +  0.000008(DxCL) . 2  Relations between medium branch crown component dry weight and the  independent variables retained for prediction are shown in Figures 1 5  and  16.  D X C W = Diameter X Crown Width Squared (inch X f e e t ) 2  FIGURE 15.  2  Relations between medium branch crown component oven dry weight and DxCW  2  for Douglas f i r . ON ON  CO  5oo  c 3  O Q. C  ^_  A  -C  Y-  4oo  A  0.029247 (DxCL.) + 0.0OO0O8 C D » C L > -  « >. k. Q  c  cu >  O  30o  ^_  c c o  CD Q.  E  o  o c  200  $ o w  o x: o  c ioo o  t_ CO  E  3 T3 0)  2  o  50o  I00O  i5oo  200O  2.500  3600  b"50o  40oo  450o  5000  S500  D X CL = Diameter X Crown Length (inch X feet) FIGURE 16,  Relations between medium branch crown component oven dry weight and DxCL + (DxCL) for western hemlock and western red cedar.  ON  68 G.  FINE BRANCH COMPONENT  a. Douglas f i r TABLE 27.  Relationship of fine branch crown component oven dry weight (pounds) with several independent variable combinations for 111 Douglas f i r trees. independent variables  intercept 73.7 65.9  DxCW  H DH regression coefficients  0.004352 0.007298 0.006507 0.007999  2  1.4514 1.4016 0.2857  - 0.00092 - 0.00055  DxCL  or r 2  0.06623  0.699 0.652 0.602 0.579  SEE (pounds) 81 87 92 94  After the seventh independent variable was eliminated from the totalmodel DxCW9, total tree height, D2H, and dbh times crown length remained in the multiple regression equation (Table 27).  DxCW is the most closely associ2  ated variable with fine crown component dry weight, accounting for 57.9% of the total sum of squares.  The four variables will give the best predicting  equation with the highest multiple coefficient.of determination and the lowest standard error. The two models accepted in conditioned form were the ones 2 involving DxCW and total tree height.  9  The results of retaining only DxCW^  o  would be 12% reduction in R and 13 pounds increase in the standard error of estimate.  Including another variable (H) would only mean a small improvement,  therefore, a reasonable practical solution will be a simple linear regression in the form of: W = 0.007999(DxCW ). 2  69 b. Western hemlock TABLE 28.  Relationship of fine branch crown component oven dry weight (pounds) with several independent variable combinations for 89 western hemlock trees. independent variables  intercept  21.7 20.6  DxCL  DH BA regression coefficients  0.090233 0.101186 0.087783 0.096980 0.047008  2  0.00160 0.00147 0.00014  - 50.855 - 47.336 (DxCL)" 0.000019  CW'  SEE (pounds)  or r 2  0.03167  0.827 0.822 0.785 0.777 0.785  36 37 40 41 40  The most important variable for predicting fine branch crown component dry weight is crown length times dbh (Table 28), which alone accounts for 77.7% of the total sum of squares while D H and basal area, the two lowest 2  contributors, account for 45.8% each.  Conditioned and maximum models were  significantly different for the equations listed with intercepts. The estimating power of the f i r s t two equations in Table 28 is 2 about the same.  The remaining functions, when compared on the basis of R  and standard error of estimate figures, also demonstrate similarity equations three and five being exactly the same and slightly lower figures for equation 2 four., Since two different functions yield exactly the same R  and SEE figures  the curvilinear form of DxCL is more practical because i t does not include the extra D H variable. 2 The predicting equation is: W = 0.047008(DxCL) + 0.000019(DxCL) .  70 c. Western red cedar TABLE 29.  Relationship of fine branch crown component oven dry weight (pounds) with several independent variable combinations for 112 western red cedar trees. independent variables DxCL  intercept  0.024879 0.028179 0.017792 0.031658 0.022392  - 6.1  C.volume BA regression coefficients 0.00055 0.00041 0.00060  - 9.7676 - 2.2207  0.00031  (DxCL) 0.000002 2  R'2 or 0.884 0.870 0.856 0.814 0.817  SEE (pounds) 15 16 16 19 19  Table 29 l i s t s the independent variables in order of importance for describing fine branch crown component dry weights of western red cedar trees.  The most closely associated independent variable with fine crown com-  ponent dry weight is crown length times dbh with a simple coefficient of determination of 0.814. Crown length times dbh, gross crown volume, basal area, p and D H in a multiple regression w i l l produce the best prediction with the 2 highest R  and lowest standard error.  Conditioning was unjustified statis-  t i c a l l y for the equation involving DxCL alone.  Although no change in the  standard error and only a small gain in variation-accounted-for will result when (DxCL)  is included in the function with DxCL, but to make western red  cedar crown component equations uniform and regression coefficients additive the curvilinear form of DxCL is desirable. 2 The predicting function i s : W = 0.022392(DxCL) + 0.000002(DxCL) . Relations between fine branch crown component dry weight and the independent variables retained for prediction are shown in Figures 17 and 18.  D X CW* = Diameter X Crown Width Squared (inch X f e e t * ) FIGURE 17.  Relations between fine branch crown component oven dry weight and DxCW  2  for Douglas f i r .  D X CL= Diameter X Crown Length (inch X feet) FIGURE 18. Relations between fine branch crown component oven dry weight and DxCL + (DxCL) for western hemlock and western red cedar.  73 H. NEEDLE COMPONENT a. TABLE 30.  Douglas f i r  Relationship of needle crown component oven dry weight (pounds) with several independent variable combinations for 111 Douglas f i r trees.  independent variables R or r  SEE (pounds)  0.688 0.651 0.590 0.564  172 181 195 200  2  DxCW  intercept - 177.0 - 162.6  2  H DH regression coefficients  0.009418 0.014856 0.013095 0.016310  DxCL  2  3.3477 3.2558 0.6155  2  0.12226  - 0.00194 - 0.00127  A multiple regression with the four variables shown in Table 30 will give the best description for needle component dry weight of Douglas fir.  DxCW is the most important single variable. 2  Individual contribution  of variables to the total sum of squares in decreasing order are DxCW  2  (56.4%), dbh times crown length (48.0%), total tree height (31.7%), and D H 2  (23.2%).  The differences between conditioned and maximum models were signif2  icant for the f i r s t two equations.  The consequences of retaining only DxCW  in the regression equation are apparent from Table 30. Including another 2 variable (total tree height) besides DxCW  only slightly improves the co-  efficient of determination and the standard error of estimate.  The addit-  ional gain would hardly be practical, therefore, the following equation will give a satisfactory estimate of needle component dry weight for Douglas f i r : W = 0.01631(DxCW ). 2  74 b. Western hemlock TABLE 31.  Relationship of needle crown component oven dry weight (pounds) with several independent variable combinations for 89 western hemlock trees.  independent variables intercept  56.3  DxCL  D_H H regression coefficients  0.157179 0.193680 0.149260 0.166786 0.131984  0.00093 0.00131 0.00025  - 1.011 - 1.859  CW  2  0.08096  (DxCL) 0.000018 2  2 R or r_3_  SEE (pounds)  0.787 0.789 0.744 0.738 0.746  77 77 84 84 84  The five most important variables for describing western hemlock needle component dry weight are listed in Table 31.  The single variable most  closely associated with needle component dry weight is dbh times crown length. Differences between maximum and conditioned models were insignificant for a l l variable combinations but one. A multiple regression with independent variables of crown length times dbh, D H, and total tree height w i l l give the best oven dry weight prediction.  Comparison of the various equations in  Table 31 on the basis of SEE reveals that the f i r s t two and the last three are exactly the same. Although the simple linear regression of DxCL on needle dry weight has the same SEE as the same variable in curvilinear form, the latter is suggested for prediction because i t has a slightly higher coefficient of determination and i t would also conform to the other hemlock crown component functions. The predicting equation i s : W = 0.131984(DxCL) + 0.000018(DxCL) . 2  75 c. Western red cedar TABLE 32.  Relationship of needle crown component oven dry weight (pounds) with several independent variable combinations for 112 western red cedar trees.  independent variables DxCL 0.170574 0.186368 0.217621 0.169393 0.150460  BA CL regression coefficients - 41.1366 - 15.3023 - 15.8790  1.7854 1.1273  DH  SEE (pounds)  2  0.001013  (DxCL) 0.000006 2  0.848 0.844 0.840 0.809 0.812  97 98 99 108 107  The multiple regression, including the independent variables shown in Table 32 w i l l give the best description of western red cedar needle component dry weight.  The total sum of squares attributable to the single  most important variable, crown length times dbh, is 80.9%.  The differences  between conditioned and maximum models were insignificant for a l l variable combinations.  Compared on the basis of R  2  and SEE values the f i r s t three  multiple regression equation in Table 32 are about the same; perhaps the one including only two variables is the most practical for prediction.  For con-  formity of predicting equations of western red cedar crown components and additivity of regression coefficients the curvilinear form of crown length times dbh is more desirable. The predicting function i s : W = 0.15046(DxCL) + 0.000006(DxCL) . 2  Relations between needle crown component and the independent variables retained for prediction are shown in graphical form in Figures 19 and 20.  7O000  D X C W = Diameter X Crown Width Squared (inch X f e e t ) 2  FIGURE 19.  2  Relations between needle crown component oven dry weight and DxCW for Douglas f i r .  D X CL= Diameter X Crown Length (inch X feet)  9  FIGURE 20. Relations between needle crown component oven dry weight and DxCL + (DxCL)- for western hemlock and western red cedar.  78 TABLE 33.  equation Total-tree  Comparison of simple linear regressions includin;g the most important and most convenient variables for the various predicting equations for oven dry weight species F H C  Bole-wood  F H C  Bole-bark  F H C  Total-crown  F H C  Large branches  F H C  Medium branches  F H C  independent variable  intercept  regression coefficient  r  SEE (poun<  2  DH BA DH BA D2H BA  0.059265 2035.55 0.071955 2037.58 0.037297 935.084  0.961 0.944 0.980 0.918 0.906 0.859  1746 2110 774 1553 1257 1538  DH BA DH BA DH BA  0.044119 1504.80 0.056537 1600.63 0.028292 707.06  0.982 0.937 0.990 0.927 0.926 0.866  926 1680 436 1148 873 1150  DH BA DH BA DH BA  0.007908 270.68 0.008406 235.71 0.003928 98.11  0.984 0.953 0.927 0.842 0.926 0.864  153 258 185 267 121 161  0.080017 206.22 0.816580 212.11 0.610849 120.23  0.588 0.268 0.767 0.426 0.779 0.291  1006 1347 356 559 414 742  - 8.3  0.048776 129.65 0.458503 115.98 0.342192 64.80  0.580 0.260 0.732 0.385 0.745 0.257  649 866 220 333 254 435  29.1 - 15.0 2.1 - 16.7 5.0  0.006931 17.66 0.072905 20.85 0.061589 12.28  0.612 0.314 0.783 0.445 0.758 0.290  77 103 33 52 44 75  2  2  2  2  2  2  2  2  DxCW BA DxCL BA DxCL BA  2  DxCW BA DxCL BA DxCL BA  251.1 -232.5 - 49.5 -183.1 39.6  2  DxCW BA DxCL BA DxCL BA  103.7 -173.2 - 62.2  2  Continued  79  TABLE 33. (continued) equation  species  independent variable  Fine branches  F  DxCW BA DxCL BA DxCL BA  H C F  Needles  H C  intercept  2  DxCW BA DxCL BA DxCL BA  39.6 -20.6 - 0.8 - 6.1 4.3  2  78.6 11.5 38.6  regression coefficient  r  2  SEE (pounds)  0.007999 19.32 0.096980 25.95 0.031658 6.47  0.579 0.272 0.777 0.458 0.814 0.327  94 125 41 64 19 36  0.016310 39.58 0.166786 49.31 0.169393 36.68  0.564 0.264 0.738 0.452 0.809 0.341  200 261 84 123 108 201  In order to compare the simple linear regression of the most important variable with that of the most convenient, simple linear regressions of component  dry weights on basal area were calculated.  Results are summarised  in Table 33. When the two methods of estimation are compared on the basis of r  2  and standard error of estimate i t is evident from Table 33 that basal area w i l l give much poorer results.  Total-tree, bole-wood, and bole-bark dry weights  estimated with basal area would yield on the average 5.2% less information and 11.6% higher standard error with extremes of 1.7 - 8.5% for r and 4 - 20% for 2  SEE.  The differences are more pronounced for crown component dry weights with  35.8% reduction in variation accounted for and 38.97. increase in the standard error of estimate with minimum and maximum values of 28.6 - 48.8% for r and 24 - 617. for standard error.  Therefore, based on the analysis of the collect-  ed data a component dry weight estimating system with basal area alone, though most convenient and highly desirable, is not justified.  A compromise might be  effected by use of measured tree dbh, or estimated basal area per acre, with estimated height.  80 The relative dry weights of crown components are shown for the present study along with Fahnestock's (1960) figures in Table 34.  TABLE 34.  Species  Relative oven dry weights of crown components based on 112 Douglas f i r , 89 western hemlock and 113 western red cedar sample branches.  large  medium  large plus medium Haney  fine  needles  needles  fine  large plus medium Fahnestock^-  Fir  47  14  61  13  26  27  12  61  Hemlock  39  13  52  14  34  23  15  62  Cedar  40  11  51  6  43  36  5  59  In biomass studies the predicted values calculated from the component equations are expected to add up to the predicted value derived from the total equation.  In other words, the sum of crown component weights should be equal  to total-crown weight. exist.  Very often this is not the case and discrepancies do  Through personal communication (Kozak, 1969) the author was able to  establish the conditions under which the components do add up to the total. These conditions are: a) Exactly the same model must be fitted for a l l the components and total equations. b) If transformation is used on the dependent variable, the transformation is linear in scale. c) A l l the equations are fitted from the same observations. (1) Based on sample branches from each third of tree crowns of three trees of each species.  81  Since the above conditions are met in the present study, i t can be assumed that the sum of the regression coefficients for the 4 crown components (large, medium, fine, needles) should be equal to the regression coefficient for total-crown. The coefficients in Table 35 verify this assumption where crown component additivity holds true for a l l three species.  The same applies  to the regression coefficients in Table 33 where crown component and totalcrown weights were fitted with a common independent variable (basal area). TABLE 35. Summary of predicting equations for the various component dry weights. independent variables  R or r 2  equation  species  Total-tree Bole-wood Bole-bark Total-crown Large Medium Fine Needles  F  Total-tree Bole-wood Bole-bark Total-crown Large Medium Fine Needles  H  Total-tree Bole-wood Bole-bark Total-crown Large Medium Fine Needles  C  DH 2  DxCL DxCW (DxCL) re gression coefficients 2  0.059265 0 .044119 0.007908  0 .071955 0 .056537 0 .008406  0.037297 0.028292 0 .003928  2  0.301496 0.099398 0.029247 0.022392 0.150460  SEE pounds  0.961 0.982 0.984 0.588 0.580 0.612 0.579 0.564  1746 926 153 1006 649 77 94 200  19 14 13 83 92 69 73 76  0.000255 0.000203 0.000015 0.000019 0.000018  0.980 0.990 0.927 0.808 0.821 0.798 0.785 0.746  774 436 185 323 180 31 40 84  16 11 34 63 74 54 59 59  0.000072 0.000056 0.000008 0.000002 0.000006  0.906 0.926 0.926 0.794 0.773 0.783 0.817 0.812  1257 873 121 400 240 42 19 107  29 27 27 65 80 66 54 50  0.080017 0.048776 0.006931 0.007999 0.016310  0.165095 -0.052963 0.039065 0.047008 0.131984  2  82 DISCUSSION AND CONCLUSION Results showed that diameter at breast height (D) and total tree height (H), or more precisely, the combined form (D H) of these two inde2  pendent variables is the most important single estimator of total-tree, bolewood and bole-bark dry weights for the three species investigated.  This was  to be expected since so much of the weight estimating system was based on volume of bole-wood and bole-bark. It was assumed that total-tree dry weight (bole-wood, bole-bark plus total-crown) will be best described by the best stem component estimator plus the most important independent variable describing total-crown dry weight.  This assumption held for western hemlock and western red cedar where  the two most important independent variables for estimating total-tree dry weight were D H (most important for stem components) and DxCL (most important for crown components).  Douglas f i r did not follow the same pattern, D H  a n  d  DxCL being the two most important variables for total-tree and DxCW^ instead of DxCL being the most important single estimator for total-crown dry weight. 2  For a given product of D H, hemlock has the largest and cedar the least total-tree dry weight in pounds. Apart from the differences in specific gravity this can be reasonably explained by the differences in height for a given diameter.  Douglas f i r is usually taller than hemlock and cedar, and 2  consequently w i l l have a larger D H value than either hemlock or cedar for a 2 given dbh.  For a given product of D H, hemlock and cedar w i l l have larger  diameters resulting in higher bole-wood dry weight for hemlock (hemlock tapers least) and a lower value for cedar (cedar tapers most and also has lowest specific gravity) than for Douglas f i r . Since bole-wood on the average makes up approximately 70% of total-tree dry weight i t will be the de-  83 ciding factor in determining the magnitude of the regression coefficients and will follow the pattern described above regardless of the relative distribution of total-crown weight between species. Total bole-wood dry weight is the highest for hemlock, lowest for 9  cedar and intermediate for Douglas f i r for a given product of D H.  In add-  ition to the reasons discussed for total-tree weight, differences in bolewood weight between species can be attributed in part to actual differences in bark thickness and averaged differences in wood specific gravity. . To estimate the component weights just discussed, dbh and total tree height must be known. These two parameters can be measured most easily and accurately and they are usually recorded for almost every kind of stand or individual tree investigations involved in forestry research.  Fahnestock  (1960) and Baskerville (1965 b) found that the most precise way to estimate biomass is to solve each component equation for every individual tree and convert the total for a l l trees to a per unit area basis.  To illustrate the  gross errors arising from the use of several average parameters, Baskerville showed -50.2% underestimate and 447.8% overestimate as compared to a l l tree summation figures.  Applying mean dbh and tree height in this study resulted  in similar deficiencies, and showed an underestimate of approximately 46% for total tree and stem components compared to the every tree summation figures. It is obvious then that the "average" tree approach should only be used when rough estimates are required as suggested by Baskerville. 2 The reduced importance of D H in crown component determinations is demonstrated through Tables 18 to 32, where D H 2  is the second best estimator  for hemlock crown components, third best for f i r and for some of the components i t is retained only as the fourth parameter in the four-best-variable  84 combinations for cedar.  This just simply illustrates the point that crown  measurements (crown length, crown width) w i l l , as they obviously should, describe crown component weights better than an estimating system based on stem parameters. Results indicated that the most important single variables to describe crown component weights are DxCW and DxCL. Diameter times crown width 2  squared was the best single independent variable for a l l Douglas f i r crown component determinations. Both the combination and the order of elimination of the four-best-variables were the same for the five components analysed. For western hemlock and western red cedar, diameter times crown length was the most important single variable for a l l crown components. Storey et^ al. (1955) reported somewhat similar findings using diameter at base of live crown and weight times crown length as dependent variable.  This method  has two drawbacks from the point of practical application: the f i r s t one is the use of diameter at base of live crown (difficult to obtain), and the second is the use of weight times crown length rather than weight alone as the dependent variable. Fahnestock (1960) showed that crown weight is proportional to the product of dbh and crown length which also holds for the present study with the exception of Douglas f i r for which crown width seems more important. Probably the only reasonable explanation for this is that hemlock and cedar crowns are more or less similar.  Storey ejt al_. (1955) and Fahnestock (1960)  reported that tolerant species have more needles and fine twigs than intolerant species. . This trend was definitely noticable when hemlock and cedar, two very tolerant species, were compared to intolerant Douglas f i r .  Expressed in  per cent of total-crown weight, needles and fine twigs in hemlock made up 48%  85 and  in cedar 49% of the total crown compared to 39% for Douglas f i r . 2 Since the curvilinear form ( DxCL + (DxCL)  ) of DxCL in most cases  improved estimation, and because the data showed more of a curvilinear than linear trend this form was used for a l l hemlock and cedar crown component estimation.  For a given product of DxCL hemlock crown components, with the  exception of needles, are larger than cedar values.  This is due to the d i f f -  erences in specific gravity and perhaps to some extent to the differences in form.  Comparing the two species in the same age group cedar would usually  tend to have a larger dbh than hemlock because of butt-swell especially for older trees, and consequently hemlock must have longer crown length (higher crown weight) to yield the same product. Total-tree, bole-wood and bole-bark weights can be estimated more accurately than crown component weights.  Storey e_t a l . (1955) for total-  crown prediction reported standard error of estimates of 67% for Douglas f i r , 63% for western hemlock and 307» for western red cedar.  Comparable figures  from the present study, using the best four-variable multiple regressions, are  75, 59, and 55% for f i r , hemlock and cedar respectively.  It is evident  from these figures that crown components were highly variable and widely dispersed about the mean. Even though crown components are so highly variable, an objective estimating method is better than none at a l l , which was nicely phrased by Fahnestock (1960) when he stated "Any objective method of calculating slash quantity is vastly superior to the guesswork used heretofore". Comparisonsof present results with findings of others were impossible on the basis of regression coefficients because of logarithmic transformations used by most of the previous investigators in this f i e l d .  However,  dbh and crown length data from Storey et al_. (1955) applied to the functions  86 developed in this study allowed some comparison.  On the average, western  hemlock trees from Haney showed 170 pounds heavier crowns than the ones reported by Storey et_ al^. and western red cedar showed the same trend with 90 pounds more crown weight. Kellogg and Keays (1968) reported total above-ground dry weights of 2858, 1809 and 447 pounds for three western hemlock trees from the Research Forest at Haney. Applying their dbh and height measurement figures to the o D H function developed in this study to estimate total-tree oven dry weight for western hemlock gave comparable results of 2655, 1741 and 390 pounds. For  the same heights and diameters the present study shows on the average 87  pounds heavier western hemlock trees than figures reported for eastern hemlock by Young et a l . (1964).  Of course such comparisons as these are only  approximate because the present study assumes average values for bole and bark specific gravity. In conclusion, oven dry weight estimates of total-tree, bole-wood and bole-bark can be obtained for south coastal Douglas f i r , western hemlock and western red cedar trees by using regression equations developed in this study.  Variation in dry weight accounted for will be over 90 per cent for any  one species.  Estimation should not be attempted outside the range of data on  which the equations were based.  Crown component weights proved highly vari-  able and consequently can only be estimated with much less accuracy.  The  derived functions should be field tested for r e l i a b i l i t y before accepting them for general estimating purposes.  87 BIBLIOGRAPHY BASKERVILLE, G.L. 1965a. Dry matter production in immature balsam f i r stands. For. Sci. Mon. No. 9. 42 pp. BASKERVILLE, G.L. 1965b. Estimation of dry weights of tree components and total standing crop in conifer stands. Ecology 46: 867-869. BASKERVILLE, G.L. 1966. Dry-matter production in immature balsam f i r stands: roots, lesser vegetation, and total stand. For. Sci. 12(1): 49-53. BELLA, I.E. 1968. Estimating aerial component weights of young aspen trees. Can. Dept. of For. & Rur. Dev., Information Report MS-X-12. 36 pp. BROWN, J.K. 1963. Crown weights in red pine plantations. States For. Exp. Sta., Res. No. LS-19. 4 pp.  U.S.F.S. Lake  BROWN, J.K. 1965. Estimating crown fuel weights of red pine and jack pine. U.S.F.S. Lake States For. Exp. Stat., Res. Pap. LS-20. 12 pp. CHANDLER, CC. 1960. Slash weight tables for westside mixed conifers. U.S.F.S. Pacif. Sthwest For. & Range Exp. Sta., Tech. Pap. No. 48. 21 pp. DAVIS, K.P. 1959.  Forest fire control and use.  McGraw-Hill.  DOBIE, J. 1965. Factors influencing the weight of logs. from B.C. Lumberman, September 1965. 4 pp.  584 pp.  Re-printed  DRAPER, N.R. and H. SMITH. 1966. Applied regression analysis. John Wiley and Sons, Inc. 407 pp. DYER, R.A. 1967. Fresh and dry weight, nutrient elements and pulping characteristics of northern white cedar. Maine Agr. Exp. Sta., Tech. Bull. 27. 40 pp. FAHNESTOCK, G.R. 1960. Logging slash flammability. U.S.F.A. Intermtn. For. & Range Expt. Sta., Res. Pap. No. 58. 67 pp. FAHNESTOCK. G.R. and J.H. DIETERICH. 1962. Logging slash flammability after five years. Intermtn. For. & Range Expt. Sta., Ogden, Res. Pap. No. 70. 15 pp. FREESE, F. 1964. Linear regression nethods for forest research. U.S.F.S. Res. Pap. FPL-17. 136 pp. HARADA, H. and H. SATO. 1966. On the dry matter and nutrient contents of the stem of mature cryptomeria trees, and their distribution to the bark, sapwood and heartwood. Jour, of Jap. For. Soc. 48(8): 315-324.  88 HARDY, S.S. and G.W. WEILAND. 1964. Weight as the basis for the purchase of pulpwood in Maine. Maine Agr. Expt. Sta., Tech. Bull. No. 14. 63 pp. JOHNSTONE, W.D. 1967. Analysis of biomass, biomass sampling methods, and weight scaling of lodgepole pine. Univ. of B.C., Fac. of For., M.F. thesis. 153 pp. JOHNSTONE, W.D. 1968. Some observations of the biomass of lodgepole pine trees. Can. Dept. For. Mimeo. 11 pp. KEEN, R.E. 1963. Weights and centres of gravity involved in handling pulpwood trees. Pulp and Paper Research Institute of Canada, Tech. Rep. No. 340. 93 pp. KELLOGG, R.M. and J.L. KEAYS. 1968. Weight distribution in western hemlock trees. Bi-Monthly Res. Notes. Dept. of Fisheries of Canada, 24(4): 32-33. KENNEDY, E.I. 1965. Strength and related properties of woods grown in Canada. Dept. of For., Public No.1104. 51 pp. KIILL, A.D. 1967a. Fuel weight tables for white spruce and lodgepole pine crowns in Alberta. Dept. of For. and Rur. Dev., Public. No.1196. 13 pp. KIILL, A.D. 1967b. Weight of fuel complex in 70-year-old lodgepole pine stands of different densities. IUFRO, Munich V: 819-829. KITTREDGE, J. 1944. Estimation of the amount of foliage of trees and stands. Jour. For. 42: 905-912. KOZAK, A. and J.H.G. SMITH. 1965. A comprehensive and flexible multiple regression program for electronic computing. For. Chron. 41(4): 438-443. KOZAK, A. 1966. Multiple correlation coefficient tables up to 100 independent variables. Univ. of B.C., Fac. of For., Res. Note 57. 3 pp. KOZAK, A. 1969. Uses of conditioned regressions in forestry. Fac. of For., Mimeo.3pp. KOZAK, A. 1969.  Univ. of B.C.,  Personal Communications.  MAGDANZ, H. 1965. Weights and volumes of tree components. Columbia Cellulose Co. Ltd., Terrace Woods Div. Mimeo. 76 pp. MORRIS, W.G. 1958. Influence of slash burning on regeneration, other plant cover, and fire hazard in the Douglas f i r region. U.S.F.S., P.N.W. Res. Pap. No. 29. 49 pp. MURARO, S.J. 1964. Surface area of fine fuel components as a function of weight. Dept. of For. Public. No. 1080. 12 pp.  MURARO, S.J. 1966. No.1153.  Lodgepole pine logging slash. 14 pp.  Dept. of For. Public.  MURARO, S.J. 1967. Methods and needs for evaluating performance of prescribed burns. IUFRO, Munich V: 843-865. OSBORN, J.E. 1968. Influence of stocking and density upon growth and yield of trees and stands of coastal western hemlock. Univ. of B.C., Fac. of For., Ph.D. thesis. 396 pp. OVINGTON, J.D. 1956. The form, weights and productivity of tree species grown in close stands. New. Phytol. 55(2): 289-304. SMITH, J.H.G., KER, J.W., and J. CSIZMAZIA. 1961. Economics of reforestation of Douglas f i r , western hemlock, and western red cedar in the Vancouver Forest District. Univ. of B.C., Fac. of For., For. Bull. No.3. 144 pp. SMITH, J.H.G. and R.E. BREADON. 1964. Combined variable equations and volume-basal area ratios for total cubic foot volumes of the commercial trees of B.C. For. Chron. 40(2): 258-261. SMITH, J.H.G. and A. KOZAK. 1967. Thickness and percentage of bark of the commercial trees of British Columbia. Univ. of B.C., Fac. of For., Mimeo. 33 pp. SMITH, J.H.G. 1968a. Simulation of forest fuels. For., Mimeo. 7 pp.  Univ. of B.C., Fac. of  SMITH, J.H.G. 1968b. 1967-8 Progress Report EMR F-53, Univ. of B.C., Fac. of For., Mimeo 8 pp. SMITH, J.H.G. 1968c. Some estimates of amounts of forest fuels for the B.C. Coast. Univ. of B.C., Fac. of For., Mimeo. 8 pp. SMITH, J.H.G. and J. KURUCZ. 1969. Amounts of bark potentially available for some commercial trees of British Columbia. Univ. of B.C. , Fac. of For., Mimeo. 8 pp. SNEDECOR, G.W. 1956.  Statistical methods.  Iowa State College Press.  534 pp  STIELL, W.M. 1969. Crown development in a white spruce plantation. Forestry Branch, Dept. of Fisheries and Forestry. Public. No.1249. 12 pp. STOREY, T.G., FONS, W.L. and F.M. SAUER. 1955. Crown characteristics of several coniferous tree species. U.S.F.S., Div. of Fire Res., Interim Tech. Rep. AFSWP-416, 99 pp. TADAKI, Y. 1965. Productivity of an acacia mollissima stand in higher stand density. Jour, of Jap. For. Soc. 47(11): 384-391.  90 TADAKI, Y. and Y. KAWASAKI. 1966. Primary productivity of a young cryptomeria plantation with excessively high stand density. Jour, of Jap. For. Soc. 48: 350-360. VAN SLYKE, A.L. 1964. An evaluation of crown measures for coniferous trees and stands. Univ. of B.C., Fac. of For., Mimeo. 50 pp. VAN WAGNER, C.E. 1968. The line intersect method in forest fuel sampling. For. Sci. 14(1): 20-26. WEETMAN, G.F. and R. HARLAND. 1964. Foliage and wood production in unthinned black spruce in northern Quebec. For. Sci. 10: 80-88. YOUNG, H.E., STRAND, L. and R. ALTENBERGER. 1964. Preliminary fresh and dry weight tables for seven tree species in Maine. Maine Agr. Exp. Sta., Tech. Bull. 12. 76 pp. YOUNG, H.E. and A.J. CHASE. 1965. Fiber weight and pulping characteristics of the logging residue of seven tree species in Maine.- Maine Agr. Exp. Sta., Tech. Bull. 18. 44 pp.  APPENDIX I - SCIENTIFIC NAMES OF TREES  Abies balsamea (L.) M i l l .  Balsam f i r  Abies concolor (Gord. and Glend.)  White f i r  Abies grandis (Dougl.) Lindl.  Grand f i r  Acer rubrum L.  Red maple  Betula papyrifera March.  White birch  Cryptomeria japonica  Suji  Larix occidentialis Nutt.  Western larch  Libocedrus decurrens Torr.  Incense cedar  Picea engelmannii Parry  Engelmann spruce  Picea glauca (moench.) Voss.  White Spruce  Picea mariana (Mill.) B.S.P.  Black spruce  Picea rubens Sarg.  Red spruce  Pinus contorta Dougl.  Lodgepole pine  Pinus lambertiama Dougl.  Sugar p ine  Pinus monticola Dougl.  Western white pine  Pinus ponderosa Laws.  Ponderosa pine  Pinus resinosa A i t .  Red pine  Populus sp. L.  Aspen  Populus tremuloides Michx.  Trembling aspen  Psendotsuga menziesii (Mirb.) Franco  Douglas f i r (coast)  Pseudotsuga menziesii var. Glauca (Beissn.)  Douglas f i r (interior)  Thuja occidentialis L.  Northern white cedar  Thuja plicata Donn.  Western red cedar  Tsuga heterophylla (Raf.) Sarg.  Western hemlock  APPENDIX II COMPONENT WEIGHTS PLOTTED OVER VARIOUS INDEPENDENT VARIABLES.  30  60  120  180  2.40  300  D H = Diameter Squared X Total Tree Height ( i n c h 2  FIGURE II-l.  360 2  420  480  Xfeet) in Thousands  Total-tree dry weight on D H for Douglas f i r . 2  VO  20  CO  X3  c o (0 3  16  (0 TJ C 3 O CL  12  o  <D  Q  i  B 41o  X  »  *  lii_L  50  60  qo  120  150  D H = Diameter Squared X Total Tree Height ( i n c h 2  FIGURE II-2.  T o t a l - t r e e dry weight on D H 2  f o r western hemlock.  180 2  2IO  X feet) in Thousands  240  x  16  •*-  oiiiiilLl  80  40  l2o  160  24 O  200  2 80  D H = Diameter Squared X Total Tree Height ( i n c h Xfeet) in Thousands 2  FIGURE II-3.  Total-tree dry weight on D H for western red cedar.  2  3 20  X  20  W XJ  2  • Basal area  3  o s: \-  D H  x  c o w  16  •a c 3 o Q.  "D O O 5 •  a> o  CD  2  o  4  X X  I-  Basal Area in Square Feet 60  120  180  240  30O  D H = Diameter Squared X Total Tree Height ( i n c h 2  FIGURE II-4.  360 2  X feet) in Thousands  Total bole-wood dry weight on D H and basal area for Douglas f i r . 2  420  48o  DH • Basal area  x  2  Basal Area in Square Feet 490  4-  4: no  4-  110  ISO  D H= Diameter Squared X Total Tree Height (inch X feet) in Thousands 2  FIGURE I I - 5 .  2  Total bole-wood dry weight on D^H and basal area f o r western hemlock.  2.40  x D H • Basal area 2  x  x X  X  •  X  x£* i-2  0  •  :  i  .  6o  3  2. I  D  Basal Area in Square Feet I  2  ,  liO  4  i  5 I  6 i  180  ,  2.40  ?  1  B I  ,  300  <]  |0  1  H = Diameter Squared X Total Tree Height ( i n c h  1_  160 2  X feet) in Thousands  URE I I - 6 . Total bole-wood dry weight on D H and basal area for western red cedar. 2  420  480  »  X  xD H • Basal area 2  x 'BBL5£2  Basal Area in Square Feet  . 1  ,  1  1  feo  D FIGURE II-7.  , iZo  2  _ J  ,  1  ISO  , 240  1  1  ,  1  1  50O  H= Diameter Squared X Total Tree Height ( i n c h  360 2  ,  ,  420  X feet) in Thousands  Total bole-bark dry weight on D H and basal area for Douglas f i r . Z  L_  1 4BO  x D H • Basal area 2  •  X  X  X  •  • • X  X X  Basal Area in Square Feet X  • ••  4 5o  5  6  l BO 120 1S0 2lO qo D H = Diameter Squared X Total Tree Height ( i n c h X feet) in Thousands  60  2  2  FIGURE II-8. Total bole-bark dry weight on D H and basal area for western hemlock.  24o  x D H • Basal area 2  X X x  X  x x  Basal Area in Square Feet i.Vx" °  X  •!•••?• 1  «1> °  1  3  1 H !O  4  1  5  .  6  I B1O  I  ,  , 2<K>  7  8  I  T  3oo  q  10  i  3 fic o  D H = Diameter Squared X Total Tree Height ( i n c h 2  2  11 i  X feet) in Thousands  URE I I - 9 . Total bole-bark dry weight on D H and basal area for western red cedar. 2  ll 4-2o i _  \0-  X»» J »  0  »X'>x >x * X  xx | >_ »  16  8  D X CW  2  24-  32  40  48  56  = Diameter X Crown Width Squared (inch X f e e t ) i n Thousands  FIGURE 11-10. Total-crown dry weight on DxCW2 for Douglas f i r .  2  64  66  0  8  16  D X CW  2  24  ~~  32  40  48  56  = Diameter X Crown Width Squared (inch X f e e t ) i n Thousands 2  FIGURE 11-11. Large branch crown component dry weight on DxCW for Douglas f i r . 2  64"  68  840  r**  X  x  *  X *..  *  16  D X CW FIGURE 11-12.  2  24  32 .  40  56.  48  = Diameter X Crown Width Squared (inch X f e e t ) in Thousands 2  Medium branch crown component dry weight on DxCW for Douglas f i r .  64  69  X  800h (0  c 3  O 640  • o c o a.  4BOf-  E o o  c S o  320  o  JZ o c o v. ffi C0  IfeO X  X  '  X  « >>  _ X "X  "x x x x„ »  ir  Z4  40  96  48  64  —I 68  D X CW "Diameter X Crown Width Squared (inch Xfeet ) in Thousands 2  2  FIGURE 11-13. Fine branch crown component dry weight on DxCW' for Douglas f i r .  o  , » • »*  »*»  .  16  2*  »  40  48  56  0 X CW2 *Diameter X Crown Width Squared (inch X feet2 ) in Thousands FIGURE 11-14. Needle crown component dry weight for Douglas f i r .  «4  68  28l-  k  £  a  —  0 X CL= Diameter X Crown Length (inch X feet) in Hundreds FIGURE 11-15. Total-crown dry weight for western hemlock.  ^  10 T3  3  S  q  a.  i  s  i  e  :  21  :  2  ?  D X CL= Diameter X Crown Length (inch X feet) in Hundreds FIGURE 11-16. Large branch crown component dry weight for western hemlock.  2T  30  3  O O. 240<P  >» w W*>-  O  c • c o o. £ 120o u u c o CD  E  2  ts  16  24  D X CL= Diameter X Crown Length (inch X feet)in Hundreds FIGURE 11-17.  27  i  SO  Medium branch crown component dry weight f o r western hemlock.  o i—•  Fine Branch Crown Componentry Weight (pounds) 5 —  ?  ?  —  o  —i  S o 1  * 8  1—  O  *m  "rH"  _  JL  3  6  9  O.  IS  Ift  21  ,  24.  D X CL = Diameter X Crown Length (inch X feet) in Hundreds GURE 11-19. Needle crown component dry weight for western hemlock.  27  _ »,XX>*X*X •  6  X* « XX ,  1  a.  ;  1  ia  1  jS  — .  1  io  1  Ie  1  4  1  z  4  ©  D X CL*Diameter X Crown Length (inch X feet)in Thousands CURE 1 1 - 2 0 .  Total-crown dry weight on DxGL for western red cedar.  - j —  5T  to 4>  xxx ^* 3  x  Ay./  x  xx  x i  'x  IB  24  30  36  42  48  54  O X CL= Diameter X Crown Length (inch X feet) in Hundreds  FIGURE 11-21. Large branch crown component dry weight on DxCL for western red cedar.  r-'  r—i  (0  c 3  O  a  <T 400-  o  320-  «  c o o.  e  o o c * -O o u c o tw CD  £  240-  160-  X  X  80-  ,x  oU  rf-  ,  XX  .  .  «"  '  18  24  30  36  AX  48  D X CL* Diameter X Crown Length (inch X feet) in Hundreds  FIGURE 11-22.  Medium branch crown component dry weight on DxCL for western red cedar.  54  to x>  _ 200|O Q.  a> 160=5 >\  Q c 120c o a. E o o 80c 5 o  a  U  c o  40 •  00  » x  a> c ii  0  6  12  18  24  30  36  42  48  D X CL= Diameter X Crown Length (inch X feet)in Hundreds  FIGURE 11-23. Fine branch crown component dry weight on DxCL for western red cedar.  54  X  6  IZ  18  24  iO  36  42  48  D X CL= Diameter X Crown Length (inch X feet) in Hundreds  FIGURE 11-24. Needle crown component dry weight on DxCL for western red cedar.  54  

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