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Analysis of biomass, biomass sampling methods, and weight scaling of lodgepole pine Johnstone, W. D. (Wayne David) 1967

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A N A L Y S I S O F BIO MASS, BIO MASS S A M P L I N G METHODS,. A N D W E I G H T S C A L I N G O F L O D G E P O L E PINE  by  W. D.  JOHNSTONE  B. S. F. , U n i v e r s i t y of B r i t i s h Columbia, 1966  A T H E S I S S U B M I T T E D IN P A R T I A L F U L F I L M E N T OF THE REQUIREMENTS FOR THE DEGREE  OF  MASTER OF FORESTRY  in the Department of Forestry  We accept this thesis as conforming to the r e q u i r e d standard  T H E UNIVERSITY O F BRITISH C O L U M B I A June, 1967  In  presenting  for  an  that  advanced  the I  thesis  for  Department  shall  further  partial  the  make  agree  it  that  freely  representatives.  his  of  this  of  thesis  for  permission.  Forestry  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, Canada 29  may  June,  1967  Columbia  be  of  British  available  permission  or  by  fulfilment of  University  purposes  my w r i t t e n  Department  at  in  scholarly  publication  without  thesis  degree  Library  study.  or  this  for  granted It  is  financial  for  the  Columbia,  I  reference  and  extensive by  the  requirements  copying  Head  understood gain  shall  of  this  my  that not  of  agree  be  copying allowed  ABSTRACT  T r e e and tree component weights of 63 forest-grown lodgepole pine trees were investigated.  Data were collected f r o m one tenth-  acre plot located i n south western A l b e r t a .  Both g r a p h i c a l and  multiple r e g r e s s i o n techniques were used.  Of the independent  v a r i a b l e s tested, tree b a s a l area was most c l o s e l y related to the component weights, with the exceptions of bole b a r k weight and total stem d r y weight.  The f r e s h and d r y weights of bole b a r k were most  c l o s e l y associated with tree height, and total stem d r y weight was m o s t c l o s e l y associated with dbh. V e r y r e l i a b l e estimates of t r e e and tree component weights were obtained using r e g r e s s i o n techniques and the independent v a r i a b l e s p r e v i o u s l y mentioned.  The proportions of the component weights of the total tree weights were determined.  The proportions were highly v a r i a b l e  and widely d i s p e r s e d about the mean.  The tree c h a r a c t e r i s t i c most  c l o s e l y associated with the various proportions v a r i e d for the component being analysed.  The proportion of the total tree weight  contained i n the stem, slash, bark and bole wood d e c r e a s e d with i n c r e a s i n g tree size. The proportion represented b y the needles, branches, merchantable stem, and crown i n c r e a s e d with tree size.  ii  The crown and needle c h a r a c t e r i s t i c s of lodgepole pine were investigated.  T r e e size, whether m e a s u r e d as s t e m weight i n pounds  or cubic foot s t e m volume (ob), was d r y needle weight (in pounds).  most c l o s e l y c o r r e l a t e d with  The number of needles per cubic foot  of stem volume i n c r e a s e d with i n c r e a s i n g t r e e size. c h a r a c t e r i s t i c s of lodgepole pine are highly v a r i a b l e . was  significantly related to needle width.  The needle Needle length  Needle length was  not  significantly related to any t r e e c h a r a c t e r i s t i c s .  The need to develop reliable sampling methods for b i o m a s s and fire control studies was  discussed.  Double sampling with r e g r e s s i o n  appeared to offer accurate estimates with a m i n i m u m of weight m e a s u r e ment. The number of t r e e s r e q u i r e d to obtain a sample mean within plus or minus 10 per cent of the population mean at the 95 per cent confidence l e v e l i s too l a r g e to be p r a c t i c a l for most b i o m a s s and f i r e control studies.  A higher standard e r r o r of estimate i s p r o b a b l y  m o r e desirable, thus allowing a greater number of conditions to be sampled i n o r d e r to i n c r e a s e the representativeness of the study.  The mutual relationship between t r e e weight and tree volume was i n v e s t i g a t e d . T r e e volume was highly c o r r e l a t e d with t r e e weight. Reliable estimates of t r e e weight were obtained f r o m t r e e volume. V a r i a t i o n i n m o i s t u r e content and specific gravity, within and between trees was  analyzed.  These v a r i a b l e s were s u r p r i s i n g l y u n i f o r m and  appear to pose only m i n o r p r o b l e m s i n weight scaling, for lodgepole pine.  iii  ACKNOWLEDGEMENTS  The w r i t e r wishes to express his s i n c e r e thanks to Dr. Smith for his guidance, advice,  and encouragement.  J.H.G.  T h e w r i t e r is  also greatly indebted to Drs. P. G. Haddock, and A. Kozak for their c r i t i c a l review and advice, and to M e s s r s . D. D. Munro, and W. J e f f r e y for their encouragement. and M r s .  W.  The assistance of Dr. A. Kozak  E. F r o e s e , i n programming, plotting, and analysing the  data is gratefully acknowledged.  The w r i t e r also would like to thank the Canadian Department of F o r e s t r y and R u r a l Development, for making the data u s e d i n this thesis available.  Sincere thanks are due,  his advice and assistance;  to M r . C. L . Kirby, f o r  to M r . A. D. K i i l , for making the data on  needle and b r a n c h m o i s t u r e contents available; to Mr. Stan Lux, for his assistance i n the field work, and specific gravity and to M r . F r e d Stock, for the draughting;  determinations;  a l l of whom are employed  by the Canadian Department of F o r e s t r y and R u r a l Development, Calgary,  Alberta.  Attendance at the U n i v e r s i t y was facilitated b y financial assistance f r o m the Canada Department of F o r e s t r y and R u r a l Development, and b y the F a c u l t y of F o r e s t r y , U n i v e r s i t y of B r i t i s h Columbia, i n the f o r m of a University Forest  Fellowship.  iv  TABLE OF  CONTENTS Page  ABSTRACT ACKNOWLEDGEMENTS  i iii  T A B L E OF CONTENTS  iv  LIST O F T A B L E S  vii  LIST O F F I G U R E S  xi  INTRODUCTION  1  DATA COLLECTION  5  A DISCUSSION O F BIOMASS  11  F a c t o r s A f f e c t i n g O r g a n i c Matter P r o d u c t i o n  11  Stand F u e l s  18  Methods of A n a l y s i s  19  Results of A n a l y s i s  24  T r e e and component weight relationships P r o p o r t i o n of component to total tree relationships Some crown and r e l a t e d c h a r a c t e r i s t i c s of lodgepole pine Summary S A M P L I N G F O R BIOMASS  24 58 75 81 84  Introduction  84  Methods of A n a l y s i s  87  Results of A n a l y s i s  89  Summary  92  V  Page WEIGHT SCALING  9 4  Introduction  94  Methods of A n a l y s i s  98  D i s c u s s i o n of Some Internal F a c t o r s which A f f e c t T r e e Weight M o i s t u r e content Specific g r a v i t y x  201 102 103  Methods of A n a l y s i s  108  Results of A n a l y s i s  109  Within t r e e v a r i a t i o n i n specific gravity and m o i s t u r e content Between t r e e v a r i a t i o n i n specific g r a v i t y and mois.ture content Summary CONCLUSIONS BIBLIOGRAPHY  109 113 H9 i2Z  123  APPENDICES: I  II  A S u m m a r y of P r e v i o u s Investigations of B i o m a s s Foliage, and Slash.  136  L o g a r i t h m i c Relationships of T r e e and T r e e Component F r e s h Weights (lb) on Dbh (in).  139  III-l  The Relationship Between F r e s h T o t a l Stem P r o portion (%) and Crown Width (ft.).  HI-2  The Relationship Between D r y T o t a l Stem P r o portion (%) and Crown Width (ft.).  141  The Relationship Between F r e s h Merchantable Stem P r o p o r t i o n (%) and Dbh (in).  142  III-3  140  vi III-4  III-5  III-6  111-7  111-8  III-9  III-10  III-11  111-12  III-13  111-14  The Relationship Between D r y Merchantable Stem P r o p o r t i o n (%) and Dbh (in.).  143  The Relationship Between F r e s h Bole Wood P r o p o r t i o n (%) and Dbh (in).  144  The Relationship Between D r y Bole Wood P r o p o r t i o n (%) and Dbh (in.).  145  The Relationship Between F r e s h Needle P r o p o r t i o n (%) and Crown Length (ft.).  146  The Relationship Between D r y Needle P r o p o r t i o n (%) and Crown Width (ft. ).  147  The Relationship Between F r e s h B r a n c h P r o p o r t i o n (%) and T r e e B a s a l A r e a (sq. ft. ).  148  The Relationship Between D r y B r a n c h P r o portion (%) and Crown Width ( f t . ) .  149  The Relationship Between F r e s h Crown P r o p o r t i o n (%) and Crown Width (ft. ).  150  The Relationship Between D r y C r o w n P r o portion (%) and Crown Width (ft.) .  151  The Relationship Between F r e s h Slash P r o p o r t i o n (%) and T r e e Height (ft. ),  152  The Relationship Between D r y Slash P r o portion (%) and T r e e Height (ft. ).  153  vii  LIST O F T A B L E S  TABLE 1.  2.  3.  4.  5.  6.  7.  8.  9.  Page Mean, Standard Deviation, Minimum, and M a x i m u m Values of the T r e e C h a r a c t e r i s t i c s used as Independent V a r i a b l e s , for 63 L o d g e pole Pine T r e e s .  24  Mean, Standard Deviation, Minimum, and M a x i m u m Values of Weight i n Pounds for the T r e e C h a r a c t e r i s t i c s u s e d as Dependent V a r i a b l e s , for 63 Lodgepole Pine T r e e s .  25  The Simple C o r r e l a t i o n Coefficients Between T r e e and Component Weights and Some T r e e C h a r a c t e r i s t i c s , for 63 Lodgepole P i n e T r e e s .  26  R e g r e s s i o n Equations Illustrating the Relationship of T o t a l T r e e F r e s h Weight (lb) with S e v e r a l Independent V a r i a b l e s , for 63 Lodgepole Pine T r e e s .  28  R e g r e s s i o n Equations Illustrating the Relationship of T o t a l T r e e D r y Weight (lb) with S e v e r a l Independent V a r i a b l e s , for 63 Lodgepole Pine T r e e s .  29  R e g r e s s i o n Equations Illustrating the Relationship of T o t a l Stem F r e s h Weight (lb) with S e v e r a l Independent V a r i a b l e s , for 63 Lodgepole Pine T r e e s .  31  R e g r e s s i o n Equations Illustrating the Relationship of Total Stem D r y Weight (lb) with S e v e r a l Independent V a r i a b l e s , for 63 Lodgepole Pine T r e e s .  33  R e g r e s s i o n Equations Illustrating the Relationship of Bole Wood F r e s h Weight (lb) with S e v e r a l Independent V a r i a b l e s , for 63 Lodgepole Pine T r e e s .  35  R e g r e s s i o n Equations Illustrating the Relationship of Bole Wood D r y Weight (lb) with S e v e r a l Independent V a r i a b l e s , for 63 Lodgepole Pine T r e e s .  37  R e g r e s s i o n Equations Illustrating the Relationship of B a r k F r e s h Weight (lb) with S e v e r a l Independent V a r i a b l e s , for 63 Lodgepole Pine T r e e s . R e g r e s s i o n Equations Illustrating the Relationship of B a r k D r y Weight (lb) with S e v e r a l Independent V a r i a b l e s , for 63 Lodgepole Pine T r e e s . R e g r e s s i o n Equations Illustrating the Relationship of Needle F r e s h Weight (lb) with S e v e r a l Independent V a r i a b l e s , for 63 Lodgepole Pine T r e e s . R e g r e s s i o n Equations Illustrating the Relationship of Needle D r y Weight (lb) with S e v e r a l Independent V a r i a b l e s , for 63 Lodgepole P i n e T r e e s . R e g r e s s i o n Equations Illustrating the Relationship of B r a n c h F r e s h Weight (lb) with S e v e r a l Independent V a r i a b l e s , for 63 Lodgepole P i n e T r e e s . R e g r e s s i o n Equations Illustrating the Relationship of B r a n c h D r y Weight (lb) with S e v e r a l Independent V a r i a b l e s , for 63 Lodgepole Pine T r e e s . R e g r e s s i o n Equations Illustrating the Relationship of C r o w n F r e s h Weight (lb) with S e v e r a l Independent V a r i a b l e s , f o r 63 Lodgepole Pine T r e e s . R e g r e s s i o n Equations Illustrating the Relationship of C r o w n D r y Weight (lb) with S e v e r a l Independent V a r i a b l e s , for 63 Lodgepole Pine T r e e s . R e g r e s s i o n Equations Illustrating the Relationship of Slash F r e s h Weight (lb) with S e v e r a l Independent V a r i a b l e s , for 63 Lodgepole Pine T r e e s . R e g r e s s i o n Equations Illustrating the Relationship of Slash D r y Weight (lb) with S e v e r a l Independent V a r i a b l e s , for 63 Lodgepole Pine T r e e s . Mean, Standard Deviation, Minimum, and M a x i m u m Values of the P r o p o r t i o n (as a per cent) of the Component Weight to the T o t a l T r e e Weight, for 63 Lodgepole Pine T r e e s .  IX  TABLE  21.  22.  23.  24  25.  Page  Simple C o r r e l a t i o n Coefficients Between the P r o p o r t i o n of component Weight to T o t a l T r e e Weight and S e v e r a l T r e e C h a r a c t e r i s t i c s , for •63 Lodgepole Pine T r e e s .  61  Mean, Standard Deviation, M a x i m u m and M i n i m u m Values of S e v e r a l C r o w n C h a r a c t e r i s t i c s , for 63 Lodgepole Pine T r e e s .  75  Simple C o r r e l a t i o n Coefficients Between S e v e r a l T r e e and Crown C h a r a c t e r i s t i c s , for 63 Lodgepole Pine Trees.  76  Simple C o r r e l a t i o n Coefficients Between T r e e Volume and Weight, and Crown Volume, C r o w n Surface A r e a , D r y Needle Weight, and Number of Needles, for 63 Lodgepole Pine T r e e s .  78  Mean, Standard Deviation, M i n i m u m and M a x i m u m Values, obtained f c r A v e r a g e Needle Length (mm) and Number of Needles per H a l f G r a m (dry Weight) of 63 Lodgepole P i n e T r e e s , 81  26  27.  28  29  30.  A S u m m a r y of the B e s t Simple L i n e a r Relationships Between T r e e and Component Weight (lb) and the Independent V a r i a b l e s Measured, for 63 Lodgepole Pine T r e e s .  82  The Number of Sample T r e e s R e q u i r e d to have the Sample Mean within + 10 and_+20 P e r Cent of the Population Mean at the 95 P e r cent Confidence L e v e l .  89  M e a n and Standard E r r o r of Mean Values Obtained U s i n g Double Sampling for T o t a l T r e e F r e s h Weight (lb).  90  A C o m p a r i s o n of the Sum of T o t a l T r e e F r e s h Weight (lb) of 30 Randomly Selected T r e e s as E s t i m a t e d by Two Sampling Methods, for 63 Lodgepole Pine T r e e s .  91  Mean, Standard Deviation, M a x i m u m and M i n i m u m Values of Specific G r a v i t y and M o i s t u r e Content for 545 D i s c s of Lodgepole Pine.  109  The C o r r e l a t i o n s of M o i s t u r e Content and Specific G r a v i t y to Height, Dob, Dib, Age, and Mean R a d i a l Growth Rate of Section M e a s u r e m e n t s of 63 Lodgepole Pine T r e e s . The C o r r e l a t i o n Coefficients Between Specifi G r a v i t y and M o i s t u r e Content, and S e v e r a l T r e e C h a r a c t e r i s t i c s for 63 Lodgepole P i n e Trees.  xi  LIST O F FIGURES  Figure 1  2  3  4  5  6  7  8  9  10  Page The Relationship Between Total T r e e F r e s h Weight (lb) and T r e e B a s a l A r e a (square feet) at B r e a s t Height.  30  The Relationship Between Total T r e e DryWeight (lb) and T r e e B a s a l A r e a (square feet) at B r e a s t Height.  32  The Relationship Between T o t a l Stem F r e s h Weight (lb) and T r e e B a s a l A r e a (square feet); at B r e a s t Height.  34  T h e Relationship Between T o t a l Stem DryWeight (lb) and Dbh (in).  36  T h e Relationship Between Bole Wood F r e s h Weight (lb) and T r e e B a s a l A r e a (square feet) at B r e a s t Height.  38  The Relationship Between Bole Wood D r y Weight (lb) and Dbh (in).  39  T h e Relationship Between B a r k F r e s h Weight (lb) and T r e e Height (ft).  42  The Relationship Between B a r k D r y Weight (lb) and T r e e Height (ft.)  44  The Relationship Between Needle F r e s h Weight (lb) and T r e e B a s a l A r e a (square feet) at B r e a s t Height.  46  The Relationship Between Needle D r y Weight (lb) and T r e e B a s a l A r e a (square feet) at B r e a s t Height.  48  xii  Figure  11  12  13  14  15  16  17  18  19  20  Page The Relationship Between B r a n c h F r e s h Weight (lb) and T r e e B a s a l A r e a ( s q u a r e feet) at B r e a s t Height.  50  The Relationship Between B r a n c h D r y Weight (lb) and T r e e B a s a l A r e a (square feet) at B r e a s t Height.  51  The Relationship Between Crown F r e s h Weight (lb) and T r e e B a s a l A r e a (square feet) at B r e a s t Height.  53  The Relationship Between Crown D r y Weight (lb) and T r e e B a s a l A r e a (square feet) at B r e a s t Height.  55  The Relationship Between Slash F r e s h Weight (lb) and T r e e B a s a l A r e a (square feet) at B r e a s t Height.  5Y  The Relationship Between Slash D r y Weight (lb) and T r e e B a s a l A r e a (square feet) at B r e a s t Height.  59  The Relationship Between Specific G r a v i t y and P o s i t i o n i n the T r e e .  112  The Relationship Between M o i s t u r e Content and P o s i t i o n i n the T r e e .  114  The Relationship Between A v e r a g e T r e e Specific G r a v i t y and B r e a s t Height Specific G r a v i t y .  ug  The Relationship Between A v e r a g e T r e e M o i s t u r e Content and B r e a s t Height M o i s t u r e Content.  120  INTRODUCTION  In an attempt to obtain me.aningful data for the a s s e s s m e n t of the productivity of forest trees, the component weights of 63 lodgepole pine t r e e s (Pinus contorta Dougl. var. liatifolia Engelm.) were gathered. of the t r e e s .  No data were obtained for the subterranean parts  In addition, information was  gathered on the m o i s t u r e  contents and specific gravities of the t r e e s .  The f i e l d work was  conducted during the summer of 1966.  A c c o r d i n g to Ovington (1962) b i o m a s s can be defined as "the total quantity of o r g a n i c matter present i n the e c o s y s t e m at a stated time and may  be related to p a r t i c u l a r o r g a n i s m s or groups  of o r g a n i s m s B i o m a s s ,  therefore, i s a m e a s u r e of net b a s i c or  p r i m a r y productivity of an e c o s y s t e m which can be restated as the amount of energy i n the f o r m of photosynthate stored by the p r o d u c e r organisms, which i n the case of forest communities the t r e e s .  are p r i m a r i l y  It should be noted that the t e r m net productivity i s used  which r e f e r s to the energy produced by the plant i n excess of the amount of organic matter contained i n those organs shed or r e m o v e d  2  f r o m the t r e e and l o s s e s through r e s p i r a t i o n , and thus i s stored by the plant.  T h i s might also be t e r m e d apparent photosynthesis or  net a s s i m i l a t i o n .  O d u m (1959) i n his d i s c u s s i o n of the fundamentals of ecology suggested six possible methods of m e a s u r i n g productivity. T h e s e included:  1.  The harvest method whereby the amount of organic matter was measured.  2.  The oxygen method i n which the amount of oxygen produced i s measured.  3.  The carbon dioxide method involving the m e a s u r e m e n t of the amount of carbon dioxide taken i n by the plant.  4.  The radio'.active m a t e r i a l s method where i n m a r k e d m a t e r i a l s were measured.  5.  The raw m a t e r i a l s method whereby the raw m a t e r i a l s taken i n by the plant were measured.  6.  The chlorophyll method i n which the amount of chlorophyll present was m e a s u r e d .  B i o m a s s analysis i s , of course, a f o r m of the f i r s t method mentioned.  This method appears to be the most p r a c t i c a l due to  the m a s s i v e and complex nature of forest ecosystems.  Thus it  3  attempts to m e a s u r e productivity, although not n e c e s s a r i l y the yield of raw  to man  of f o r e s t trees, which i s governed by the a v a i l a b i l i t y  materials,  including  solar energy, and other environmental influences  man.  In the past, f o r e s t management was  c h a r a c t e r i z e d by a m o r e  or l e s s ' l a i s s e z - f a i r e ' attitude because of the self-sustaining nature of the r e s o u r c e and therefore forest r e s e a r c h was P r o d u c t i v i t y was was  not c o n s i d e r e d v i t a l .  generally considered as yield to man  m e a s u r e d on a volume b a s i s .  and as such  However, as pointed out by  Ovington (19 62), due to population p r e s s u r e , the need to convert m o r e f o r e s t e d land to a g r i c u l t u r a l use, forest products,  and the i n c r e a s e d value of  multiple and m o r e intensive use of f o r e s t e d land  is inevitable. T h i s point of view is shared by Young (1964) r e s u l t i n g in his proposal of the complete tree concept, and it prompted Woods (I960) to put f o r w a r d his concept of energy flow s i l v i c u l t u r e .  Coincident with intensification of f o r e s t r y p r a c t i c e s there w i l l undoubtedly be an i n c r e a s e d demand for knowledge of such factors as f o r e s t organic matter, energy, water, and factors of the environment including soil, climate, and the influence of  man.  B i o m a s s analysis affords an opportunity to m e a s u r e some of these factors.  It w i l l provide quantitative information, which was  often unavailable, b a s i c to a m o r e complete understanding of productivity and related p r o c e s s e s .  previously  In s i l v i c u l t u r e i t offers an opportunity to m e a s u r e the photosynthetic machine and the effects of stand improvement on the ecosystem. It can be u s e d to analyse f e r t i l i z e r t r i a l s , the flow of nutrients, and the amount of nutrients r e m o v e d f r o m the site by various harvesting methods.  B i o m a s s m e a s u r e s are useful i n  watershed r e s e a r c h i n determining the amount of forest cover which influences the interception, evaporation, infiltration, and t r a n s p i r a t i o n of a forested area.  B i o m a s s estimates can greatly a s s i s t m e n s u r a t i o n -  ists concerned with understanding tree and stand growth, and with weight scaling.  F i r e control s p e c i a l i s t s can use b i o m a s s data in  their endeavors to a s s e s s f i r e dangers and f i r e effects on habitat,  by  aiding them i n m e a s u r i n g quantities of fuels before and after logging. F i n a l l y , the m e a s u r e m e n t of b i o m a s s gives an indication of the food supply available to insects, fungi, and wild l i f e .  The  author hopes that the results presented i n this thesis w i l l  assist f o r e s t e r s i n the management of lodgepole pine, a species which is becoming i n c r e a s i n g l y important i n the western portions of Canada and the United States.  It is also hoped that it w i l l i l l u s t r a t e some of  the p r o b l e m s associated with b i o m a s s sampling for this species.  5  DATA COLLECTION  A l l of the data used i n this study were gathered on the Kananaskis  F o r e s t E x p e r i m e n t Station near Seebe, which i s located  approximately fifty m i l e s due west of Calgary, A l b e r t a . is located i n the SE1  The  station  section of the Subalpine F o r e s t Region (Rowe,  1959).  One  square tenth-acre plot was  selected for this study. The  species composition of the plot was predominantly lodgepole pine, with some western white spruce ( P i c e a glanca (Moench) Voss var. albertiana (S. Brown) Sarg. ) i n the understory. of a s i m i l a r age (approximately 100  The pine t r e e s were  years old), and since the t r e e s  grew within such a s m a l l a r e a i t can be assumed that any differences o c c u r i n g i n the resulting analysis can not be attributed to the influence of climate, or geographic location.  P a s t plot r e c o r d s indicate that i n 1938 the stand contained 3005 stems per a c r e with a b a s a l a r e a of 195.6  square feet per acre.  present (1966) plot data indicate that the stand now  contains  The  1020  stems per a c r e with a b a s a l a r e a of 227.7 square feet per acre. The mean t r e e dbh was  6.12 inches.  Lodgepole pine contributes 5, 147  cubic feet (calculated f r o m volume formulae p r e p a r e d by Smith and  6  Munro (1965))of the total volume p e r a c r e (5, 624 cu. ft.) found i n the stand.  P r i o r to felling, the plot boundaries were located and each tree was tagged.  M e a s u r e m e n t s of diameter at b r e a s t height (dbh),  average crown width (the average of two m e a s u r e m e n t s taken at right angles at the widest part of the l i v e crown) total tree height, and l i v e crown length (the length f r o m the tip to the lowest whorl of l i v e branches), were made.  In addition, a stem map showing the exact  location of each tree and its crown was p r e p a r e d .  The plot was then felled.  A n attempt was made to maintain a  f a i r l y constant stump height at 1 foot above ground l e v e l .  A dial  scale with a capacity of 500 pounds was used to weigh the t r e e s . The f i r s t weight obtained was that of the entire t r e e above stump height (including branches and foliage).  The entire stem (the total tree less  branches and foliage) was then weighed and f i n a l l y the merchantable stem weight to a 4. 0 i n c h top diameter outside bark was obtained.  The foliage was then clipped f r o m the l a r g e r b r a n c h parts and p l a c e d i n b u r l a p sacks. to m i n i m i z e drying.  These sacks were then p l a c e d i n the shade  Discs, approximately one i n c h i n thickness were  then sawn f r o m the stem.  These discs were sawn at stump height,  b r e a s t height, eight feet above stump height, and at eight foot lengths thereafter to the top of the tree.  7  F o l l o w i n g cutting, the diameter outside bark of each disc  was  m e a s u r e d and r e c o r d e d on a s t e m analysis sheet. These discs were p l a c e d i n polyethylene bags which were sealed to prevent drying.  The bagged samples were subsequently t r a n s p o r t e d to the drying and weighing f a c i l i t i e s .  T h i s was  c a r r i e d out as frequently as possible  so that the samples were r a r e l y allowed to d r y i n the woods for m o r e than four hours before reweighing.  Upon a r r i v a l at these facilities each bag of foliage plus twigs was weighed and this weight was number.  r e c o r d e d a c c o r d i n g to tree and bag  The bags were then p l a c e d i n a drying shed where the  temperature was maintained at approximately 85°C.  E a c h disc  was  weighed and then p l a c e d i n a gas drying oven i n which a temperature of 100°C was  maintained.  Upon completion of the n e c e s s a r y drying p e r i o d (usually 24 hours i n the case of the d i s c s and s e v e r a l weeks for the foliage bags) the discs and foliage were r e m o v e d f r o m the drying facilities, r e weighed, and their d r y weights r e c o r d e d a c c o r d i n g to the appropriate tree and bag or disc number coinciding with the f r e s h weights.  Thus  it was p o s s i b l e to obtain the m o i s t u r e contents of the discs, e x p r e s s e d in t e r m s of per cent as:  MC  (%)  =  F r e s h weight (gm) - D r y weight (gm) F r e s h weight (gm)  ^  1 Q Q  8 Radial growth was then m e a s u r e d on each disc.  Since  considerable  shrinkage had r e s u l t e d f r o m the drying a l l the r a d i a l growth m e a s u r e ments made on the d r i e d discs were c a r r i e d out along an average diameter line equal to the average diameter m e a s u r e d and r e c o r d e d immediately after the tree sections were cut i n the woods.  The  actual f r e s h volume inside and outside bark was determined f r o m Reineke charts.  Since specific gravity measurements were not i n c o r p o r a t e d i n the o r i g i n a l study plans, a l l measurements of volume for specific gravity calculations a r e on an oven d r y wood b a s i s .  No attempt was  made to b r e a k the sections into e a r l y wood or late wood, o r into sapwood o r heartwood and thus a l l measurements are b a s e d only upon c r o s s - s e c t i o n measurements.  T h e volume measurements were  obtained b y i m m e r s i n g a pie-shaped section (sector), cut f r o m each disc, into water and m e a s u r i n g the volume of water displaced.  The  specific g r a v i t y at various heights within each t r e e was obtained f r o m the ratio of the oven-dry weight of each sector to its d i s p l a c e d volume. The specific gravities, oven-dry volume basis, can be converted to green volume b a s i s using the f o r m u l a f r o m the F o r e s t r y Handbook (S.A.F.,  1961):  Po =  ' Pg s  -  1.0 - 0. 28 P g  9  thus:  Pg  =  Po 1.0+0. 28Po  where: P g = specific gravity green volume basis Po = specific gravity oven-dry volume basis.  The laborious and tedious task of removing a l l of the needles f r o m twigs and other extraneous matter gathered f r o m the crowns of the trees p r o v e d to be the most time consuming phase of the entire project.  B y t r i a l and e r r o r it was found that the only acceptable  method to a c c o m p l i s h this was to pluck, by hand, each fascicle of pine needles (which, unlike the spruce needles were held tenaciously to the twigs).  The cleaned needles (without f a s c i c l e s ) were then r e p l a c e d  in the bags and  reweighed.  A handful of needles was then withdrawn f r o m one of the bags of needles collected for each tree. T h r e e of the longest and shortest needles contained i n each handful were m e a s u r e d for length and width. In addition, fifteen needles were randomly drawn f r o m the remainder of those i n each handful and these were m e a s u r e d for length only. F i n a l l y , the number of needles i n one-half g r a m of oven-dry needles was  counted.  A s mentioned p r e v i o u s l y only the d r y weights of the needles on each tree were obtained.  U s i n g data on needle m o i s t u r e content,  p r o v i d e d by K i i l (1967), it was  also possible to calculate the f r e s h  needle weights of each tree.  The weight of green branches for each  tree was obtained b y subtracting the weight of green needles f r o m the f r e s h weight of crown m a t e r i a l s (needles plus branches). The d r y b r a n c h weight p e r tree was then obtained by multiplying the f r e s h b r a n c h weights times the m o i s t u r e content of b r a n c h wood, obtained f r o m K i i l (1967).  Since the volumes, inside and outside bark, of each tree were known, it was possible to calculate the d r y weight of the bark of each tree b y multiplying the bark volume by the specific gravity of bark obtained f r o m Wahlgren (1967).  Since no data appears to be available  on the m o i s t u r e content of lodgepole pine bark, the value reported for jack pine (Pinus banksiana Lamb.) b y B e s l e y (1967), was u s e d to convert d r y bark weights to green bark weights.  The proportions of each component (needles, branches, boles and bark) of the total above ground weight were obtained.  This was  a c c o m p l i s h e d b y obtaining the percentage that the weight of each component contributed to the weight of the total tree weight.  Upon completion of the data collection it was found that complete data on only 63 pine trees were available.  Consequently, the results  presented i n this thesis, are b a s e d on data collected f r o m these 63 trees only.  11  A DISCUSSION O F BIOMASS  F a c t o r s Affecting Organic Matter P r o d u c t i o n  C o n i f e r s a r e generally m o r e productive than deciduous trees, although there i s a tendency for the latter to occupy better sites. Ovington (1956) r e p o r t e d that conifers proved to be the m o r e p r o ductive when the two o c c u r r e d under s i m i l a r conditions. were c o n f i r m e d by Whittaker (1966).  These results  Tadaki (1966) suggested a  reasonable range for the leaf b i o m a s s of deciduous b r o a d l e a v e d forests to be only 2. 0 to 3. 0 oven-dry tons p e r hectare while that for e v e r g r e e n coniferous forests would be 9.0 to 15.0 oven-dry tons p e r hectare.  E n v i r o n m e n t a l factors are v e r y important determinants of organic matter production and generally the amount of matter produced annually decreases f r o m the equator towards the poles.  B a z i l e v i c and  Rodin (1966), and Rodin and B a z i l e v i c (1966) r e p o r t e d that the amount of organic matter contained i n tropic and subtropic communities greatly exceeds that produced by temperate communities.  These  results tend to suggest that organic production i n c r e a s e s with i n c r e a s i n g temperature and length of growing season, although exceptions to this may occur with >. Pseudotsuga m e n z i e s i i (Mirb.) F r a n c o , Sequoia spp. , 1  and Eucalyptus spp.  Comprehensive compilations of the results  of many studies on organic matter have been p r e p a r e d by Scott (1955), Ovington (1962), B r a y and G o r h a m (1964), T a d a k i (1966), B a z i l e v i c and Rodin (1966), and Rodin and B a z i l e v i c (1966).  E n v i r o n m e n t a l factors such as light, temperature,, moisture, m i n e r a l nutrition, the p h y s i c a l and c h e m i c a l p r o p e r t i e s of the soil, atmospheric carbon dioxide, toxjcindustrial gases, and such agents as insects and fungii w i l l greatly influence the productivity of a forest complex.  O d u m (1959) noted that the rate of production of an eco-  s y s t e m i s i n e q u i l i b r i u m (inflows balance outflows of m a t e r i a l s and energy) with the supply or the rate of inflow of the m i n i m u m l i m i t i n g constituent ("Law  of the Minimum").  Results r e p o r t e d by M a r : M o l l e r (1947), Kittredge (1948), Scott (1955), L a M o i s (1958), B r o w n (1963 and 1965) V a i d y a (1963), B r a y and Q o r h a m (1964), Ando (1965), and Tadaki (1966) indicate that the amount of o r g a n i c matter per unit a r e a contained i n the crowns of t r e e s d e c r e a s e s with reduced site quality. H a t i y a et al. (1966) r e p o r t e d that site quality did not significantly influence seasonal variations i n leaf and l e a f - f a l l amounts.  Whittaker (1966) concluded  f r o m his investigations that b i o m a s s d e c r e a s e d f r o m m e s i c to x e r i c sites and f r o m low to high elevations.  A c c o r d i n g to Witkamp (1966)  the total o r g a n i c m a s s weight (including trees, vegetation, litter and humu and s o i l organic matter) d e c r e a s e d with d e c r e a s i n g s o i l m o i s t u r e .  13 Witkamp's results indicated that the total weight of ground vegetation, litter, and humus on top of m i n e r a l s o i l d e c r e a s e d less than c o r r e s ponding tree volume, as the water holding capacity of the soil decreased.  T h e r e are two schools of thought concerning the influence of stand density on the amount of canopy matter contained i n a stand. M a r : M o l l e r (1947) found that i n closed stands thinning had little influence on the amount of foliage present. T h i s was Ovington (1956),  supported by  Weetman and H a r l a n d (1964), W i l l i s t o n (1965),  T a d a k i (1966), and K a t i y a et a l . (1966). These results suggest that trees attempt to m a x i m i z e light utilization, i . e . the leaf biomass per tree i n c r e a s e d as the light intensity i n c r e a s e d and stand density decreased. M e m b e r s of the opposing school include Molchanov (1949), Scott (1955), Dimock (1958)'; L a M o i s (1958), Stiell (1962), D i e t e r i c h (1963), Reukema (1964), B a s k e r v i l l e (1965 b), Metz and Wells (1965), and B o y e r and Fahnestock (1966), who  r e p o r t e d that thinning  considerably reduced the amount of l i t t e r f a l l per unit area, and thus suggesting a decrease i n the amount of crown m a t e r i a l present. Reukema (1966) r e p o r t e d that the growth and yield of r e g u l a r l y spaced planted t r e e s d e c r e a s e d i n i t i a l l y as density decreased. However as the stand grows older, the faster growth rate per tree of the trees in less dense stands may are  be great enough to offset the fact that there  fewer trees than i n the dense stands and thus the total production  of the low density stands may stands.  eventually exceed that of high density  14  B a s k e r v i l l e (1965 b) suggested that Mar: may  M o l l e r ' s findings  be true for intolerant species but not for tolerant species.  Tadaki (1966) c a r r i e d out a comprehensive s u m m a r y of much of the r e s e a r c h r e p o r t e d on leaf b i o m a s s and concluded that there were l a r g e s i m i l a r i t i e s i n the amount of foliage produced not only for the same and r e l a t e d species but also for deciduous, evergreen, broadleaved, and needle f o r e s t formations.  C e r t a i n l y one would expect that as  the density of the over*»story i n c r e a s e d the b i o m a s s of the understory vegetation would decrease.  T h i s i s supported by the results  of B a s k e r v i l l e (1966).  It would also be l o g i c a l to expect the b i o m a s s of fully stocked stands to i n c r e a s e d i r e c t l y with stand density up to the point at which heavy i r r e g u l a r m o r t a l i t y o c c u r s .  In dense stands at full stocking  (Smith, 1966 a), one can expect that b i o m a s s w i l l i n c r e a s e d i r e c t l y with the depth of live crown which decreases with b a s a l a r e a per acre (Smith, Ker,  and C s i z m a z i a ,  1961).  The influence of stand density on stand development has been d i s c u s s e d by Dahms (1966), and Stiell (1966).  Growth-density  relationships were d i s c u s s e d by Reukema (1966), and B e r g (1966). Smith (1966 b) d i s c u s s e d the financial implications of stocking control.  The total amount of foliage displayed by a tree i s r e l a t e d to such factors as tree size, competition, and site conditions. It  appears that those conditions that favor i n c r e a s e d tree growth w i l l result i n i n c r e a s e s i n the amount of foliage supported by a tree.  A number of investigations, too numerous to summarize,  here were abstracted by Johnstone (1967  a) and the results of these  investigations unanimously indicate that the weight of foliage per tree i n c r e a s e s with i n c r e a s e s i n tree dbh and b a s a l area per t r e e . H a l l (1965) reported that a strong relationship existed between the amount of s t e m growth at any point i n the tree and the amount of foliage present above that point.  S i m i l a r results are reported by  Tadaki (1966).  Strong relationships between the weight of foliage and branches, and height growth have been reported by Ovington (1956), V a i d y a (1963), Weetman and H a r l a n d (1964), and T a d a k i and  Kawasaki (1966).  A c c o r d i n g to Ovington (1956) the weight of the canopy i n c r e a s e s as tree age i n c r e a s e s .  Ovington (1962) suggested that the productivity  of young trees i n c r e a s e s r a p i d l y up to approximately 35 years of age, levels off for a short p e r i o d and then declines. that there was  Tadaki (1966) reported  a r a p i d i n c r e a s e i n leaf b i o m a s s during the pole stage  of development reaching a m a x i m u m when the canopy closed then a decline o c c u r r e d .  Molchanov (1949) reported the needle weight  of pine t r e e s to be d i r e c t l y proportional to volume i n c r e m e n t less of t r e e age.  regard-  16  In addition to Molchanov (1949) s e v e r a l other r e s e a r c h e r s including Kittredge (1948), Poljakova-Mincenko (1961), T a d a k i et al.(1962), Satto (1962), and Z y r j c e v (1964) have observed high correlations between changes i n foliage amount and growth i n c r e m e n t s . Siminov (1961) r e p o r t e d l i n e a r relationships between leaf and stem weights, stem and b r a n c h weights, and b r a n c h and leaf weights.  The amount of organic matter contained i n branches i n c r e a s e s with tree size.  If this amount i s subdivided into the amounts com-  p r i s e d of dead and l i v i n g matter i t can be seen that there i s v e r y little branch matter of a dead nature until crown closure o c c u r s . A f t e r this time the dead b r a n c h component i n c r e a s e s as a result of the lower branches dying due to shading.  Ovington (1957) r e p o r t e d that  the weights of l i v i n g and dead branches may be approximately equal in older t r e e s .  B a s k e r v i l l e (1965 b) r e p o r t e d that the amount of live  branches i n c r e a s e d and the amount of dead branches d e c r e a s e d as stand density decreased.  L a M o i s (1958) r e p o r t e d that the weight  of dead branches i s strongly influenced by site and that good site qualities hasten the appearance of dead branches and speed the dying of branches.  Some of the factors effecting natural pruning and its  related factors were intensively analyzed by Smith, Ker, and C s i z m a z i a (1961), and by B a i l e y (1964).  The amount of bole m a t e r i a l constitutes the greatest weight of any component i n a tree.  The proportion of the total tree weight  contained i n the bole i n c r e a s e s with tree size, and it appears f r o m Ovington's (1957) work with Scots pine (Pinus s y l v e s t r i s L.) that this proportion i n c r e a s e s with age.  Ovington reported that the ratio  of oven-dry bole weight to oven-dry canopy weight and to canopy a r e a i n c r e a s e s as tree size i n c r e a s e s .  It appears, therefore, that  although the weights of tree components i n c r e a s e with tree size the proportion of these components to total tree weight decreases with the exception of the bole component.  B a s k e r v i l l e (1965 b) r e p o r t e d  that although the amount of wood produced i s unaffected by density the amount of bole wood i s .  stand  B a s k e r v i l l e ' s data suggested  that i n s m a l l trees m o r e total growth goes into stem wood and less into foliage than i n l a r g e t r e e s ; S i m i l a r r e s u l t s to B a s k e r v i l l e ' s were reported by Satoo and Senda (1966).  B a s k e r v i l l e ' s results therefore  appear to be i n d i r e c t opposition to Ovington's. may  T h i s contradiction  have r e s u l t e d because the s m a l l diameter t r e e s m e a s u r e d by  B a s k e r v i l l e were probably suppressed trees having c y l i n d r i c a l f o r m e d boles and sparse crowns. Results presented by B a s k e r v i l l e on bark proportion are not i n agreement with those presented by Smith and Kozak (1967) for most of the c o m m e r c i a l tree species of B r i t i s h Columbia.  C e r t a i n l y one would expect to observe a situation s i m i l a r  to the one presented by Ovington (1957).  18  Stand F u e l s Of the many factors which govern the behaviour of fire, the quantity of fuel available i s the most constant and e a s i l y m e a s u r e d variable.  B y using weight measurement it is p o s s i b l e to obtain  an indication of the quantity of fuel and thus the potential energy release.  In f o r e s t r y the most important fuel i s s l a s h or the residue  left following the h a r v e s t i n g of an area.  It is important for the  f o r e s t e r to be able to accurately estimate the quantity of s l a s h i n order to establish the size and cost of the disposal job or protection requirement.  The quantity of s l a s h w i l l also greatly influence the  s i l v i c u l t u r a l treatment n e c e s s a r y to create conditions favorable for regenerating new  stands.  Following logging any attempt to estimate the quantity of s l a s h is almost i m p o s s i b l e because of the i r r e g u l a r and i n t e r l a c e d nature of the s l a s h on the ground. of ease and accuracy,  Consequently, the best method, i n t e r m s  appears to be a p r e - h a r v e s t estimate.  By  using an appropriate equation or s l a s h quantity table i n conjunction with a stand table it is p o s s i b l e to obtain an estimate of future expected slash d i s p o s a l  requirements.  Slash weight tables have been constructed by s e v e r a l r e s e a r c h e r s including B r u c e (1951), and Chandler (I960).  Equations to be u s e d  for s l a s h weight p r e d i c t i o n have been developed by Fahnestock (I960) for western conifers, by B r o w n (1963 and 1965), and D i e t e r i c h (1963)  for r e d pine (Pinus r e s i n o s a Ait.), and by K i i l (1965), and M u r a r o (1964  and 1966) for lodgepole pine.  In addition, many of the methods  used for the estimation of b i o m a s s or foliage quantities, mentioned in preceding parts of this report, can be applied.  Many of the methods  and r e s u l t s reported p r e v i o u s l y have failed to establish the size distribution of the various slash components, which greatly influence the potential f i r e hazard, and rate of spread.  However, these r e s u l t s  should not be considered meaningless and as Fahnestock (I960) pointed out, any objective method of estimation i s vastly superior to guesswork.  A s u m m a r y of previous r e s e a r c h on b i o m a s s foliage and slash is presented i n Appendix I.  Method of A n a l y s i s The The  data were analysed using multiple r e g r e s s i o n techniques  r e g r e s s i o n p r o g r a m d e s c r i b e d by Kozak and Smith (1965) and the  U n i v e r s i t y of B r i t i s h Columbia's I. B. M. 7040 e l e c t r o n i c computer were u s e d for the analysis. T r e e component weights, and the p r o portions of the weights of the component to the total tree weight were used as dependent v a r i a b l e s with the independent v a r i a b l e s diameter at b r e a s t height i n inches (dbh), tree height i n feet (Kit. ) crown length i n feet (CL), crown width i n feet (CW), in feet (Ht. L C ) ,  height to l i v e crown  and tree b a s a l a r e a i n square feet (BA).  The  20 independent and dependent variable analysed were always i n the units p r e v i o u s l y mentioned.  The following were used as dependent variables i n the r e g r e s s i o n analyses of tree and component weights: a) T o t a l T r e e Weight - The weight of a l l of the components (including needles, branches, cones, bole wood, and bark) above a one foot stump.  The f r e s h weights were  m e a s u r e d i n the field and the d r y weights were obtained by the addition of the d r y needle weight plus the d r y s t e m weight plus the d r y b r a n c h weight. b) T o t a l Stem Weight - The weight of the total s t e m (the total tree l e s s the sum of the branches plus needles plus cones).  The f r e s h weight was obtained by f i e l d m e a s u r e -  ments and these were converted to a d r y weight b a s i s using the average of the m o i s t u r e content m e a s u r e m e n t s for each t r e e . c) Needle Weight - The weight of the cleaned and d r i e d needles was obtained by actual measurement. The f r e s h weight of the needles was calculated using needle m o i s t u r e content data p r o v i d e d by K i i l (1967). d) B r a n c h Weight - Neither the f r e s h nor d r y b r a n c h weights were m e a s u r e d directly.  The f r e s h b r a n c h weight was  determined by subtracting the sum of the f r e s h stem and f r e s h needle weights f r o m the total tree f r e s h  weight.  The d r y weight of branches was  calculated  by reducing the f r e s h b r a n c h weight by b r a n c h m o i s t u r e content data provided by K i i l (1967). e) Bole B a r k Weight - Neither the f r e s h nor d r y b a r k weights were measured. The volume of bark was obtained f r o m Reineke charts and this volume was converted to d r y weight using bark specific gravity data pro\ided by Wahlgren (}967) .  Because of the unavailability of b a r k  m o i s t u r e content data for lodgepole pine; m o i s t u r e content data for jack pine bark (Besley, 1967) was used. f) B o l e Wood Weight - The bole wood weight was calculated by reducing the total s t e m weight by the weight of bark. g) C r o w n Weight - C r o w n weight excludes the weight of the m a i n bole within the crown and i s the weight of the branches plus needles.  The f r e s h crown weight was  m e a s u r e d i n the field. The d r y crown weight was  cal-  culated by adding the d r y weight of the branches plus the dry weight of the needles. h) Slash Weight - Slash weight is the weight of the needles plus the weight of the branches plus the non-merchantable top weight. F r e s h slash weights were obtained i n the field. The weights of d r y s l a s h were determined f r o m the sum of the d r y weight of needles and branches plus the difference between the total stem and the merchantable s t e m weights adjusted for a m o i s t u r e content deter-  22 mination taken f r o m a part of the stem located within the  crown.  i) Merchantable Stem Weight - The merchantable s t e m is the weight of the stem between a one foot stump and a four inch top. The f r e s h weight was determined by direct measurement and this weight was reduced by the average moisture content of each tree to obtain the d r y weight of the merchantable bole.  The proportions of the weight of each of the components, d i s c u s s e d previously, to the weight of the total tree were related to the independent v a r i a b l e s dbh, height, crown length, crown width, height to live crown, and tree b a s a l a r e a using multiple r e g r e s s i o n techniques.  A n additional analysis was c a r r i e d out to relate tree c h a r a c t e r i s t i c s to crown and needle c h a r a c t e r i s t i c s . F o r purposes of this analysis it was assumed that the geometric f o r m of lodgepole pine crowns i s that of a parabola. The formulae for the volume and surface a r e a of:  a p a r a b o l a are:  2 Crown Volume (Cr. Vol.) =  H R  CL  2 Crown Surface A r e a (Cr. S.A.) = %  it R rr-  .2 (R  3/ 2, 'Z 3 + 4 CL ) - R  where:  "If = 3. 1416 R = crown radius = (crown width / 2) C L = crown length  The number of needles per tree was calculated by multiplying the number of needles per half g r a m times the weight of needles p e r tree i n grams.  Needle c h a r a c t e r i s t i c s were studied and the  relationship of needle length on needle width established using a simple l i n e a r r e g r e s s i o n .  In addition, needle c h a r a c t e r i s t i c s were  also r e l a t e d to tree c h a r a c t e r i s t i c s using r e g r e s s i o n analysis.  Using regression, techniques,  the crown c h a r a c t e r i s t i c s :  crown volume, crown surface area, d r y needle weight, and number of needles per tree were related to tree s t e m volume (ob) i n cubic feet and to total tree weight i n pounds.  A multiple r e g r e s s i o n of the  number of needles p e r cubic foot of volume (ob) on dbh, height, and b a s a l a r e a (bh) was used to study the productive efficiency of the different s i z e d t r e e s .  U s i n g r e g r e s s i o n analysis, the same thre  independent v a r i a b l e s were related to the d r y needle weight and number of needles per cubic foot of crown volume and per square foot of crown surface  area.  24 Results of A n a l y s i s T r e e and component weight relationships.  Table 1 presents the means, standard deviations, and m i n i m u m and m a x i m u m values of the independent v a r i a b l e s used in the analyses.  Table 1. Mean, Standard Deviation, M i n i m u m and M a x i m u m Values of the T r e e C h a r a c t e r i s t i c s used as Independent V a r i a b l e s for 63 Lodgepole Pine T r e e s .  Standard Deviation  Minimum Value  6.48  1. 668  4. 30  10. 90  Height (ft)  58. 46  6. 444  45. 00  72. 00  C L (ft)  17. 24  5. 940  8. 00  32. 00  CW(ft)  4. 79  1. 321  2. 50  8. 80  41. 22  5. 070  25. 10  50. 80  Independent Variables D B H (in)  Ht. L C (ft) B A (sq. ft. )  Mean  0. 24  0. 131  0. 10  Maximum Value  0. 65  It should be noted i n the p r e c e d i n g table that the size range of the t r e e s f r o m which the data were collected is v e r y narrow.  No  attempt should be made to apply the formulas developed i n this thesis beyond the dimension range of these t r e e s .  The means, standard deviations, m i n i m u m values, and m a x i m u m  25  values o f the dependent v a r i a b l e s are presented i n Table 2.  Table 2.  Dependent Variable  Mean, Standard Deviation, Minimum and Maximum Weights i n Pounds f o r the Tree C h a r a c t e r i s t i c s used as Dependent V a r i a b l e s , f o r 6 3 Lodgepole Pine Trees  Mean  Standard Deviation  Minimum Value  Maximum Value  T o t a l Tree::Fresh Dry  437-95 234.92  278.71 141.78  126.00 78.16  1,I83.OO  T o t a l StennFresh Dry  387.59 208.55  238.38 120.68  107.00 72.01  1,0^9.00 530v03  Fresh Dry  21.60 11.05  ' 16.79 8.59  1.95 1.00  73-95  Fresh Dry  28.76  28.64  15.31  15.24  2.04" 1.09  153.56 81.74  30.68  Needle: Branch:  640.13  37.84  Bole Bark: Fresh Dry  21.17  24.32 16.78  7-75 5-35  -A 121.35 ; 83.73  Bole Wood: Fresh Dry  369.50 196.08  228.01 113.59  99.16 66.60  \989.04  Crown:  Fresh Dry  50.37 26.36  22.54'  4.00 2.09  209.00 110.11  Slash:  Fresh Dry  108.5^ 57-03  20.34  62.00 25.31  233.00 122.11  36.85  ^495.02  Simple c o r r e l a t i o n c o e f f i c i e n t s ( r ) between the dependent and independent v a r i a b l e s are shown i n Table 3.  26  Table 3 .  The Simple C o r r e l a t i o n C o e f f i c i e n t s Between Tree and Component Weights and Some Tree C h a r a c t e r i s t i c s f o r 63 Lodgepole Pine Trees.  Independent V a r i a b l e s  Dependent Variables DBH T o t a l Tree: Fresh Dry T o t a l Stem: Fresh  Needle:  Branch:  Bole Bark:  Bolewood:  Slash:  0.886**  CL  CW  Ht.LC  0.732** 0.821**  BA  0.268*  0.986**  O . 9 8 0 * * O . 8 8 9 * * 0.716**  0.799**  0.290*  0.982**  O . 9 7 9 * * 0.894**,  0.808**  0.280*  0.980**  O . 8 9 8 * * 0.712** O . 7 8 1 * * 0.307*  0.974**  0.782**  Dry  0.977**  Fresh  0 . 9 0 7 * * 0 . 7 7 3 * * 0 . 7 2 4 * * 0 . 8 1 5 * * 0.133ns  0.90b**  Dry  0 . 9 0 7 * * 0 . 7 7 3 * * 0 . 7 2 4 * * O . 8 1 5 * * 0.133ns  0.968**  Fresh  0 . 8 7 9 * * 0 . 7 2 3 * * O . 6 1 9 * * 0 . 7 9 2 * * 0.196ns  O.908**  Dry  O . 8 7 9 * * 0 . 7 2 5 * * O . 6 1 9 * * 0 . 7 9 2 * * 0.196ns  0.908**  Fresh  0.839** O.819** 0.680** O . 6 7 4 * *  Dry  O . 8 3 9 * * 0 . 8 1 9 * * 0 . 6 8 0 * * 0 . 6 7 4 * * 0.245hs  Fresh  O . 9 7 9 * * O.89O** 0.728** O . 8 0 8 * * 0.278*  0.981**  O.975** O.891** O.706**  0.779**  0.306*  0.983**  Fresh  0.941** O.786** O.696**  0.847**  0.183ns  0.961**  Dry  0.940** 0.785** O . 6 9 5 * *  0.846**  0.184ns  0.960**  Fresh  0.770** 0.623** O . 5 4 9 * * O . 6 7 8 * * 0.l49ns  0.802**  Dry  O . 7 8 2 * * 0 . 6 4 1 * * 0 . 5 3 8 * * 0 . 7 2 5 * * 0.184ns  0.809**  Dry Crown:  0.982**  HT  * * s i g n i f i c a n t at the 0 . 0 1 p r o b a b i l i t y  0.245ns  0.848** 0.848**  level  ^ s i g n i f i c a n t at the 0 . 0 5 p r o b a b i l i t y l e v e l ns not s i g n i f i c a n t at the 0 . 0 5 p r o b a b i l i t y l e v e l (Note:' These notations w i l l be used, as defined above, throughout the remainder of t h i s t h e s i s ) .  27  I t can be seen f r o m the r e s u l t s i n T a b l e 3 t h a t i n a l l cases,  with  t h e e x c e p t i o n s , o f t o t a l stem d r y w e i g h t , b a s a l a r e a p e r t r e e i s most c l o s e l y a s s o c i a t e d w i t h the w e i g h t v a r i a b l e s .  Dbh  i s second o n l y  t o b a s a l a r e a e x c e p t f o r t o t a l stem d r y w e i g h t where the  situation  i s reversed.  H e i g h t t o l i v e crown i n a l l cases i s p o o r l y c o r r e l a t e d  w i t h t r e e and  component w e i g h t s .  The p o s i t i v e v a l u e s o f a l l the  c o e f f i c i e n t s show t h a t t h e w e i g h t s o f t h e t r e e s and t r e e components increase with increasing tree size.  The  r e g r e s s i o n r e l a t i o n s h i p s presented  f o r t r e e and  i n the f o l l o w i n g s e c t i o n s  component w e i g h t and f o r the p r o p o r t i o n o f t h e component  t o the t o t a l t r e e w e i g h t are o f a l i n e a r form. formulae presented  Generally,  the  i n the l i t e r a t u r e have been o f a l o g a r i t h m i c  t r a n s f o r m a t i o n form.  Transformed v a r i a b l e s are not presented;  Mn  t h e f o l l o w i n g s e c t i o n because i t i s f e l t t h a t the narrow range o f t h e d a t a and h i g h a c c u r a c y o f the l i n e a r form do n o t r e q u i r e transformation.  Logarithmic  r e g r e s s i o n s equations  the  are p r e s e n t e d  in  Appendix I I .  The  r e g r e s s i o n techniques  used result,, i n the b e s t p o s s i b l e f i t  o f t h e r e g r e s s i o n l i n e or s u r f a c e .  The  techniques  c o n d i t i o n t h e r e g r e s s i o n r e l a t i o n s h i p s and may  be i n e r r o r f o r v e r y s m a l l t r e e s .  do n o t , however,  consequently,  the  equations  28 In the following r e s u l t s the standard e r r o r of estimate i s e x p r e s s e d both i n absolute units and as a p e r cent of the mean, the latter i s isolated by brackets and i s presented i n the discussions of the results only.  These percentages are included to facilitate  comparisons of the relative v a r i a b i l i t y .  a. total tree weight (lb) T a b l e s 4 and 5 present the independent v a r i a b l e eliminations f r o m the multiple r e g r e s s i o n analyses of total tree f r e s h weight and total tree d r y weight.  In addition, the simple l i n e a r  regression  equations of total tree f r e s h and d r y weight on dbh are presented i n the appropriate tables. i) f r e s h weight basis Table 4.  R e g r e s s i o n Equations Illustrating the Relationship of T o t a l T r e e F r e s h Weight (lb) with S e v e r a l Independent V a r i a b l e s , for 63 Lodgepole Pine T r e e s . Inder »endent V a r i a b l e s Ht. L C CW DHH C:L  Intercept  *  BA -305.51  1892.3  22. 170 23. 322  -320.46  1892.3  4.  *  -277.52  1888.7  290 4. 063"  -105.85  2087.7""  0. 829  •JU -J>  •JU  -17.480 0. 976 0. 976  164.07  E  45. 18 44. 82  •JU *JU  0.  E  45. 58  0. 976  489" 10. 838 5. 5. 043"  - 73.71 2095. 9 -625.64  S  •JU «J>  4. 690* 5. 842"11.152 -10.164  1782.2  2  •JU  •JU-JU  -305.52  11. 152 -10.167  *  9 7 5 " "  45. 21  0.973""  46. 72  0. 976  46. 52  0. 964"" 53. 24  29  As can be seen f r o m the preceding  results 97. 6 p e r cent of  the v a r i a t i o n i n the f r e s h weight of the total tree above the ground can be accounted for by the independent variable, tree b a s a l area, with a standard e r r o r of 46. 52 lb. (10. 6%).  Dbh accounted for 94.4  per cent of the v a r i a t i o n and had a standard e r r o r of estimate of 53. 20 lb. (12. 1%). As can be seen f r o m T a b l e 4 dbh, crown width, and tree height do not significantly contribute to the multiple r e g r e s s i o n equation and it appears that there is v e r y little advantage i n using a multiple r e g r e s sion instead of a simple l i n e a r r e g r e s s i o n of total tree f r e s h weight on tree dbh or b a s a l area.  The relationship between total tree f r e s h  weight and t r e e b a s a l area i s presented i n F i g u r e 1.  ii) d r y weight b a s i s  T a b l e 5.  Intercept BA  R e g r e s s i o n EquationsHlustrating the Relationship of T o t a l T r e e D r y Weight (lb) with S e v e r a l Independent V a r i a b l e s , for 63 Lodgepole Pine T r e e s . 2 Independent V a r i a b l e s R Ht. L C CL DBH CW Ht  -163.79  865. 4  4.431  4.247 8.545  -1.077  -163.79  865. 4  2. 401  2.217  8.546  -1.077  -166.93  862. 7  2.451  2.285  7.838  SE E 26. 68  -2.030 0. 968  0. 968""" 26. 44 26. 22  0. 968  •A.  -154.45  949.9  0. 968""" 26. 03  2.755" 2. 547  - 67.73 1050. A""'" 1. 121  0. 966  26. 66  - 24. 25 1061. 6  0. 964  27. 01  -305.05  83.296  0. 960  **  .28. 49  30  o o o d T T F Wt.  o o o  S E_'  =  ( l b ) = 2095.9 B A ( s q f t ) - 73-71 1+6.52 l b  r  = O.976  d  o o o  o o o  •  o  o _  o o o d  o o o d  .080  ,160  .21+0  .320  ,UO0.\  .1+80  .560  Basal Area ( s q f t ) F i g u r e 1.  The R e l a t i o n s h i p Between T o t a l T r e e F r e s h Weight ( l b ) and T r e e B a s a l A r e a ( s q f t ) a t B r e a s t H e i g h t .  .6U0  31  B a s a l a r e a was the best single v a r i a b l e for accounting for the variation i n total tree d r y weight.  B a s a l a r e a accounted for 96. 4  per cent of the total v a r i a t i o n with a standard e r r o r of estimate of 27. 01 lb (11. 5%).  The second best variable was dbh which accounted  for 96.0 p e r cent of the v a r i a t i o n and had a standard e r r o r of estimate of 28.49 lb (12.1%).  The use of a multiple r e g r e s s i o n did not i m p r o v e  the relationship and therefore, i t appears that a simple l i n e a r r e g r e s sion of total tree d r y weight on b a s a l a r e a or dbh i s most satisfactory. The relationship between total t r e e d r y weight and t r e e b a s a l area is presented i n F i g u r e 2.  b. total s t e m weight (lb) i) f r e s h weight b a s i s T o t a l s t e m weight i s the weight of the bole wood plus bark above a one foot stump.  The elimination of the independent  variables  for the dependent v a r i a b l e s total s t e m f r e s h and d r y weight are presented i n T a b l e s 6 and 7, respectively.  Table 6.  R e g r e s s i o n Equations Illustrating the Relationship of T o t a l Stem Weight (lb) with S e v e r a l Independent V a r i a b l e s , for ,63 Lodgepole P i n e Trees.  Intercept  Independent V a r i a b l e s BA  Ht. L C  CL  16.430 16.430  17.520  CW  R DBH  5.274  5.139  5.274  5.141  2  SE  Ht  -10.88  0.967  45.77  -355.63  1398. 1  -355.64  1398. 1*"*  5. 552"  -348.08  1453.  5. 7 5 5 ^  .819"5.433  0.967""  -326.55  1507. 1  5. 641""  . 596"  0 . 9 6 6 " ' l 44.  -102.03 1767. 4 " ' - 47.30 1781. .4 -518.95  64l"  *  1. 4 i r  E  0.967""45.37 44.98 79  0 . 9 6 l " " 47. 64 0.961 47. 76 139.840  0.957  49. 55  32  o o o o  N O o o o  T T D.Wtv S E E  c  vc  (lb) = =  106l.6a.A  27.01 lb  (sq ft)  -  2H.25  .2 _ O.96U  U'N  o o o o  CO  o o o  &  O  o o o  '0  CM CO  O o o  0* CM  o o o  d  o o o  d co  o o o —  080  ,l60  .2^0  .320  .400  I  A80  —  ,560  Basal Area (sqft) F i g u r e 2. The R e l a t i o n s h i p Between T o t a l Tree Dry Weight (lb) and T r e e B a s a l A r e a ( s q f t ) a t B r e a s t Height.  .61+0  33  A s can be seen by the results presented i n T a b l e 6 , 9 6 . 1 p e r cent of the v a r i a t i o n i n total stem weight i s accounted for b y the independent v a r i a b l e b a s a l a r e a with a standard e r r o r of estimate of 4 7 . 7 6 lb ( 1 2 . 3 % ) .  U s i n g dbh as the independent v a r i a b l e accounts for  9 5 . 7 percent of the v a r i a t i o n with a standard e r r o r of estimate of 4 9 . 5 5 lb ( 1 2 . 8 % ) .  A s was the case with total tree weight, i t appears  that there i s little to be gained f r o m using a multiple r e g r e s s i o n instead of a simple l i n e a r r e g r e s s i o n of s t e m weight on b a s a l a r e a o r dbh.  The relationship between total s t e m f r e s h weight and tree b a s a l  a r e a i s presented i n F i g u r e 3 .  ii) d r y weight b a s i s Table 7 .  R e g r e s s i o n Equations Illustrating the Relationship of T o t a l Stem D r y Weight (lb) with S e v e r a l Independent V a r i a b l e s , for 6 3 Lodgepole P i n e T r e e s .  Intercept  Independent V a r i a b l e s BA  Ht. L C  - 1 9 0 . 89  6 0 2 . 157" 4 . 6 8 6  - 1 9 0 . 89  602.152"  - 1 6 6 . 08  784.887"" 3.513  -180. 4 6  i f f  749-232  CW  CL 4. 479  •-4.152  2 . 8 4 8 " 2 . 641 3. 2 2 6 "  -4.152  DBH 16.874 1 6 . 874  -3.630  SE  Ht -1.838  0 . 9 5 9 " " 25. 7 7 -0. 959  ## ##  0 . 958  •X-  3.589"  R  3. 3 7 6 "  25. 5 4 25.47  0 . 958  25.41 2 6 . 70  vt>*t,.  -  6 5 . 55  882.415"" 1. 424  0. 9 5 3  -  1 0 . 33  8 9 6 . 592  0 . 9 4 9 " " 27. 3 9  -249. 04  70.588  0.952""  26. 70  The best single independent v a r i a b l e for p r e d i c t i n g total s t e m d r y weight was dbh which accounted for 9 5.2 p e r cent of the v a r i a t i o n i n the  34 Figure 3.  o o o • o o  H  The R e l a t i o n s h i p Between T o t a l Stem F r e s h Weight.(Ib) and T r e e B a s a l A r e a ( s q f t ) a t B r e a s t  T S F Wt. ( l b ) = 1781.1+ B A ( S q f t ) - 1+7.30 =  1+7.76  = O.96I  O OA  O O O d CO  rH  <H O  O ' O O  W  O H  N  '  -P  d C-  bD  •H _  w (D  a  o o o• o VO  <u  -P W rH  a5  -P O EH  o o o• o  o o o d  -=t-  o o o d  oo  o o o d CvJ  o o o .320  . .1+00  Basal Area ( s q f t )  Height.  dependent v a r i a b l e and had a standard e r r o r of estimate of 26. 70 l b . (12.8%).  B a s a l a r e a alone accounted for 94.9 p e r cent of the  v a r i a t i o n i n the d r y weight of the total s t e m with a standard e r r o r of estimate of 27. 39 l b . (13. 1%).  The s m a l l gain i n standard e r r o r does  not warrant the use of a multiple r e g r e s s i o n equation. The relationship between total s t e m d r y weight and dbh i s presented i n F i g u r e 4.  c. bole wood weight (lb.) Bole wood weight can be defined as the weight of the total s t e m minus the weight of the bark.  Table 8 presents the elimination of  the independent v a r i a b l e s f r o m the multiple r e g r e s s i o n for bole wood f r e s h weight,  and i n T a b l e 9 the elimination of the independent  variables  f r o m the multiple r e g r e s s i o n for bole wood d r y weight a r e presented. i) f r e s h weight b a s i s T a b l e 8.  , Intercept J  J  BA  R e g r e s s i o n Equations Illustrating the Relationship of B o l e Wood F r e s h Weight (lb) with S e v e r a l Independent V a r i a b l e s , for 63 Lodgepole P i n e T r e e s . Independent V a r i a b l e s * Ht. L C CL CW DBH  -301.86  1361.3 *"* 6.670 7.43Z  -301.86  2 R  __, SE  Ht 0.967""  43.66  1361.3"" 4. 396"5. 159" 3.934 7.726  O.967"'*  43.28  -290.50  1444.9 " 4. 700" 5.427"4. 173  0.967  42.92  -273.97  1485.9"" 4.613" 5.255  O.967""  42.68  - 95.08  1693.3"" 1.242.  0.963"'"' 44.49  - 46.89  1705.7  O.962""  44.55  0.958""  46.96  -497.97  3.934 7.726 -2.273  133.816  B a s a l a r e a p r o v e d to be the best single independent  variable.  B a s a l a r e a accounted for 9 6 . 2 p e r cent of the v a r i a t i o n with a standard  36  8  F i g u r e h.  o o  The R e l a t i o n s h i p Between T o t a l Stem D r y Weight ( l b )  and T r e e Diameter a t B r e a s t H e i g h t ( i n ) .  LfN  T S D Wt. ( l b ) = 70.588 D.b.h. ( i n ) = 2U9.0U o o o d  S E-g'-  =  26.70  lb  r  2  =  0.952  o o o d o  o o o d  o o o d o  ro  8  o  LfN CM  o o o d o  CM  o o o d  LfN  o o o d o  o o o d  LfN  4.000  4.8000  5.600  6.400 DBH  7.200 (in)  8.000  8.800  9.600  e r r o r of 46.96 l b . (12.7%).  No advantage can be gained f r o m u s i n g a  multiple r e g r e s s i o n as opposed to a simple r e g r e s s i o n of bole wood f r e s h weight on b a s a l a r e a o r dbh.  The relationship between bole wood  f r e s h weight and t r e e b a s a l a r e a i s presented i n F i g u r e 5.  ii) d r y weight b a s i s  Table 9-  R e g r e s s i o n Equations Illustrating the Relationship of Bole Wood D r y Weight (lb) with S e v e r a l Independent V a r i a b l e s , for 63 Lodgepole Pine T r e e s .  Intercept  Independent V a r i a b l e s BA  Ht. L C  CL  6.632 6.199  CW  DBH 18.654  -5.076  18.655  SE  £  Ht  -153.78  576.8  -153.78  576.8" 2.051  -126.35  778. 8"" 2. 785"2. 266"-4. 499  0.957"" 24. 26  -144.18  734. 6  0.956  '24.30  - 60.75  831. 3"" 1. 307"  0.953  '24.93  - 10.05  844. 3  1.618  -5.076  R  2. 879 " z . 451 *  -234.56  -4.581  0.958  24.49  0.958"" 24.27  0.950""25.56 66.430  0.95l"^25.23  The best independent v a r i a b l e p r o v e d to be dbh which accounted for 95. 1 p e r cent of the v a r i a t i o n i n d r y bole wood weight with a standard e r r o r of estimate of 25.23 l b . (12.9%).  T h i s was slightly better than  b a s a l a r e a which accounted for 95. 0 p e r cent of the v a r i a t i o n and had a standard e r r o r of 25.23 l b . (12.9%).  The r e s u l t s suggest that there  is v e r y little to be gained f r o m using a multiple r e g r e s s i o n .  The  relationship between bole wood d r y weight and dbh i s presented i n F i g u r e 6.  Figure 5.  The R e l a t i o n s h i p Between Bole Wood Fresh Weight? ( l b )  and Tree B a s a l Area (sq f t ) a t Breast Height. B W F Wt.  ( l b ) = 1705.7 B A ( s q f t ) - 46.89  S E :  44.55  E  0.080  7160"  =  r2T40"  lb  .320  Aob~  Basal Area (sq f t )  ~48o"  T560"  7640  39  o o o  F i g u r e 6.  The R e l a t i o n s h i p Between B o l e Wood D r y Weight ( l b ) and  6  T r e e Diameter a t B r e a s t H e i g h t ( i n ) .  o LfN  B W D Wt. ( l b )  o o o  S E  E  =  = 66M  25.23 l b  D.b.h. ( i n ) - 23^.56 r  2  = 0.951  d -3-  ;  o o d o  o  o o o d  ir\| m  o o o d o on  o o o d Lf\ CM  O O  o d o  CM  o o o d  o o o d o  r-l  o o o d  'i+.ooo  1+.800  5.600  6.400 DBH  7.200 (in)  8.000  8.800  9.600  4o d. bole bark weight ( l b ) The e l i m i n a t i o n s of the regression c o e f f i c i e n t s from the m u l t i p l e l i n e a r regressions o f the weight o f f r e s h and dry bole bark are presented i n Tables 10 and 11, r e s p e c t i v e l y . i ) f r e s h weight basis Table 10.  Intercept  BA  Regression Equations E l l u s t r a t i n g the Relationship of Bole Bark Fresh Weight (lb) on Several Independent "Variables, f o r 63 Lodgepole Pine Trees.  Ht.LC  Independent:. V a r i a b l e s CL * DBH Ht  CW  R  2  SE^ _  -37.13 315.459** 1 7 . 9 3 8  18.286  -20.29I4* - I 5 . 9 6 U 0 . 2 0 1 O . 7 6 9 * * 1 2 . 2 9  -36.54 315.985**  17.847  18.191  -20.164* -15.882  -35.88 321.146**  19.849** 2 3 . 2 6 8 * * - 2 0 . 6 3 4 *  -68.69  91.444**  -13.00 155.980**  I.185**  O.769**  12.18  0 . 7 7 0 * * 12.07  I.636*  0.136  - 7-73 157.333  O.75I**  12.45  0.721**  13.07  0 . 7 2 0 * * 12.98  12.231  -48.61 -150.07  0 . 7 0 4 * * 13.34 3.092  0.671**  14.06  Tree b a s a l area accounted f o r the most v a r i a t i o n ( 7 2 . 0 per cent) of f r e s h bole bark weight w i t h a standard error o f estimate o f 12.98 lb. (42.3$).  The second best v a r i a b l e was dbh. Dbh accounted f o r  7 0 . 4 per cent o f the v a r i a t i o n and had a standard error o f estimate o f 13.34  l b . (43.5$).  As demonstrated by the r e s u l t s i n Table 10 the use  of a m u l t i p l e regression improved the r e l a t i o n s h i p because the c o n t r i b u t i o n to the explained v a r i a t i o n by the other v a r i a b l e s was s i g n i f i c a n t .  The  r e l a t i o n s h i p between bole bark f r e s h weight and tree height i s presented  41  m  Figure 7. i i ) dry weight b a s i s Table 11.  Regression Equations I l l u s t r a t i n g R e l a t i o n s h i p o f Bole Bark Dry Weight ( l b ) w i t h Several Independent V a r i a b l e s , f o r 63 Lodgepole Pine Trees. o  Intercept  BA  Independent V a r i a b l e s Ht.LC CL DBH  Ht.  CW  R  -25.63 217.767** 12.174  12.414  -14.014* -10.812 0.139  0.769** T37m3  -25.22 218.131** 12.110  12.348  -13.924* -10.75^  0.769** 8.4o  -24.77 221.626** -47.42  63.077**  - 8.98 107.623**  1.370** 1.606** -14.243*  0.770** 8.33  0.818*  0.751** 8.59  1.129**  0.094  0.721** 9.02 0.720** 8.95  - 5.33 108.558 8.439  -33.5^  0.704** 9.21 2.133  -103.55  0.671** 9.70  A m u l t i p l e l i n e a r r e g r e s s i o n o f bole bark dry weight on the combination of t r e e b a s a l area, crown length, height t o l i v e crown and diameter at breast height was the most r e l i a b l e estimate. v a r i a b l e s combined accounted  These four  f o r 77.0 per cent o f the v a r i a t i o n w i t h  a standard e r r o r of estimate o f 8.33 l b ( 3 9 T h e  elimination of  diameter at breast height from the m u l t i p l e r e g r e s s i o n d i d not r e s u l t i n a l a r g e increase i n the standard e r r o r or a large decrease i n the amount o f the v a r i a t i o n accounted f o r . Tree b a s a l area was the best s i n g l e independent v a r i a b l e accounting f o r 72.0 per cent o f the v a r i a t i o n w i t h a standard e r r o r o f estimate o f  42  o o Figure 7.  The Relationship-Between Bark Fresh Weight ( l b ) and Tree Height ( f t ) .  o  B.F. Wt. ( l b ) = 3.092 Ht. ( f t ) - 150.07  SE  E  = 14.06 lb"  0.671  r-l  rH x: •H CU  £w  '  O O• o o r-i  a;  u !H  a5  eQ  O .o eg  o  VD  O  O  CM  20.00  30.00  4o..oo  50.00  Height ( f t )  60.00  70.00  80.00  43  8.95 l b . ( 4 2 . 2 $ ) .  The r e l a t i o n s h i p between bole bark dry weight and  tree height i s presented i n Figure 8. e. needle weight ( l b ) Table 12 presents the e l i m i n a t i o n of the r e g r e s s i o n c o e f f i c i e n t s from the r e l a t i o n s h i p o f f r e s h needle weight on s e v e r a l independent variables.  The e l i m i n a t i o n of'the regression c o e f f i c i e n t s from the  m u l t i p l e r e g r e s s i o n o f dry needle weight on the same independent v a r i a b l e s i s presented i n Table 13.  i ) f r e s h weight b a s i s Table 12.  Regression Equations I l l u s t r a t i n g R e l a t i o n s h i p o f Fresh Needle Weight (lb), w i t h Several Independent V a r i a b l e s , for 63 Lodgepole Pine Trees.  Intercept  Independent V a r i a b l e s DBH  Ht.LC  CW  CL  BA  -21.05 9.068  -0.572  2.640* -0.081  -10.760  -21.05 9.068  -0.592  2 . 6 4 o * -0..101  -10.760  -19.14 8.168** -0.566  2.630* -0.084  R Ht.  -0.020  2  SE  E  0.860** 6750 0.860**  6.55  0.860**  6.49  -21.31 7.862** -0.507** 2.685*  0.860**  6.44  - 1 9 . 2 2 9 . 6 1 5 * * -0..522**  0.845**  6.71  - 3 7 . 5 9 6 9.132  0.823**  7.13  0.825**  7.09  -6.79  116.279  There appears to be very l i t t l e d i f f e r e n c e between the r e l a t i o n s h i p s of f r e s h needle weight on tree b a s a l area and dbh.  Basal area accounted  for 82.5 per cent of t h e v a r i a t i o n i n f r e s h needle weight, w i t h a standard error o f estimate o f 7.09 l b ( 3 2 . 8 $ ) .  The independent v a r i a b l e o f dbh  44  Figure 8 .  The Relationship Between Bark Dry Weight ( l b ) and Tree Height (ft).  B.D.  Wt.  (lb) = 2.133  S Eg = 9 - 7 0 l b  f .00  I  30.00  r  1  Uo.oo  ( f t ) - 103-55  Ht. 2  i  =  0.671  I  50.00  Height ( f t )  I  60.00;  I  70,00  I  80.00  accounted for 82. 3 per cent of the v a r i a t i o n and had a standard e r r o r of estimate of 7. 13 lb (33. 0%)  A multiple r e g r e s s i o n did not offer a  large improvement and reduced the standard e r r o r of estimate by only 0. 38 lb (1. 8%) compared to the standard e r r o r obtained using b a s a l area. The relationship between needle f r e s h weight and t r e e b a s a l a r e a i s presented i n F i g u r e 9.  ii) d r y weight b a s i s  Table 13.  Intercept DBH  R e g r e s s i o n Equations Illustrating the Relationship of D r y Needle Weight (lb) with S e v e r a l Independent V a r i a b l e s , for 63 Lodgepole Pine T r e e s . Independent V a r i a b l e s Ht. L C  CW  Ht  BA  CL . 103  -10.77  4.640  -0.251"" 1. 351* -0. 052  - 9.79  4. 179""-0. 247" 1. 346  -10.90  4.023  -0.260  - 9.84  4.920  -0.267  -19-24  4.673  - 3.47  -5.506  -0.043  0. 860  SE _:E  si- «J>. 3. **  0.860 0. 860 0. 860 0.  ** 845 **  0. 823 59.499  3. 35 3. 32  T"V'  1.374  35  **  0.825  3. 29 3.43 3. 65 3. 63  T h e r e appears to be no advantage to be gained by using a multiple r e g r e s s i o n for predicting d r y needle weight. The  independent  variables dbh and b a s a l a r e a accounted for 82. 3 and 82. 5 per cent of the v a r i a t i o n respectively. The standard e r r o r of estimate using dbh is 3. 65 lb (33. 0%), and using the independent v a r i a b l e b a s a l a r e a 3. 63 lb (32.9%)-  B y virtue of its e a s i e r estimation, dbh i s p r e f e r a b l e  Basal Area ( sq f t )  47 to b a s a l area.  The relationship between needle d r y weight and tree  b a s a l a r e a i s presented i n F i g u r e 10.  f. branch weight (lb) Tables 14 and 15 present the independent v a r i a b l e eliminations f r o m the multiple r e g r e s s i o n s of f r e s h and d r y branch weight, respectively, on s e v e r a l independent v a r i a b l e s .  i) f r e s h weight b a s i s  T a b l e 14.  Intercept 71. 17 71. 17  R e g r e s s i o n Equations Illustrating the Relationship of F r e s h B r a n c h Weight (lb) with S e v e r a l Independent V a r i a b l e s , f o r 63 Lodgepole Pine T r e e s . 2 Independent V a r i a b l e s R DBH Ht. L C Ht. CL CW  BA  *T»'P  504.934  24.370  3. 238 2. 148 3.238 0. 427  504.927** -24.369 *p*p  59- 09  532. 092'"" -29.026  60. 20  502. O O 5 " " - 2 6 . 4 4 8 " "  3. 637 3. 648"  0.255  -2.419 -0.698  1.721  "P*P  0. 870 *>p-p  0.870  520.277  -19. 63  198. 220  •-25. 510  0.856 0. 824  15.094  -69. 09  10. 86 10. 77  ** 10.  0.867 0. 866  -P*P  67. 12  ^ E Hi  79  10. 76  ** 11.04 *# 12. 12 ••p-ir*  0. 773  13. 76  The best single independent v a r i a b l e i s b a s a l a r e a with accounts for 82.4 p e r cent of the v a r i a t i o n with a standard e r r o r of estimate of 12. 12 lb (42. 1%).  The relationship appears to be a m u l t i p l e r e g r e s s i o n  of f r e s h b r a n c h weight on the independent v a r i a b l e s b a s a l a r e a and dbh. This relationship r e m o v e s 85.6 per cent of the v a r i a t i o n and has a  o  o o o  Figure 1 0 .  J-  The  and T r e e B a s a l A r e a ( s q f t ) a t B r e a s t  o o o  Height.  N D Wt. (lb) = 5 9 . 4 9 9 B A (sq f t ) - 3 . 4 7 SE = 3.63 lb r = 0.825  VD ro  48  R e l a t i o n s h i p Between Needle Dry Weight ( l b )  *' • • j  2  t  O O O  CM  m  o o o CO CM  s— H  V  o oo  S  «  CM  •p  &  M •H <U  5: >>  Q  O O O  o  *  CM  <U H  tJ(U (U  oo o VO H  o o  o  o o o  l—  CO*  o o o  o o o  .080  160  ,240  .320 Basal Area  .400. (sq f t )  .480  .560  76^0  49 standard e r r o r of 11.04 lb (58. 3%). The relationship between branch f r e s h weight and t r e e b a s a l a r e a i s presented i n F i g u r e 11.  ii) d r y weight b a s i s  Table 15.  Intercept BA  R e g r e s s i o n Equations Illustrating the Relationship of D r y B r a n c h Weight (lb) with S e v e r a l Independent V a r i a b l e s , f o r 63 Lodgepole Pine T r e e s . 2 Independent V a r i a b l e s R DBH ICW.. J H t ; L C Tit. CL  ^E  37. 88  268.767  -12. 972  1.724  1.190  -1.334  0.962 0.870**  5.78  37. 88  268.764"" -12. 971  1.724  0.227  -0.372  0.870""  5.73  31. 45  283.223  -15. 450  1. 936 ' 0. 136  0. 867 " 5. 74  32. 04  267.208  -14. 078  1.942'  0.866"""  5.73  35. 73  276. 9 34"" -13. 579  0.856""  5.87  10. 45  105.509  0.824  6.45  36. 77  **  T  **  8.. 034  •A. «.»> 0.773  7. 33  The best independent v a r i a b l e for predicting d r y branch weight i a b a s a l area. T h i s v a r i a b l e accounted for 82.4 p e r cent of the v a r i a t i o n with a standard e r r o r of estimate of 6. 45 lb (42. 1%).  Dbh attributed  77. 3 p e r cent of the v a r i a t i o n with a standard e r r o r of estimate of 7. 33 lb (47.9%). The best multiple r e g r e s s i o n for predicting d r y branch weight u s e d b a s a l a r e a and dbh, accounting for 85. 6 p e r cent of the variation^and had a standard e r r o r of estimate of 5. 87 lb (38. 3%). The relationship between b r a n c h d r y weight and tree b a s a l a r e a i s presented i n F i g u r e 12.  g. crown weight (lb) C r o w n weight can be defined as the weight of the branches plus  50  0.80  JJ  B r . F Wt.  ( l b ) = 1 9 8 . 2 2 B A .(sq f t ) -  S E E ;  12.12  =  r  lb  2  =  19.63  0.824  L  .160  .240  .320  .400  .48o  .560  Basal Area (sq f t ) F i g u r e 11.  The R e l a t i o n s h i p Between Branch F r e s h Weight ( l b )  and T r e e B a s a l A r e a ( s q f t ) a t B r e a s t  Height.  .640  o o o d ' ,  ON |  Br. D Wt. (Ib) = 1 0 5 . 5 0 9 B A. (sq. f t ) - 10.45  O O  S Eg  = 6.45  lb.  r  2  =  51  0.824  o eg  o o o d  o o o d  VO  '.080  ,l60  .240  .320  .400  .480  .560  B a s a l A r e a (sq. f t ) Figure 1 2 .  The R e l a t i o n s h i p Between Branch Dry Weight (lb) Tree  B a s a l A r e a (sq. f t ) at B r e a s t  Height.  and  .640  52 needles.  The elimination*of r e g r e s s i o n coefficients f r o m the multiple  r e g r e s s i o n s of f r e s h crown weight and d r y crown weight on s e v e r a l independent v a r i a b l e s are presented i n Tables 16 and 17, respectively.  i) f r e s h weight b a s i s  Table 16.  Intercept  BA  R e g r e s s i o n Equations Illustrating the Relationship of F r e s h Crown Weight (lb) with S e v e r a l Independent V a r i a b l e s , for 63 Lodgepole Pine T r e e s . CW  Independent V a r i a b l e s DBH Ht. CL -15.303  -4. 116  3. 317  -15.302  -0. 863  0. 064  5. 848  -15.484  -0. 849  556. 02  6. 324  -23.266"  -42.76  265. 83'""  5. 896  26. 41  314.50  50. 12  494. 19' "  5. 878  50. 11  494.17"  5. 879  50. 76  498.26  35. 17  -106.68  *v* '1-  24.226  Ht.CL 3.253  R  2  S  0.948"" 10. 31 0. 948 0.948  If-T* 10. 22  10. 14  0.945""  10. 28  0.933  11. 26  0.923"*  12. 04  0.886'"  14.64  The best independent v a r i a b l e i s b a s a l a r e a which accounted for 92. 3 p e r cent of the v a r i a t i o n with a standard e r r o r of estimate of 12. 04 lb (24. 0%).  A m o r e reliable estimate can be obtained b y using a  multiple r e g r e s s i o n of f r e s h crown weight on the independent v a r i a b l e s b a s a l area, crown width and dbh. T h i s relationship accounted for 94. 5 per cent of the v a r i a t i o n with a standard e r r o r of estimate of 10. 28 lb (20.4%). The relationship between crown f r e s h weight and t r e e b a s a l a r e a i s presented i n F i g u r e 13.  C F WT.  .080  .160  (lb) =  .240  314.50  B A  .320 Basal Area  Figure 13.  (sq ft)  - 26Al  .400  .480  .560  (sq f t )  The R e l a t i o n s h i p Between Crown F r e s h Weight ( l b )  and Tree B a s a l A r e a ( s q f t ) a t B r e a s t  Height.  .640  54  ii) d r y weight basis  Table 17.  Intercept  BA T->  A  R e g r e s s i o n Equations Illustrating the Relationship of D r y Crown Weight (lb) with S e v e r a l Independent V a r i a b l e s , for 63 Lodgepole Pine T r e e s . 2 Independent V a r i a b l e s R CW DBH Ht. C L Ht. L C S~*11T  -r-.T-.TT  T  T  27.11  263.265  3.075  -8.332  -1.988  1.565  27.11  263.258  3.075  -8.331  -0.447  0.024  27.35  264.785"  3. 063 "  -8.399  -0.442  19.24  294.845  3.311  -12.449  -22.46  139.568""  -13.92  165.008  SE  / — T T T J - T / —  J  1.541  E  0.947  5.46  0.947  5.41  0.947"" 5.37 0.945  3.082""  5.44  0.932"" 5.97 0 . 9 2 l " " 6.37  -56.01  12.707  0.884  7.74  The best independent v a r i a b l e was b a s a l a r e a which accounted for 92. 1 p e r cent of total v a r i a t i o n with a standard e r r o r of estimate of 6. 37 lb (24. 2%).  Dbh alone accounted for 88.4 per cent of the v a r i a t i o n  with a standard e r r o r of estimate of 7.74 lb (29.4%). The v a r i a b l e s height, crown length and height to have crown did not significantly i m p r o v e the multiple linear relationship.  The relationship between  crown d r y weight and t r e e b a s a l a r e a i s presented i n F i g u r e 14.  h. s l a s h weight (lb) Slash weight i s the weight of the needles, and branches plus the unmerchantable top (less than 4 inches dob).  The results of the  elimination p r o c e d u r e for f r e s h slash weight on s e v e r a l independent v a r i a b l e s i s presented i n Table 18.  Results for the elimination of  independent v a r i a b l e s f r o m the relationship of d r y slash weight on  C D Wt. (lb) S E P  08o  = 165.008 B A (sq. f t )  = 6.37 l b  , l 6 0  .240  r  2  - 13-92  = 0.927  .320  .400  .480  . 5 6 0 .640  B a s a l A r e a (sq. f t ) F i g u r e Ik.  The R e l a t i o n s h i p Between Crown D r y Weight ( l b )  and T r e e B a s a l A r e a (sq. f t ) a t B r e a s t  Height.  56  s e v e r a l independent v a r i a b l e s i s presented i n Table 19.  i) f r e s h weight b a s i s  Table 18.  R e g r e s s i o n Equations Illustrating the Relationship of F r e s h Slash Weight (lb) with S e v e r a l Independent V a r i a b l e s , for 63 Lodgepole Pine T r e e s . 2  Intercept  Independent V a r i a b l e s DBH Ht. L C Ht. CW -37.108 6.490 -6.913 1.920  R  199.41  BA 713.293  199.41  713. 2 7 l " " -37.106" 0.518  -0.941  205.00  718.091"" -35.845" 0.548  -1.062  187.79  762.528"" -42. 778""0.289  0.692""  20.95  189.07  728.554""  0.69l"*  20.81  53.52  CL 5.972 0.698  ^E  1.920  39-859""  225.357  -1.67  21.30  0.698"" 21.11 0.697"' 20.98  0.643"" 22.19 17.001  0.592'" 23.72  A s shown i n Table 18, the best single independent v a r i a b l e i s b a s a l area, which accounts for 64. 3 p e r cent of the v a r i a t i o n with a standard e r r o r of 22. 19 lb (20.4%).  Height to l i v e crown, height, crown  width, and crown length do not i m p r o v e the r e g r e s s i o n . A multiple r e g r e s s i o n combining the independent v a r i a b l e s b a s a l a r e a and dbh accounted for 6 9 . 1 p e r cent of the total v a r i a t i o n i n f r e s h s l a s h weight and had a standard e r r o r of estimate of 20. 8 1 lb (19.2%).  The r e l a t i o n -  ship between slash f r e s h weight and tree b a s a l a r e a i s presented i n F i g u r e 15.  57  o o o  F i g u r e 15.  d  The  R e l a t i o n s h i p Between S l a s h F r e s h Weight ( l b )  and T r e e B a s a l A r e a ( s q f t ) a t B r e a s t  CM  o o o  S I . F Wt. S E  d  CM CM  E  (lb) =  = 22.19  lb  225.357  B A r  2  (sq ft)  Height.  * 53.52  = 0.643  o o o d o  CM  o o o d co  rH  o o o d vo  H  o o o d  H  O O O d  CM  O O O d o  rH  o o o d co  o o o d vo  080  ,l60  .240  .320 Basal Area  .1+00 (sq f t )  .1+80  .560  .640  58  ii) d r y weight b a s i s  Table 19.  R e g r e s s i o n Equations Illustrating the Relationship of D r y Slash Weight (lb) with S e v e r a l Independent V a r i a b l e s , for 63 Lodgepole Pine T r e e s .  Intercept BA  CW  Independent V a r i a b l e s DBH Ht. L C Ht.  R  SE  CL  E  •J**J*  86. 35  331.204  86. 35  331. 2 0 3 "  2. 951 -16.726  0. 606  -0.773  -16.726  0. 356  -0.523  2.951  0. 250 0 . 703 •3**3*  3. 250 -20. 212" 0. 227  351.-542  11. 56  *3*  703 0., 700  o>»»>  77. 32  •A.  0.  11. 66  11. 52  •3**3*  78. 30  324.767  3. 259 -17. 918"  0. 698  2. 930  0.  •XfJ*  18. 28  101. 275  26.40  125.457  0.  666  11.45  ** **  654  11. 95  12.06  *.».>  9.540  -4. 81  0. 612  12. 78  The s i n g u l a r l y best independent v a r i a b l e i s b a s a l a r e a which accounted for 65. 4 per cent of the total v a r i a t i o n i n d r y slash weight with a standard e r r o r of estimate of 12. 06 lb (21. 1%).  Dbh accounted  for 61. 2 p e r cent of the v a r i a t i o n with a standard e r r o r of 12. 78 l b (22.4%). The relationshipsbetween slash d r y weight and tree b a s a l a r e a are presented i n F i g u r e 16.  P r o p o r t i o n of component to total t r e e relationships  The means, standard deviations, m i n i m u m values and m a x i m u m values of the p r o p o r t i o n of the t r e e components' weight to the total weight of the tree, e x p r e s s e d as percentages, are presented i n Table 20.  59  Figure  l6.  The  R e l a t i o n s h i p Between S l a s h Dry Weight ( l b )  Tree B a s a l Area  (sq f t ) at Breast  Height.  and  60  Table 20.  Mean, Standard Deviation, M i n i m u m and M a x i m u m Values of the P r o p o r t i o n (as a per cent) of the Component Weight to the T o t a l T r e e Weight, for 63 Lodgepole Pine Trees. Mean  Component  T o t a l Stem:  Bark:  Needle:  Branch:  Crown:  Slash:  Minimum Value  Maximum Value  Fresh  89- 46  3. 10  81. 44  97. 39  Dry-  89. 83  3. 22  82. 80  97. 87  68. 70  14. 70  28. 30  87. 51  Dry-  68. 93  14. 58  28. 36  86. 88  Fresh  85. 21  3. 39  76. 93  93. 86  Dry  84. 48  3. 74  77. 33  93. 85  Fresh  4. 25  1. 60  0. 52  9. 31  Dry  5. 35  2. 00  0. 67  11. 10  Fresh  4. 63  1. 32  1. 28  8. 08  Dry  4. 40  1. 43  1. 10  8. 18  Fresh  5.91  2. 67  8. 88  13. 64  Dry  5.78  2. 62  8. 94  12. 77  Fresh  10. 54  3. 10  2. 61  18. 56  Dry  10. 17  3. 22  2. 13  17. 20  Fresh  31.30  14. 70  12. 49  71. 71  Dry  29.49  13. 35  13. 46  69. 45  Merchantable Stem: F r e s h  Bole wood:  Standard Deviation  .  The c o r r e l a t i o n s between the independent v a r i a b l e s (dbh, height, crown length, crown width, height to l i v e crown, and b a s a l area), and the dependent v a r i a b l e s (the component weight to total tree weight ratios) are p r e s e n t e d i n T a b l e 21.  61  Table 21.  Tree  Component  DBH  T o t a l Stem: F r e s h Dry Merchantable Fresh stem : Dry Bole Wood:  Bole Bark:  Needle:  Branch:  Crown:  Slash:  Simple C o r r e l a t i o n Coefficients Between the P r o p o r t i o n of Component Weight to T o t a l T r e e Weight and S e v e r a l T r e e C h a r a c t e r i s t i c s , for 63 Lodgepole Pine Trees.  Characteristics CL  Ht.  CW  Ht. L C  BA  -0.531  • 0. 372"" -0.414"" -0.564  0.012ns -0.533  -0.598  -0.446  • 0.461  • 0.646  -0. 026ns -0.599  0. 766""* 0. 806  0.475  0. 637  0.468  0. 760  0. 802  **  **  0.469  0. 628  -0. 396  -0. 462  Fresh  -0.423  ** -0.334  Dry  -0.491  -0.430  Fresh  -0. 132ns--0. 012ns -0.037ns-•0. 112ns  Dry  -0. 044ns--0. 086ns  -  -0.453" \•0. 551  0.104ns •-0.010ns  Fresh  0. 355  0. 270"  0.456  Dry  0.404  0. 323"  0. 467"" 0. 493  Fresh  0. 439  0. 298"  0.254*  0.437  Dry  0. 513  0.37l""  0. 3 1 l "  0. 523  Fresh  0. 531  0. 372  0.414  0.564""  Dry  0.598"" 0.446""  0.46l"  0. 646  -P-I*  0.437""  Fresh  -0.766  -0.806  -0.475  -0.637  Dry  -0.696  .-0. 718  -0.451  -0.500  0. 702 •CI*  0. 470 0. 039ns -0. 016ns -0. 058ns -0.013ns  0. 6 9 6 ' 0.422' 0.487 0.137ns -0. 054ns 'C'C  -0.192ns  0. 331  -0.137ns  0. 381"" 'P-l-  0.081ns  0.455  0.107ns  0. 527  -0.012ns  0. 533  0.026ns  0. 599 0. 702 -0.468 • -0.638 -0.384  The r e s u l t s presented in Table 21 suggest that the proportions of organic matter contained i n the total s t e m (fresh and dry), the bole wood content (fresh and dry), and the crown (fresh and dry) are most c l o s e l y associated with crown width.  The proportions of total tree weight  contained in the merchantable bole (fresh and dry), and i n the slash (fresh  62  and dry) were most highly c o r r e l a t e d with total tree height.  Basal  a r e a was the v a r i a b l e most c l o s e l y c o r r e l a t e d with the proportion of the total tree weight contained i n the bole bark ( f r e s h basis), and the branches ( f r e s h and dry). The proportions contained i n the bole bark (dry basis), and i n the needles ( f r e s h and dry) were most c l o s e l y associated with crown length.  The r e s u l t s indicate that the proportions of the total stem, bole wood, bole b a r k and s l a s h m a t e r i a l s to the total tree decrease with i n c r e a s i n g tree size. T h i s is indicated by the negative c o r r e l a t i o n coefficients.  It i s apparent that as tree size i n c r e a s e s the proportions  of the total tree contained i n the merchantable stem, branches, needles, and crown also i n c r e a s e .  Multiple r e g r e s s i o n elimination procedures, s i m i l a r to those used to establish the relationships of tree component weights on s e v e r a l independent v a r i a b l e s , were used to relate the per cent of total tree weight a s c r i b a b l e to each componentto dbh, height, crown length,  crown  width, height to l i v e crown, and b a s a l a r e a of each tree. The r e s u l t s of these percentage relationships are presented i n subsequent sections; however, unlike the weight relationships, only those r e g r e s s i o n equations containing significant r e g r e s s i o n coefficients are presented. In a l l cases, the six independent v a r i a b l e s were tested and it can be a s s u m e d that those v a r i a b l e s not appearing i n the reported equations  did not improve the relationships by r e m o v i n g a significant amount of the r e s i d u a l variation.  a. total s t e m per cent (%)  i) f r e s h weight basis The results of the analysis indicated that a multiple r e g r e s s i o n did not i m p r o v e the estimation the f r e s h total stem per cent ( F T S P ) . The two best simple l i n e a r r e g r e s s i o n s are:  F T S P (%) = 95. 789 - 1.322 SE  E  = 2. 58 %  2 r  = 0. 318"*  F T S P (%) = 92. 535 - 1.259 SE_  = 2. 6 4 %  r  CW  BA  = 0. 284  E C r o w n width accounted for 31.8 per cent of the v a r i a t i o n and b a s a l a r e a accounted for 28. 4 per cent of the v a r i a t i o n with standard e r r o r s of estimate of 2. 5 8 % (2. 9%) and 2. 6 4 % (3. 0%), r e s p e c t i v e l y . relationship of F T S P on CW  The  i s presented i n Appendix I I I - l .  ii) d r y weight b a s i s The two best independent v a r i a b l e s for relating the dry total s t e m per cent ( D T S P ) to t r e e c h a r a c t e r i s t i c s were crown width and b a s a l area. The simple l i n e a r r e g r e s s i o n s of dry total stem per cent on crown width and b a s a l a r e a are:  64  D T S P (%) = 97. 363 - 1. 574 S E _ = 2.48% E  CW  = 0.417""  r  D T S P (%) = 93.418 - 14. 707 S E _ = 2. 6 0 % E  2 t  BA  = 0. 359"'"  C r o w n width accounted for 41. 7 per cent of the v a r i a t i o n with a standard e r r o r of estimate of 2. 4 8 % (28%). The second best independent v a r i a b l e BA accounted for 35. 9 per cent of the v a r i a t i o n and had a standard e r r o r of estimate of 2. 6 0 % (2. 9%).  The relationship of D T S P in CW  i s presented  in Appendix III-2.  b. merchantable stem per cent (%)  i) f r e s h weight b a s i s The independent v a r i a b l e s crown width, height, crown length, and height to l i v e crown did not account for a significant amount of the v a r i a t i o n when combined i n a multiple r e g r e s s i o n with b a s a l a r e a and dbh. The multiple l i n e a r r e g r e s s i o n of the f r e s h merchantable s t e m per cent ( F M S P ) on b a s a l a r e a and dbh i s :  F M S P (%) = 41. 339 D B H SE^ E  = 6.40%  - 443. 226 B A R  - 91. 084  = 0. 817""  T h i s multiple r e g r e s s i o n accounted for 81.7 per cent of the v a r i a t i o n with a standard e r r o r of estimate of 6.40%  (9. 3%).  65  The two best independent v a r i a b l e s for simple l i n e a r relationships are height and dbh. The simple l i n e a r r e g r e s s i o n s of f r e s h merchantable s t e m p e r cent on height and dbh are:  F M S P (%) = 1. 839 Ht. - 38.802  S E „ = 8. 7 7 % E  = 0.650""  2 r  F M S P (%) = 24.952 + 6.748 D B H  SE=9-53%  2 r  = 0.586"*  Of the total v a r i a t i o n i n f r e s h merchantable s t e m proportion, 65. 0 per cent was attributable to height, which had a standard e r r o r of estimate of 8. 7 7 % (12. 8%).  Dbh accounted for 58. 6 p e r cent of the  v a r i a t i o n with a standard e r r o r of estimate of 9. 5 3 % (13. 9%). T h e relationship of D M S P on dbh is presented i n Appendix 111-3.  ii) d r y weight b a s i s Of the six independent v a r i a b l e s i n the multiple r e g r e s s i o n only dbh and b a s a l area contributed significant amounts to the v a r i a t i o n accounted for. T h e multiple r e g r e s s i o n of d r y merchantable stem per cent (DMSP) on dbh and b a s a l area i s :  D M S P (%) = 41. 473 D B H - 446. 259 B A - 90. 972  S E „ = 6. 3 7 % E  R  2  - 0. 815"  The multiple r e g r e s s i o n combining dbh and b a s a l a r e a accounted for  66  81.5 p e r cent of the variation. T h e standard e r r o r of this multiple r e g r e s s i o n was 6. 3 7 % (9. 2%).  Height was the best single independent v a r i a b l e accounting for 64.4 p e r cent of the v a r i a t i o n with a standard e r r o r of estimate of 8. 7 7 % (12. 7%). T h e second best independent variable, dbh accounted for 57. 8 p e r cent of the total v a r i a t i o n with a standard e r r o r of 9. 5 5 % (13.9%).  T h e simple l i n e a r r e g r e s s i o n s of D M S P on height and  dbh are:  D M S P (%) = 1. 815 Ht. - 37. 154 S E _ = 8. 7 7 % E  2 r  = 0. 644  **  D M S P (%) = 25.857 + 6. 645 D B H  S E _ = 9. 5 5 % E  = 0. 578  The relationship of D M S P on dbh i s presented i n Appendix III-4.  c. bole wood p e r cent (%)  i) f r e s h weight b a s i s The most satisfactory independent v a r i a b l e s for accounting for the v a r i a t i o n a s s o c i a t e d with f r e s h bole wood p e r cent ( F B W P ) were crown width and dbh.  The use of a multiple r e g r e s s i o n did not  account for a significant amount of additional variation. T h e simple l i n e a r r e g r e s s i o n s of f r e s h bole wood p e r cent on crown width and dbh are:  67  F B W P (%) = 90. 889 - 1. 186 CW  S E ^ = 3.03% E  2 r  = 0.914"*  F B W P (%) = 90. 779 - 0. 859 D B H S E _ = 3. 1 0 % E  =0. 179  r  Crown width accounted for 21.4 per cent of the v a r i a t i o n and 17.9 per cent of the v a r i a t i o n was attributable to dbh, with standard e r r o r s of estimate of 3. 0 3 % (3. 6%) and 3. 1 0 % (3. 6%), respectively.  The  relationship of F B W P on dbh i s presented in Appendix III-5.  ii) d r y weight basis , S i m i l a r r e s u l t s to those obtained for the f r e s h bole wood per cent were obtained for the d r y bole wood per cent (DBWP). The use of a multiple l i n e a r r e g r e s s i o n  did not i m p r o v e the relationship of  d r y bole wood per cent to tree c h a r a c t e r i s t i c s and the best simple l i n e a r independent v a r i a b l e s were crown width and dbh.  The simple  r e g r e s s i o n s of d r y bole wood per cent on crown width andfclbha r e :  D B W P (%) = 91.936 - 1. 559 CW S E „ = 3. 1 5 % E  2 r  = 0. 303""  D B W P (%) = 91. 614 - 1. 101 D B H S E _ = 3. 2 8 % E  r  = 0. 2 4 l " "  C r o w n width accounted for 30.3 per cent of the v a r i a t i o n with a standard e r r o r of estimate of 3. 1 5 % (3. 7%).  Dbh accounted for 24. 1 per cent  68 of the total v a r i a t i o n and had a standard e r r o r of estimate of 3. 2 8 % (3. 9%).  The relationship of D B W P on dbh i s presented in Appendix  III-6.  d. bole b a r k p e r cent (%)  i) f r e s h weight basis No significant r e g r e s s i o n equation could be found to relate the f r e s h bark weight p e r cent to the tree c h a r a c t e r i s t i c s dbh, height, crown length, crown width, height to l i v e crown, and b a s a l area.  ii) d r y weight basis None of the independent v a r i a b l e s tested, either i n d i v i d u a l l y or i n combination, provide a relationship which accounted for a significant amount of the total v a r i a t i o n of the d r y b a r k p e r cent.  a. needle p e r cent (%)  i . f r e s h weight basis The independent v a r i a b l e s dbh, crown width, height to live crown, and b a s a l a r e a contributed significantly to the v a r i a t i o n accounted for when combined i n a multiple l i n e a r r e g r e s s i o n for relating the f r e s h needle p e r cent ( F N P ) to s e v e r a l tree c h a r a c t e r i s t i c s . The multiple l i n e a r relationship of F N P on these  independent  variables i s : F N P (%) = 2. 591 D B H + 0.487 CW-0. 125Ht.LC-32. 151BA-1. 505 SE^  = 1. 05 %  R  2  = 0.411"  The preceding multiple r e g r e s s i o n removed 41. 1 per cent of the v a r i a t i o n and had a standard e r r o r of estimate of 1. 0 5 % (22. 6%).  The best simple l i n e a r r e g r e s s i o n was the f r e s h needle per cent on crown length.  F N P (%) = 2. 883 + 0. 102 C L  S E _ = 1. 1 9 % E  = 0.208  r  T h i s relationship accounted for 20. 8 per cent of the v a r i a t i o n and offered a standard e r r o r of estimate of 1. 1 9 % (25. 7%).  Dbh alone accounted for only 12. 6 p e r cent of the v a r i a t i o n with a 1. 2 5 % (26.9%) standard e r r o r of estimate. The relationship of F N P on C L i s presented i n Appendix 111=7.  ii) d r y weight b a s i s S i m i l a r r e s u l t s to those obtained for the f r e s h needle per cent were obtained f o r the d r y needle per cent (DNP). The multiple r e g r e s s i o n of d r y needle per cent on dbh, crown width, height to l i v e crown and b a s a l a r e a accounted for 41. 9 p e r cent of the v a r i a t i o n and had a standard e r r o r of estimate of 1. 13% (23. 7%). The equation of this multiple r e g r e s s i o n i s : DNP  (%) = 2. 586 D B H + 0. 578 CW SE  r  E  = 1. 1 3 %  R  2  - 0. 119 Ht. LC-32. 080 B A  = 0.419*'"*  70  Crown width was the best independent v a r i a b l e for relating d r y needle per cent to a single independent v a r i a b l e by means of a simple l i n e a r r e g r e s s i o n . The simple linear relationship of d r y needle per cent on crown length i s :  DNP  (%) = 1. 833 + 0. 536  SE  E  = 1.26%  r  CW = 0. 243""  Crown width accounted for 24.3 p e r cent of the v a r i a t i o n and had a standard e r r o r of estimate of 1. 2 6 % (28. 6%). The relationship of D N P on CW  i s p r e s e n t e d i n Appendix 111-8.  f. branch p e r cent (%)  i) f r e s h weight b a s i s The results of the analysis indicated that the use of a multiple r e g r e s s i o n of the f r e s h branch p e r cent ( F B P ) on dbh, height, crown length, crown width, height to l i v e crown did not account for s i g n i f i cantly m o r e v a r i a t i o n than the simple linear r e g r e s s i o n of f r e s h b r a n c h per cent on b a s a l a r e a alone. The second best simple linear r e l a t i o n ship was f r e s h b r a n c h p e r cent on dbh. The equations of the two simple linear regressions are:  F B P (%) = 3. 646 + 9. 258 B A S E ^ = 2. 4 0 %  r  = 0. 207" *  FBP  (%) = 1. 344 + 0. 704  SE  E  = 2.42%  _  2  DBH  = 0. 193"""  B a s a l a r e a and dbh accounted for 20. 7 and 19- 3 per cent of the variation, r e s p e c t i v e l y . The standard e r r o r s of estimate u s i n g b a s a l a r e a was  2. 4 0 % (40. 6%) and using dbh was  relationship of F B P  2.42% (40. 9%).  The  on B A i s presented i n Appendix III-9.  ii) d r y weight b a s i s A s was  the case with f r e s h b r a n c h per cent there i s apparently  no advantage to be gained by using a multiple r e g r e s s i o n to relate dry b r a n c h per cent (DBP) to t r e e size. The two best simple l i n e a r r e g r e s s i o n s were based on the independent v a r i a b l e s b a s a l a r e a and crown width. T h e s e equations are:  DBP  (%) = 3. 202 + 10. 541  S E _ = 2.25% E  DBP SE  = 0.278'"  r  (%) = 0. 804 + 1. 039  E  =2. 2 5 %  BA  2 r  CW  = 0. 274"""  The independent v a r i a b l e b a s a l a r e a accounted for 27.8 per cent of the v a r i a t i o n and had a standard e r r o r of 2. 2 5 % (38.9%).  C r o w n width  accounted for 27.4 per cent of the v a r i a t i o n with a standard e r r o r of 2. 2 5 % (38. 9%). The relationship of D B P Appendix 111-10.  on CW  i s presented i n  72  j. crown p e r cent (%)  i) f r e s h weight b a s i s T h e r e i s no advantage to using a multiple l i n e a r r e g r e s s i o n relationship because the independent v a r i a b l e s dbh, height, crown length, height to l i v e crown, and b a s a l a r e a do not contribute significantly to the relationship once f r e s h crown p e r cent ( F C P ) has been adjusted f o r crown width. The b a s a l a r e a is the second best independent v a r i a b l e . The simple l i n e a r r e g r e s s i o n s of f r e s h crown per cent on crown width and b a s a l a r e a a r e :  F C P (%) = 4. 211 + 1. 322  S E _ = 2. 5 8 % E  r  CW  =0. 318""  F C P (%) = 7.465 +12. 591 B A  S E _ = 2. 6 4 % E  r  =. 0. 284""  The r e g r e s s i o n of f r e s h crown per cent on crown width accounts for 31.8 per cent of the v a r i a t i o n and had a standard e r r o r of estimate of 2. 5 8 % (24. 5%).  B a s a l a r e a accounted for 28. 4 per cent of the  v a r i a t i o n with a standard e r r o r of estimate of 2. 6 4 % (25.0%). The relationship of F C P on CW  i s presented i n Appendix IH—11-  ii) d r y weight b a s i s A s with f r e s h crown weight,  crown width and b a s a l a r e a were  the two independent v a r i a b l e s most c l o s e l y a s s o c i a t e d with d r y crown  73  per cent (DCP). Nothing was  gained f r o m using a multiple r e g r e s s i o n .  The r e g r e s s i o n equations of d r y ratio on crown width and b a s a l a r e a are: DCP  (%) = 2. 637 + 1. 574  SE  DCP  =Z.48%  =  2 r  CW  °->18  (%) = 6. 582 + 14. 708  S E _ = 2. 6 0 %  2  r  Jii  BA  = 0. 359'  The v a r i a t i o n accounted for by crown width amounted to 41.8 per cent of the total variation. C r o w n width offered a standard' e r r o r of estimate of 2.48%  (24.4%). B a s a l a r e a accounted for 35.9 per cent of the  v a r i a t i o n with a standard e r r o r of estimate of 2. 6 0 % (25. 6%). relationship of D C P  on CW  The  i s p r e s e n t e d i n Appendix 111-12.  h. s l a s h per cent (%)  i) f r e s h weight b a s i s The best relationship for d e s c r i b i n g the f r e s h s l a s h per cent (FSP) was  a multiple r e g r e s s i o n of f r e s h s l a s h per cent on dbh and b a s a l  area. The addition of the other independent v a r i a b l e s did not s i g n i f i cantly improve this relationship. The multiple r e g r e s s i o n equation i s :  F S P (%) = 191. 082 - 41. 339 D B H SE  E  = 6. 4 0 %  r  = 0. 817""  + 443. 222  BA  74  The two v a r i a b l e s combined accounted for 81.7 per cent of the v a r i a t i o n with a standard e r r o r of estimate of 6.40%  (20.4%).  The best simple l i n e a r relationship i s :  F S P (%) = 138. 801 - 1. 839 Ht. S E _ = 8. 7 7 % E  r  = 0. 650""  Height alone accounted for 69-0 per cent of the total v a r i a t i o n with a standard e r r o r of estimate of 8. 7 7 % (28. 0%). The relationship of F S P on Ht. i s presented i n Appendix III-13.  ii) d r y weight b a s i s The addition of the independent v a r i a b l e s height, crown width, crown length, and height to l i v e crown did not contribute significantly to the accounted for v a r i a t i o n i n dry slash per cent (DSP) after it has been adjusted for dbh and b a s a l area. The multiple r e g r e s s i o n of dry slash per cent on dbh and b a s a l area accounted for 61.2 per cent of the v a r i a t i o n with a standard e r r o r of estimate of 7. 7 8 % (26. 4%). The multiple l i n e a r r e g r e s s i o n equation i s :  DSP  (%) = 160. 681 - 33. 913 D B H SE  E  = 7. 7 8 %  + 363. 137  BA  = 0. 672""  The best simple l i n e a r r e g r e s s i o n i s that of d r y s l a s h per cent on height. The simple l i n e a r equation i s :  75  DSP (%) = 116. 443 - 1. 487 Ht.  S E _ = 9. 3 7 % E  2 r  = 0. 515"""  Height accounted for 51.5 p e r cent of the v a r i a t i o n and had a standard e r r o r of estimate of 9- 37%. (31. 8%). The relationship of DSP on Ht. is presented i n Appendix 111-14.  Some crown and related c h a r a c t e r i s t i c s of lodgepole pine. Table 22 presents the means, standard deviations, and m a x i m u m and m i n i m u m values obtained for the crown c h a r a c t e r i s t i c s analysed.  Table 22.  Mean Standard Deviation, Maximum, and M i n i m u m Values of S e v e r a l C r o w n C h a r a c t e r i s t i c s , for 63 Lodgepole Pine T r e e s .  Crown Characteristics  D r y Needle Weight (lb) Number of Needles  Mean  Standard Deviation  Maximum  Minimum  11 . 05  8. 59  37. 84  1. 00  245 . 878  197. 362  892,, 525  34, 473  41. 22  5. 07  50. 80  25. 10  17. 24  5. 94  32. 00  8. 00  4. 79  1. 32  8. 80  2. 50  C r o w n volume (cu. ft. )  388. 94  390. 48  2,067. 93  120.26  Crown surface a r e a '(sq. ft.)  598. 68  218. 40  1,255. 21  256.63  Height to L i v e  Crown(ft)  Crown length (ft) Crown width (ft)  The crown c h a r a c t e r i s t i c s of lodgepole pine a r e highly v a r i a b l e i n nature as pointed out by the data presented i n Table 22. Height to  76 l i v e crown appears to be the most constant of the variables m e a s u r e d and the number of needles per tree exhibited the widest range (having a coefficient of v a r i a t i o n of 80. 27 p e r cent).  C o r r e l a t i o n coefficients (r) between the crown c h a r a c t e r i s t i c s and s e v e r a l tree c h a r a c t e r i s t i c s a r e shown i n Table 23.  Table 23.  Simple C o r r e l a t i o n Coefficients Between S e v e r a l T r e e and Crown C h a r a c t e r i s t i c s , for 63 Lodgepole P i n e T r e e s .  Crown Characteristic  Tree Characteristic Ht.  DBH •A.  vU  CL  CW  BA  Ht. L C •A.  -A.-A.  0. 982  Dry needle weight  0. 907  0 . 773  0. 724"" 0. 815"" 0. 133ns  Number of needles  0. 867  0 . 729  0. 680  0. 788  0. 130ns  0. 908  •-0 . 323  0. 231  1 .. 000  0.691  5JCSJC  •j*  -X*  Height to l i v e crown 0. 305"  0 . 489  Crown length  0. 720  0 .668"" 1.000"" 0. 553  C r o w n width  0. 818  0 .691"" 0 .553"" 1.000"" 0. 231ns  •A**A>  Crown volume  •A.  vt, 0  **  -0. 323"  •A. -A.  •A. -A-  •A..A.  0. 610  0. 870 •A» «A- . 728 Crown surface area 0. 9 5 l " " 0 .903"" 0. 718  ** 0. 730 •A#«A» 0. 820  0.975  0. 211ns  0.804"" 0. 289  0. 885 •A.  si*  0. 963  A s can be seen f r o m the correlations p r e s e n t e d i n T a b l e 23, the crown c h a r a c t e r i s t i c s studied were most c l o s e l y associated with b a s a l a r e a and dbh, with the exception of crown volume which i s most  strongly  c o r r e l a t e d with crown width. The preceding results indicate that size of the various crown characteristics i n c r e a s e s as tree size i n c r e a s e s with the exception of crown length which decreases as the height to l i v e crown i n c r e a s e s .  The following simple l i n e a r r e g r e s s i o n  equations  77 are the best simple l i n e a r relationships for relating crown size to t r e e size both s t a t i s t i c a l l y and p r a c t i c a l l y .  a. D r y needle weight: D.N. Wt. (lb) = 59-499 B A - 3.47 SE  E  = 3. 63 lb (32. 9%)  = 0.825""  r  b. Number of needles: N N = 102. 595 D B H - 419. 194 S E „ = 99. 131 (41. 31%) E  = 0. 752"*  2 r  c. Height to l i v e crown: Ht. L C (ft) = 35. 21 + 0. 926 Dbh (in) S E _ = 4. 83 ft (12%) E  = 0.093  d. C r o w n length: C L (ft) = 9. 827 + 33. 066 B A S E „ = 4. 09 (23. 72%) E  2 = 0.533  e. C r o w n width: CW  (ft) = 0. 587 + 0. 648 D B H SE_, = 0. 765 (16. 0%) E  = 0.670  f. C r o w n volume: C r . vol. (cu. ft.) = 2, 635. 58 B A - 54. 47 SE  = 185. 15 (31.2%)  r  2  = 0.784**  78  g. Crown surface  area:  CR. S. A. (sq.ft.) = 1, 511.49 B A + 229. 68 S E = E  92.45 (15.4%)  = 0.824"""  r  Table 24 presents the simple c o r r e l a t i o n coefficients between s e v e r a l crown c h a r a c t e r i s t i c s and tree volume i n cubic feet (ob), and total t r e e weight i n pounds.  Table 24.  Simple C o r r e l a t i o n Coefficients Between T r e e Volume and Weight, and C r o w n Volume, Crown Surface A r e a , D r y Needle Weight, and Number of Needles, for 63 Lodgepole P i n e Trees.  Crown C h a r a c t e r i s t i c  T r e e Volume (db) T o t a l T r e e Weight  D r y needle weight  0.911  0. 935  C r o w n surface a r e a  0. 903  0. 909  Number of needles  0. 873  0. 904  C r o w n volume  0.866'  0. 882  F r o m the p r e c e d i n g c o r r e l a t i o n coefficients (Table 24) i t can be concluded that there i s a strong association between the size of a tree and the size of that tree's crown. weight are most  Both tree volume and total tree  c l o s e l y c o r r e l a t e d with d r y needle weight. Simple  l i n e a r r e g r e s s i o n techniques r e v e a l e d that d r y needle weight accounted for 83 and 87 per cent of the total v a r i a t i o n for tree volume and total t r e e weight r e s p e c t i v e l y .  The following simple l i n e a r r e g r e s s i o n equation was obtained for r e l a t i n g the number of needles supported by one cubic foot of t r e e  79  volume (ob) to tree dbh. NN/cu. f t . v o l . = 1 5 , 6 2 6 + 1 , 9 3 0 . 8  DBH  SE = 9 , 8 9 1 needles/cu. f t . ( 3 5 . 1 $ ) E  r  2  = O.098*  This r e l a t i o n s h i p , suggested that the number o f needles per cubic foot volume increases as t r e e s i z e increases, thus i t appears that l a r g e r . trees have a greater capacity f o r future photosynthate production than small t r e e s .  However the standard error o f the r e l a t i o n s h i p was very  high and the regression only accounted f o r 9«8 per cent o f the t o t a l variation. Results o f the a n a l y s i s o f number o f needles and dry needle weight per square foot o f crown surface area, and per cubic foot o f crown volume i n d i c a t e d that these dependent v a r i a b l e s were most c l o s e l y associated w i t h tree dbh. The r e l a t i o n s h i p s i n v o l v i n g crown volume were poorly c o r r e l a t e d w i t h dbh and i t accounted f o r only 9«0 per cent of the t o t a l v a r i a t i o n i n number of needles per cubic foot crown volume and 1 2 . 0 per cent o f the v a r i a t i o n i n pounds per cubic foot crown volume. Dbh d i d , however, account f o r 5 8 . 9 P  e r  cent o f the v a r i a t i o n i n dry  needle weight per square foot crown surface area and ' 5 1 . 0 per cent o f the v a r i a t i o n i n number o f needles per square foot crown surface area. The simple l i n e a r regressions i n v o l v i n g crown surface area are:  80  D.N.Wt/sq.ft. = 0.00374 dbh - 76.26 SE  = 0. 00525 (32%)  2 r  = 0. 589  W  E NN/sq. ft. = 80.55 dbh -151.18 S E = E  132.85 (36%)  r  =0.510  T h e r e appears to be v e r y little relationship between average needle length and tree size whether e x p r e s s e d i n t e r m s of t r e e height or dbh, and with crown size e x p r e s s e d as d r y needle weight.  A multiple  r e g r e s s i o n of average needle length on dbh, height, and d r y needle weight accounted for only 7. 8 p e r cent of the v a r i a t i o n . T r e e height the best independent variable, accounted for 7. 3 p e r cent for the variation. The results indicated that needle length i n c r e a s e d with f r e e height.  A simple l i n e a r r e g r e s s i o n of needle length on needle width accounted for 68. 3 p e r cent of the v a r i a t i o n with a standard e r r o r of estimate of 14. 6 m m  (31%). The r e g r e s s i o n equation d e r i v e d was:  Needle length (mm) = 71. 87 Needle width (mm) S E „ = 14. 57 m m E  (27. 3%)  r  - 37. 85  = 0.683"""  The average needle length m e a s u r e d i n this study was 47. 2 m m inches) and the average needle width was 1. 18 m m  (1. 86  (0. 05 inches).  T a b l e 25 presents the means, standard deviations, and m i n i m u m s and m a x i m u m values obtained for average needle length (mm) and the  81 number of needles p e r half g r a m (dry weight) of the 63 t r e e s analyzed.  Table 25.  Mean, Standard Deviation, M i n i m u m and M a x i m u m Values Obtained for A v e r a g e Needle Length (mm) and Number of Needles per H a l f G r a m ( D r y Weight) , for 63 Lodgepole Pine T r e e s .  Needle C h a r a c t e r i s t i c  Mean  Standard Deviation  Minimum Value  Maximum Value  A v e r a g e Length (mm)  53.39  5.64  39.6  66.5  Number p e r H a l f G r a m  25.08  5.08  16.0  38.0  Summary Most t r e e and component weights a r e c l o s e l y a s s o c i a t e d with tree b a s a l a r e a and dbh. A l l of the weight v a r i a b l e s analyzed i n c r e a s e d with i n c r e a s i n g t r e e size. The best simple l i n e a r relationships between tree o r component weight and an independent v a r i a b l e a r e presented i n Table 26.  82  Table 26.  Dependent Variable  A S u m m a r y of the Best Simple L i n e a r Relationships Between T r e e and Component Weight (lb) and the Independent V a r i a b l e s Measured, for 63 Lodgepole Pine T r e e s .  Intercept  Regression Coefficient  TTFWt.  - 73.71  2,095. 90  BA  0. 976  46. 52  TTDWt.  - 24.25  1, 061. 60  BA  0.964  27. 01  TSFWt.  - 47.30  1,781. 40  BA  0.961  47. 76  TSDWt.  -249.04  Dbh  0.952 '"26. 70  BWFWt.  - 46.89  1,705. 70  BA  0.962  44. 55  BWDWt.  -234.56  66. 43  Dbh  0. 951  25. 23  BFWt.  - 75. 33  1. 598  Ht.  0.604  8.41  BDWt.  - 51.97  1. 103  Ht.  0. 604  5. 80  NFWt.  -  116.279  BA  0.825  7. 09  NDWt.  - 3.47  59.499  BA  0.825  3. 63  B r . F Wt.  - 19.63  198. 22  BA  0.824  12. 12  B r . D. Wt.  - 10.45  105.509  BA  0.824  6. 45  C F Wt.  - 26.41  314.50  BA  0.923  C D Wt.  - 13.92  165.008  BA  0. 921"" 6. 37  SI. F. Wt.  53. 52  225.357  BA  0.643"" 22. 19  SI. D. Wt.  26. 40  BA  0.654  6. 79  70. 59  125.457  Independent Variable  r  SE  12. 04  12. 06  Although the weights of the component s i n c r e a s e with tree size the proportion of the total tree weight which each component contributes v a r i e s with tree size. A s tree size i n c r e a s e s the p r o p o r t i o n of the total t r e e consisting of the merchantable bole, needles and branches i n c r e a s e s , and the p r o p o r t i o n consisting of bolewood, bole bark, and s l a s h  decreases.  The reason for the i n c r e a s i n g proportions contained i n the needles and  83  branches with i n c r e a s i n g tree size i s not clear but may be explained by the fact that although crown length i n c r e a s e s with tree size, height to l i v e crown i s r e l a t i v e l y constant r e g a r d l e s s of tree size. The independent v a r i a b l e most c l o s e l y associated with each proportion v a r i e d with the component studied.  A n analysis of the crown c h a r a c t e r i s t i c s suggested that the height to l i v e crown i s r e l a t i v e l y constant for the trees investigated. C r o w n size i n c r e a s e d with i n c r e a s i n g tree size with the exception of height to l i v e crown. D r y needle weight i s v e r y c l o s e l y associated with tree size both i n t e r m s of volume and weight.  T h e s e results  emphasize the close association between the growth of a tree and the capacity of the tree to produce photosynthate. A n i n c r e a s e i n the number of needles per cubic foot volume of trees with i n c r e a s i n g tree size suggests that large t r e e s have a greater capacity for future growth than s m a l l t r e e s . The r e s u l t s also suggested that there i s a c l o s e r association between crown surface a r e a and t r e e size than between crown volume and tree size.  The needle c h a r a c t e r i s t i c s of Lodgepole pine are highly v a r i a b l e and appear to be unrelated to tree c h a r a c t e r i s t i c s . T h e r e i s not a high degree of association between needle length and width.  84  SAMPLING FOR  BIO MASS  Introduction Although there have been numerous studies c a r r i e d out involving measurements of b i o m a s s and the weights of tree components, too little attention has been given to the suitability or r e l i a b i l i t y of the methods u s e d or the results obtained.  It i s obvious that any attempt to m e a s u r e a l l of the trees present in an a r e a i s i m p r a c t i c a l and a f o r m i d a b l e task.  The m a s s i v e nature  of the trees presentstechnical problems i n both handling and weighing the t r e e s .  Consequently, it appears that the only suitable alternative  is to r e s o r t to a method of sampling to reduce the time and effort spent on data collection.  Two  general methods have been used i n the past to estimate the  amount of o r g a n i c matter. The f i r s t method involves the  development  of. a functional relationship between the component weights and an independent v a r i a b l e such as dbh.  Then u s i n g a stand table i n conjunction  with the f o r m u l a the weight of the component per unit a r e a i s calculated. T h i s method was p i o n e e r e d by Kittredge (1944 and 1948), and has since been used by Cable (1958), Ovington and Madgwick (1959),  Fahnestock  (I960), M u r a r o (1966), K i i l (1966), and Satoo and Senda (1966).  85 The second method i s based on the component weights of a t r e e of mean dimension.  The mean t r e e m a y be established on the  b a s i s of b a s a l a r e a o r dbh (Tadaki et al. (1961,  1962, and 1963),  A t t i w i l l (1966), and Satto and Senda (1966), o r on the b a s i s of mean t r e e size (Molchanov (1949), Ovington (1956,  1957 and 1962), and  Ovington and Madgwick (1959)). The component weight p e r unit a r e a can then be obtained b y multiplying the mean tree component weight by the number of trees p r e s e n t per unit area.  T h e r e are e r r o r s inherent i n both methods. The f i r s t method assumes that the relationship developed f r o m trees i n one stand r e m a i n s constant and thus can be applied to other stands. A c c o r d i n g to Kittredge (1944) and Cable (19 58) the relationship of leaf weight on dbh is applicable to different sizes, densities, crown classes, and ages up to the age of culmination of growth and beyond that age for tolerant species i n all-aged stands.  However, Satoo (1962) r e p o r t e d  that the r e g r e s s i o n constants did change f r o m stand to stand.  Madg-  wick (1963) also suggested that the relationship between dbh and foliage weight m a y be affected b y stand structure, season of sampling, genetic variation and p o s s i b l y site quality.  S i m i l a r l y , the mean tree method has been the subject of a l a r g e amount of c r i t i c i s m (Ovington and Madgwick (19 59), Fahnestock (I960), Satoo (1962), Madgwick (1963), B a s k e r v i l l e (1965), A t t i w i l l (1966), and Satoo and Senda (1966)]. Ovington and Madgwick (1959) suggested  86  that the estimation of each different component should be considered separately.  B a s k e r v i l l e (1965) concluded that it i s u n l i k e l y that a  t r e e which i s average i n t e r m s of one component w i l l be average i n t e r m s of other components.  T h i s i s , i n a l l probability, r e l a t e d to  the fact that the proportions of the different components to the total tree change with tree size.  Another p r o b l e m a r i s e s because of the  difficulty of locating a tree of exactly average attributes.  Satoo and Senda (1966), after comparing the two methods, reported that estimates using the mean tree method underestimated the r e s u l t s obtained using the stand method.  table-functional relationship  S i m i l a r results were reported by A t t i w i l l (1966);  A t t i w i l l concluded:  "The choice of the tree of mean diameter as a sampling unit for estimating d r y weight i n forests, therefore has no t h e o r e t i c a l basis; estimates so derived m a y be s e r i o u s l y , i n e r r o r , the magnitude of the e r r o r for a p a r t i c u l a r species depending p r i m a r i l y on the distribution of diameters within the stand. The tree of mean b a s a l area i s a m o r e l o g i c a l sampling unit for estimating total dry weight. ..."  It is generally conceded that the mean tree method is l e s s desirable than the other method; however, the mean tree method does offer the advantages of speed and ease of application.  Rennie (1966) suggested a method for sampling b i o m a s s and pointed out that u s u a l l y not l e s s than 20 trees must be sampled for a r e l i a b l e statistical c o r r e l a t i o n analysis.  Rennie favored an approach  of mean b a s a l a r e a but cautioned that i t is imperative to sample enough mean trees to be within p r e - s e t confidence  limits.  Ando_et a L (1959) recommended fractional sampling of s e v e r a l t r e e s within a stand to obtain the weight of components. To obtain the weight of components for the stand the ratio of the stand b a s a l area to the s u m of the b a s a l areas of the sample trees i s m u l t i p l i e d by the s u m of the weight of components of the sample t r e e s .  Madgwick (1963) stated that the use of the average tree method gives b i a s e d results and since too many trees would be r e q u i r e d f o r random sampling, a method of stratified random sampling (random sampling within size classes) offered the best compromise.  A method  s i m i l a r to this was adopted by Weetman and H a r l a n d (1964) and by B a s k e r v i l l e (1965 a).  Method of A n a l y s i s In order to determine the number of sample trees r e q u i r e d to obtain a d e s i r e d confidence i n t e r v a l of the mean with some specified degree of confidence,  a f o r m u l a reported b y F r e e s e (1962) was used.  The f o r m u l a used was:  where:  n = number of sample trees r e q u i r e d t = tabular 't (Student's t value) 2 S = E s t i m a t e of the population  variance  d = 1 /2 confidence i n t e r v a l d e s i r e d  88  The numbers of sample trees n e c e s s a r y to have the population mean in the i n t e r v a l of +  20. 0 p e r cent of the sample mean with 95.0 p e r  cent confidence were determined.  The number of samples r e q u i r e d  for the estimation of total tree weight, total stem weight, dry needle weight, crown weight, and s l a s h weight were calculated.  The great length of time and high cost of obtaining tree and component weights, prohibit weight m e a s u r e m e n t of a l l of the trees within the study area.  In o r d e r to obtain a p r e c i s e estimate i t would  be advantageous to r e s o r t to the use of double sampling (sampling with regression).  A test of double sampling was c a r r i e d out following the  p r o c e d u r e s outlined by F r e e s e (1962). tree f r e s h weight only;  The test was applied for total  however, i t i s highly probable that s i m i l a r  results would be obtained for any tree componentx.  T r e e dbh was used  as the supplementary v a r i a b l e because of its easy estimation and its high c o r r e l a t i o n with total tree weight.  T h r e e separate intensities of double sampling were examined. Intensities of three, five and twenty tree subsamples ( s m a l l samples) were tested and i n a l l cases the l a r g e sample consisted of 63 t r e e s . T r e e s for the subsample sizes of five and twenty were chosen on a r a n d o m basis.  The trees in the three tree subsample test were selected  on a systematic basis to include the trees of having the largest, mean and s m a l l e s t dbh's.  89  In o r d e r to compare estimates obtained by the mean tree method and the stand table-functional relationship method t h i r t y trees were randomly selected.  In the f o r m e r method the s u m of the total  tree f r e s h weights were obtained by selecting the tree of mean dbh, obtaining its total tree f r e s h weight, and multiplying this by thirty. In the latter method the weights of the thirty trees were calculated f r o m the simple l i n e a r equation of total tree weight on dbh, p r e v i o u s l y i n this thesis.  developed  In addition, the actual s u m of the total  tree weights were calculated.  Results of A n a l y s i s Table 27 presents the number of trees r e q u i r e d to have the population mean i n the i n t e r v a l s of+_ 10, and 20 p e r cent of the sample mean with a 95 p e r cent confidence for the estimation of tree and component weight.  Table 27.  Estimated Variable  The Number of Sample T r e e s Required to have the Sample M e a n within Standard E r r o r s of + 10 and + 20 P e r Cent at the 95 p e r cent Confidence Level.  Number of Sample T r e e s 10% Standard E r r o r  Required  2 0 % Standard E r r o r  T o t a l T r e e Weight  161  41  T o t a l Stem Weight  151  38  Needle Weight  242  60  C r o w n Weight  291  73  46  12  Slash Weight  90  The results presented i n Table 27 suggest that a v e r y l a r g e number of trees must be sampled to ensure a 10 per cent standard e r r o r of estimate nineteen times out of twenty.  B y accepting a lower  standard e r r o r of estimate a l a r g e reduction o c c u r r e d .  It would  appear that i t i s v e r y worthwhile to accept the s m a l l iTXCr»ea&g" i  n  the  standard e r r o r i n o r d e r to obtain a l a r g e r e d u c t i o n i n the number of sample trees r e q u i r e d .  The mean total tree f r e s h weights and standard e r r o r s a s s o c i a t e d with these means obtained by double sampling a r e presented i n Table 28.  Table 28.  Mean and Standard E r r o r of Mean Values Obtained Using Double Sampling for T o t a l T r e e F r e s h Weight (lb).  Double Sampling Intensity  Mean  Standard E r r o r of Mean  20 Sample T r e e s  442.99  34.79  5 Sample T r e e s  416.80  32.32  3 Sample T r e e s  458.45  70.86  437.95  35.11  A c t u a l Value of 63 trees  The preceding results indicate that double sampling with subsample intensities of 20 and 5 t r e e s r e s u l t e d i n lower standard e r r o r s than that of the actual population f r o m which the subsamples were taken. T h i s result is due solely to chance and does not invalidate the results, as one would expect that had s e v e r a l replications of the test been  c a r r i e d out this would not have o c c u r r e d .  The results do indicate,  however, that v e r y acceptable results can be obtained though the use of double sampling.  In addition, the favorable results suggest  the d e s i r a b i l i t y of further study^with a l a r g e number of intensity replications, to establish the optimum number of subsamples to be taken and the r e l i a b i l i t y of the results obtained i n double  The sum  sampling.  of total tree f r e s h weights (in pounds) of 30 randomly  selected trees as estimated by the mean tree, and formula-stand table methods are c o m p a r e d i n Table 29-  Table 29.  Sampling  A C o m p a r i s o n of the Sum of T o t a l T r e e F r e s h Weight (lb) of 30 Randomly Selected T r e e s as E s t i m a t e d by Two Sampling Methods  Sum of T o t a l T r e e Fresh Weight (lb)  Method  T r e e of Mean  Dbh  10, 980  F o r m u l a and Stand Table  11,092  A c t u a l Weights of 30 T r e e s  11,311  The results presented i n T a b l e 29 tend to support previous results which indicate that estimates obtained by the mean tree method are l e s s than estimates obtained using the f o r m u l a stand table method. Although the difference obtained in this thesis was  s m a l l i t i s anti-  cipated that had the range of tree sizes been l a r g e r the difference  92  might also have been greater. F u r t h e r study should be devoted to establishing the magnitude of these differences for the estimation of total tree and component weights.  Summar y The technical p r o b l e m s and costs involved i n obtaining the weights of trees and components of t r e e s make it d e s i r a b l e to estimate biomass on  a sampling b a s i s .  Methods p r e v i o u s l y used were investigated and  their relative m e r i t s were discussed.  Results indicate that estimates  obtained b y the f o r m u l a stand table method exceeded these obtained by the mean t r e e method.  The number of sample t r e e s r e q u i r e d to obtain a sample mean within a specified confidence i n t e r v a l (+ 1 0 % and+_ 20%) of the population mean, 19 times out of 20, were  determined.  The u s e of double sampling with r e g r e s s i o n appears to be a v e r y p r o m i s i n g and useful tool for estimating many aspects of biomass. F u r t h e r study of double sampling should be c a r r i e d out i n o r d e r to explore the method fully, and to determine the number of subsamples n e c e s s a r y to obtain accurate estimates.  It i s apparent that i n any study of biomass, the r e s e a r c h e r must c a r e f u l l y consider the objective of his r e s e a r c h , i n t e r m s of the d e s i r e d a c c u r a c y a n d c a r e f u l l y balance this with the number of ?  samples r e q u i r e d to obtain this degree of accuracy.  In many situations  93  it probably w i l l be d e s i r a b l e to accept a lower degree of a c c u r a c y i n o r d e r to reduce the number of samples r e q u i r e d per stand, i n o r d e r to i n c r e a s e the representativeness of the study itself.  94  WEIGHT SCALING  Introduction T a r a s (1956) reported that p r o b l e m s associated with volume m e a s u r e m e n t were recognized as long ago as 1765.  In recent years  a voluminous amount of r e s e a r c h and l i t e r a t u r e has been devoted to the topic of weight scaling.  A c c o r d i n g to T a r a s (1967) the f i r s t  interest shown i n weight scaling o c c u r r e d around the late 1920's i n the Southern Pine Region of the United States.  One  of the m a j o r  reasons  for the growing interest i n weight s c a l i n g is the apparent v a r i a t i o n i n the s o l i d wood content of the cord.  Weight scaling i s being used i n management planning by some l a r g e A m e r i c a n forest product companies according to C u r t i s (1965). He r e p o r t e d that the Buckeye C e l l u l o s e C o r p o r a t i o n of F l o r i d a used weight equations i n conjunction with growth p r e d i c t i o n methods to optimize and determine their cutting schedules.  C u r t i s reported that  m o r e consistant m e a s u r e m e n t s of values, costs and quality can be obtained using a weight as opposed to a volume b a s i s . reported that the K i m b e r l y - C l a r k  C o r p o r a t i o n now  Eggen (1967)  employs weight  s c a l i n g i n their operations i n the Northeastern United States.  Weight scaling i s employed i n Canada as well. Weight scaling was  investigated as e a r l y as 1928 by the Wood M e a s u r e m e n t Committee  95  of the Canadian Pulp and P a p e r Institute according to M a r t i n S i m a r d (1959)-  and  In B r i t i s h C o l u m b i a the use of weight s c a l i n g was  approved by the Chief F o r e s t e r of the B. C. F o r e s t S e r v i c e i n  1963.  The method and requirements for setting up the s c a l i n g f a c i l i t i e s to comply with government regulation i n B r i t i s h Columbia were p r e p a r e d by F r a s e r (1964).  T h e r e are p r e s e n t l y 25 weight scaling operations  in B r i t i s h Columbia and this number w i l l l i k e l y i n c r e a s e due to the p r o v i n c i a l government's close utilization p o l i c y .  European experience with weight m e a s u r e m e n t to facilitate scaling has not been generally as favorable as on this continent. Considerable  study of weight s c a l i n g has been done i n Scandinavian  countries (Nylinder, 1967). Steinlin and Dietz (1962) stated that because of the comparatively  s m a l l amount of wood dealt with and the lack of  species homogeneity i n G e r m a n forests i t would not be p r a c t i c a l to employ weight scaling i n Germany.  Johansson (1962), and S t e m s r u d  and G u d i m (1962) advocated refinements to adjust for  variations i n  m o i s t u r e content and wood density.  Lange (1962) concluded f r o m his investigations i n southern United States that s c a l i n g by weight afforded better accounting p r a c t i c e s , eliminated conventional c o r d scaling biases, allowed a greater number of loads to be m e a s u r e d per day,  found that stumpage p r i c e s were not  a d v e r s e l y affected, disposal costs were less, better a c c u r a c y  was  obtained, and quicker, smoother operation could be achieved. S i m i l a r advantages were cited b y T a r a s (1956 and 1967), M a r t i n and S i m a r d (1959), Page (1961), Page and B o i s (1961), R o m a n c i e r (1961), F r e e m a n (1962), Lange (1962), H a r d y and Weiland (1964), B l a i r (1965), C u r t i s (1965), Dobie (1965), F o r b e s (1966), Row and Guttenburg (1966), and Eggen (1967).  Other advantages noted b y some of the above authors  included safer working conditions, and e a s i e r s c a l e r training.  T h e r e a r e however, disadvantages associated with weight scaling. The most prohibitive feature of weight scaling i s the i n i t i a l cost encountered i n setting up the weighing f a c i l i t i e s .  Because of i n c r e a s e d  m o i s t u r e loss with time following felling any p r o d u c e r who i s unable to dispose of his logs s h o r t l y after felling w i l l be penalized by i n c r e a s e d volume p e r unit of weight as his logs d r y (Eggen,  1967).  Problems  also a r i s e because defective and crooked logs m a y weight as much as sound high quality logs.  Page and B o i s (1961) pointed out the need  to adjust for size and quality i n weight scaling of sawlogs.  Guttenberg  et al. (I960), nevertheless, r e p o r t e d favorable results and stated:  "Scaling b y weight p r o m i s e s equal a c c u r a c y and greater day-to-day consistency i n p r e dicting lumber yields f r o m Southern pine sawlogs than s c a l i n g b y traditional l o g rule methods.  n  One of the m a j o r problems and limitations associated with weight s c a l i n g result f r o m the within- , and between-tree variations i n s p e c i f i c gravity and m o i s t u r e content. Hopefully, however, seasonal variations i n these factors w i l l balance out over a long p e r i o d of time  thus allowing the use of average values and making it u n n e c e s s a r y to m e a s u r e these v a r i a b l e s for e v e r y load. B e s l e y (1967).  This is the contention of  Some authors (Haygreen (1959), Steinlin and  Dietz  (1962), and Young and Chase (1965))have e x p r e s s e d a belief that the use of a dry-weight b a s i s is better.  It should be r e c o g n i z e d that this method of s c a l i n g is not a panacea for a l l scaling p r o b l e m s and i s best applied only under c e r t a i n conditions.  F a v o r a b l e conditions include a u n i f o r m distribution and  l i m i t e d number of species.  Weight scaling would also be m o r e  accurate where the ranges i n age and size are s m a l l and where the logs are free f r o m decay.  F a c t o r s affecting variations i n specific g r a v i t y  and m o i s t u r e content were d i s c u s s e d by B e s l e y (1967), Nylinder (1967), and Johnstone (1967 b), and anything which might be done to m i n i m i z e the v a r i a t i o n i n these v a r i a b l e s would also m i n i m i z e variations i n volume/ weight ratios.  In addition to the actual p r a c t i c e of scaling, weight measurement;, has s e v e r a l other possible i n d u s t r i a l applications.  K e e n (1963) has  c a r r i e d out a comprehensive study of weights and centres of g r a v i t y of s e v e r a l E a s t e r n Canadian tree species. Keen's concern i s i n the handling of pulpwood and he suggested that such data can be meaningfully employed i n equipment design and skidding studies since most equipment is rated i n t e r m s of weight.  Young and Chase (1965) also  noted the possible application of tree weight data to equipment design.  98  Samset (1962) suggested that tree weight data could be used to determine the power requirements of overhead winches or lines n e c e s s a r y to convey logs.  T u r n b u l l et al. (1965), also, noted the utility of weight  data i n studies of skidding and hauling.  Dobie (1965) stated that the advent of balloon and helicopter logging, and the i n c r e a s e d use of public transportation systems by logging concerns, w i l l necessitate an i n c r e a s e i n the knowledge of tree weight f a c t o r s .  The  assessment of freight charges on a weight basis  by r a i l companies transporting pulp chips has created a need for i n c r e a s e d knowledge of the compactibility and density of wood chips (Shultz, 1964).  F i n a l l y , i f Young's (1964) assertions that i n the future  greater utilization of logging residues such as roots, stumps, and branches which are c u r r e n t l y considered unmerchantable w i l l occur, are true, then the only p r a c t i c a b l e method of m e a s u r i n g these odd-shaped m a s s e s is on the b a s i s of weight.  Method of A n a l y s i s The  data gathered for this thesis offer little opportunity to study  weight scaling per se.  However, it i s p o s s i b l e to analyse some of  the assumptions b a s i c to the theory of s c a l i n g by weight, n a m e l y the relationship between tree weight and tree volume.  In order to analyze the relationship between tree volume and tree weight a s e r i e s of simple linear equations were developed.  Regression  equations of total tree volume (ob) i n cubic feet on total stem weight, adjusted for m o i s t u r e content, i n pounds, and on the product of total  stem weight times the mean volume/weight r a t i o of the 63 trees were examined.  In a d d i t i o n , the simple l i n e a r r e l a t i o n s h i p s between the  dependent v a r i a b l e s , fresh and dry, merchantable and t o t a l stem weights ( i n pounds) and the independent v a r i a b l e s t o t a l stem volume (ob) i n cubic f e e t , adjusted by the average wood density o f the 63 t r e e s , and 2 the combined v a r i a b l e D  H (dbh squared times tree height) were  analyzed. Results o f A n a l y s i s The mutual r e l a t i o n s h i p s between volume (ob) i n cubic feet and t o t a l stem weight ( i n pounds) were studied.  A f t e r adjustment f o r moisture  content, dry t o t a l stem weight accounts f o r 95.8 per cent of the v a r i a t i o n i n tree volume.  The regression equation i s :  Vob (cu. f t . ) = 0.04043 DSWt ( l b ) -0.207 SE  E  = 1.029  cu. f t . (12.4$)  r  2  = O.958**  The simple l i n e a r regression equation of volume (ob) i n cubic feet on the product of t o t a l stem weight ( l b ) times the mean volume/weight r a t i o ,  was:  Vob (cu. f t . ) = 0.223 + 0.9585 (TSWt x 0.02154) SEg  = O.789 cu. f t . (9.6%)  These r e s u l t s i n d i c a t e that 97.5  r  2  = 0.975**  per cent of the t o t a l v a r i a t i o n i n cubic  f e e t volume can be a t t r i b u t e d to the product o f t o t a l fresh stem weight times the mean volume to weight r a t i o .  100  The r e s u l t s i n d i c a t e d that t r e e volume (ob) i n cubic f e e t adjustment f o r wood density accounts f o r 95.7 per cent of the v a r i a t i o n i n dry t o t a l stem weight (DTSWt.) i n pounds, and 97.4 per cent of the v a r i a t i o n i n f r e s h t o t a l stem weight (FTSWt.) i n pounds using the equations: DTSWt. ( l b ) = 13.813 + O.897 (Vob (cu. f t . ) x density) SE  = 25.14 l b . (12.1$) r  E  FTSWt. ( l b ) =  = 0.957**  I.788 (Vob (cu. f t . ) x density) -O.588  = 38.4 l b . (9.9$) r  SEg  2  2  = 0.974**  Tree volume (ob) i n cubic feet adjusted f o r wood density was also used i n simple l i n e a r r e l a t i o n s h i p s w i t h f r e s h and dry merchantable stem weight ( i n pounds).  The regression equations developed are:  FMSWt. ( l b ) = I.877 (Vob (cu. f t . ) x density) -78.08 SE  E  = 38.15 l b (11.5&$) r  DMSWt. ( l b ) = 1.737 SE  E  2  = 0.977**  (Vob (cu. f t . ) x density) -53.03  = 18.28 l b (10.4$) r  2  = O.980**  Volume adjusted by density accounted f o r 98.0 per cent of the v a r i a t i o n i n dry merchantable stem weight and 97.7 per cent o f the v a r i a t i o n i n f r e s h merchantable stem weight.  101 2 The combined v a r i a b l e D H adjusted b y wood density accounted for 94. 9 p e r cent of the v a r i a t i o n i n dry total stem weight (DTSWt.) in pounds and 9 6. 0 p e r cent of the v a r i a t i o n of f r e s h total stem weight (FTSWt. ) i n pounds.  The r e g r e s s i o n equations are:  2 F T S W t . (lb) » 26. 46 + 0. 0050 (D H x density) S E _ = 47.90 lb (12.4%) r E  = 0.96o"""  DTSWt. (lb) = 26. 84 + 0. 0025 (D^H x density) O  SE  o*  = 27. 59 lb (13.2%) r- = 0.949'"" E  Simple l i n e a r r e g r e s s i o n relationships were developed u s i n g 2 f r e s h and dry merchantable stem weights on D H adjusted b y wood density.  The r e g r e s s i o n equations are: 2 FMSWt. (lb) = 0. 0052 (D H x density ) -49-66  S E _ = 48. 57 lb (14. 7%) * E  2  = 0. 963"*  DMSWt. (lb) = 0. 0027 (D^H x density) = 16. 55  SE  E  = 26. 48 lb (15. 0%)  t  = 0.958"""  D i s c u s s i o n s of Some Internal F a c t o r s Which Affect T r e e Weight The two most important factors affecting tree weight are specific gravity, and moisture content. The purpose of this chapter i s to examine the within, and between tree variations of these factors i n lodgepole pine.  102  M o i s t u r e content In excess of 50 p e r cent of the total f r e s h weight of a tree consists of water. The amount present v a r i e s not only within the tree but also with species, age, site, season, and time of day ( K r a m e r and Kozlowski, I960).  A f t e r a thorough investigation of bark m o i s t u r e  content, S r i v a s t a v a (1964) concluded that variations may also be related to exposure, temperature, atmospheric relative humidity, and to the growth conditions of the plant.  It appears, therefore,  that differences both within and between species a r e caused b y a l a r g e number of i n t e r n a l and external factors.  Perhaps the most striking v a r i a t i o n i n m o i s t u r e content within a tree i s the v a r i a t i o n between the heartwood and the sapwood. B e s l e y (1967) ,'reported that for some species the m o i s t u r e content of sapwood m a y be three times as great as the m o i s t u r e content of the heartwood, while in other species, notably E a s t e r n hemlock ( T s u g a canadensis ( L . ) C a r r . ) , and b a l s a m fir (Abies b a l s a m e a ( L . ) M i l l . ) the m o i s t u r e contents of the two types of wood m a y be equal.  M o i s t u r e content i s generally r e g a r d e d to i n c r e a s e with i n c r e a s i n g height within the tree (Raber (1937), Ovington (1956), Gibbs (1958) E t h e r i d g e (1958), K r a m e r and K o z l o w s k i (I960), and Coutts (1965)).  T h e combined effect of the type of wood (sapwood or  heartwood) and its position within the tree was investigated by N y l i n d e r (1967).  Nylinder's results indicated that the heartwood v a r i e s v e r y  103 little r e g a r d l e s s of position i n the stem but the m o i s t u r e content of sapwood v a r i e s greatly depending on position within the tree.  Etheridge (1958) reported that tree m o i s t u r e content i n c r e a s e d with tree vigor.  T h i s was  substantiated by Coutts (1965) who  reported  that dominant t r e e s have a higher m o i s t u r e content than s u p p r e s s e d trees.  Gibb's (1958) work indicated that tree m o i s t u r e content reaches  a m a x i m u m s h o r t l y before the resumption of active growth, and that the amount of m o i s t u r e diminishes through the summer and e a r l y f a l l . Summer and winter differences are consistent and  considerable  (Raber (1937), Jensen and Davis (1953), K r a m e r and K o z l o w s k i (I960), B e s l e y (1967) and Nylinder (1967).  V a r i a t i o n s i n forest tree m o i s t u r e content may  also occur  diurnally (Raber (1937), K r a m e r and K o z l o w s k i (I960), (1966)).  and J a m e s o n  T h i s situation o c c u r s when t r a n s p i r a t i o n during the  exceeds the uptake of water by the roots. The replenished  day  deficit, so created, i s  at night when t r a n s p i r a t i o n is m i n i m a l . J a m e s o n (1966)  suggested that diurnal variations follow m e t e o r o l o g i c a l  conditions.  Specific g r a v i t y Wahlgren et al. (1966) stated that specific gravity is the  simplest  and most useful index to the suitability of wood for many important uses.  Because of the strong relationship between specific gravity  and the strength p r o p e r t i e s of wood (USDA, 1965  a) specific gravity  affects s t r u c t u r a l lumber, plywood, laminated arches and beams, and  104 high-quality t r a n s m i s s i o n poles and piling. S p e c i f i c g r a v i t y i s a determinant of the shrinkage,  elasticity, hardness (resistance to wear  and marring), workability, and paintability of wood. Specific gravity or wood density i s of interest to the pulp and paper industry because it gives an indication of fibre content of a piece of wood, and thereby an indication of the possible pulp yield.  In weight scaling specific  gravity is of p r i m e importance because i t is an index of the weight per unit volume of wood, and thus i s related to volume p e r unit weight.  Many factors, including the amount of summerwood produced, growth rate, s t e m and crown c h a r a c t e r i s t i c s , position within the tree, site and geographic location, inheritance, species, tree age at the time of wood formation, specific gravity.  and the health and vigor of the tree influence  Differences i n specific g r a v i t y r e s u l t f r o m differences  i n c e l l thickness, c e l l density, c e l l length, the amount of extractives, and the volume of m e c h a n i c a l tissue (Spurr and Hsuing (1954), M c K i m m y (1959), and U S D A (1965 b)).  Summerwood,  often called latewood, i s that portion of the annual  growth r i n g f o r m e d i n the latter part of the growing season, and has thicker c e l l walls and s m a l l e r lumens than the e a r l i e r f o r m e d s p r i n g wood.  Because of these anatomical differences summerwood is  denser than springwood and consequently, as the proportion of the annual growth ring composed of summerwood i n c r e a s e s the specific g r a v i t y of the wood l a i d down during the growing season i n c r e a s e s . T h i s was demonstrated b y the r e s e a r c h of Alexander (1935), L a r s o n (1957),  105 Wakefield (1957), M c K i m m y (1959), R i s i and Z e l l e r (I960), K e i t h (1961), L i t t l e f o r d (1961), Wellwood and W i l s o n (1965), Wilfong (1966), and Nylinder ( 1967).  L a r s o n (1957) reported that the amount of  summerwood f o r m e d i s affected by t r e e age at the time of wood f o r mation, position within the tree, stand density, and p o s s i b l y the quality of the site on which the tree is growing.  Generally, there i s an i n v e r s e relationship between specific gravity and growth rata, L a r s o n (1957) and M c K i m m y (1959) r e p o r t e d that such factors as site, s t e m class, tree age,  position within the  tree, and r i n g age f r o m pith confound this relationship.  Maximum  specific g r a v i t y i s reported to be coincident with moderate growth rates (Alexander (1935), Wakefield (1957), and Keith (1961). Wellwood and Smith (1962), and F i e l d i n g and B r o w n (I960) also found significant relationships between specific g r a v i t y and rate of growth.  The m a j o r i t y of investigations have shown that specific gravity i n c r e a s e s with i n c r e a s i n g age (number of rings f r o m pith) i n species having a distinct t r a n s i t i o n between earlywood and latewood ( R i s i and Z e l l e r (I960), L i t t l e f o r d (1961), Wellwood and Smith (1962), Knigge (1963), and U S D A (1965 b)).  Because specific gravity is related to growth rate it would s e e m l o g i c a l that, i n even-aged stands, trees of a s m a l l e r size would have higher specific gravity.  T h i s hypothesis is not c o n c l u s i v e l y supported  by r e s e a r c h reported i n the past.  R i s i and Z e l l e r (I960), Wheeler  and  106  M i t c h e l l (1962), and G i l m o r e (1963) have reported that dbh i s not significantly r e l a t e d to tree specific gravity.  In opposition to these  results, Stage (1963), Christopher and Wahlgren (1964), B a s k e r v i l l e (1965 b) and the F o r e s t S e r v i c e ( U S D A 1965 b) have r e p o r t e d significant relationships of t r e e specific g r a v i t y on dbh.  Due to the method of  sampling used i n the last reference cited ( U S D A (1965 b)) the result may be l a r g e l y an age effect.  The influence of crown c h a r a c t e r i s t i c s on tree specific gravity is not c l e a r .  Spurr and H s u i n g (1954) reported that no relationship  exists between density and crown length.  Stage's (1963) r e s u l t s  indicated that the ratio of crown length to tree height was  significantly  r e l a t e d to specific g r a v i t y thus refuting L a r s o n ' s (1957) data. Knigge (1963) suggested that wood density i n c r e a s e d with i n c r e a s i n g crown size and growing space.  Wellwood and Smith (1962) reported that r a p i d l y grown crownf o r m e d wood has a lower density than b o l e - f o r m e d wood.  Other  researchers  including: L a r s o n (1957) Wahlgren and F a s s n a c h t (1959), R i s i and Z e l l e r (I960), L i t t l e f o r d (1961) Conway and M i n o r (1961), T a c k l e (1962), Stage (1963) Knigge (1963), Wahlgren et al.(1966), B e s l e y (1967), and Nylinder (1967), have reported the importance of the influence of height within the tree on specific gravity. The work of these authors indicates, however, that this influence may r e s u l t i n within, as well as, between species differences.  107 F a c t o r s such as site condition, environment, and geographic location greatly influence growth rate, summerwood formation,  stem  and crown c h a r a c t e r i s t i c s , and tree vigor and consequently influence wood density.  L a r s o n (1957), and Wilde and P a u l (1959) d i s c u s s e d  some relationships between specific g r a v i t y and s o i l p r o p e r t i e s . Physiographic  and c l i m a t i c factors were shown to influence specific  gravity by Wheeler and M i t c h e l l (1962), G i l m o r e (1963), Knigge (1963), and the U.S.  F o r e s t S e r v i c e (USDA, 1965 b).  L a r s o n (1957), McKimnmy  (1959), F i e l d i n g and B r o w n (I960), Wheeler and M i t c h e l l (1962), G i l m o r e (1963) Knigge (1963), an d the U.S. 1965  F o r e s t S e r v i c e (USDA,  a and b) o b s e r v e d changes i n specific gravity with changes i n  latitude and longitude.  One  of the major sources of v a r i a t i o n i n specific g r a v i t y between  trees is attributable to inheritance ( L a r s o n (J-957), M c K m m y (1959) K e i t h (1961), and Wellwood and Smith (1962)).  T h i s affords an  opportunity to the f o r e s t e r to develop genetically s u p e r i o r trees through selective breeding as pointed out by Stonecypher et al. (1964).  The following values for the specific gravity and density of lodgepole pine were published by the Canadian Government (Can. N. A.  and N. R. , 1956):  a. Specific Gravity: basic (gr. v o l . and o. d. wt.) = 0.40 oven-dry (o. d. vol. and o. d. wt. ) = 0.46 nominal (a. d. v o l . and o. d. wt.) = 0.41  Dept.  108  b. Density (lb/cu. ft.): green air-dry  = 40 = 29  F r o o d (1963) r e p o r t e d an average specific gravity of 0.402 for e x t r a c t i v e - f r e e lodgepole pine samples gathered i n c e n t r a l A l b e r t a . T a c k l e (1962) obtained values of 0. 392 and 0.396 for average tree and b r e a s t height s p e c i f i c gravities, respectively, for lodgepole pine. The Wood Handbook (USDA, 1955) r e p o r t e d the green volume specific gravity of lodgepole pine (as determined f r o m increment cores taken at b r e a s t height) to be 0. 38.  Method of A n a l y s i s The m a i n purpose of the analysis was to study the .within and between tree variations i n the specific gravity and moisture content of the lodgepole pine t r e e s . The data used to analyse these v a r i a b l e s were based on measurements made f r o m the discs, collected as d e s c r i b e d p r e v i o u s l y i n this thesis (see Data Collection).  The  analysis was c a r r i e d out using the same r e g r e s s i o n elimination procedure d e s c r i b e d previously, and was divided into two distinct parts.  The f i r s t p a r t of the analysis studied the within tree variations  in specific gravity and m o i s t u r e content, and the second part analyzed the between t r e e variations i n these two v a r i a b l e s .  To analyze the within t r e e variations, specific gravity (ovendry volume basis) and m o i s t u r e content ( e x p r e s s e d as a per cent of the f r e s h weight), determined at v a r i o u s heights i n the t r e e were u s e d  109  as dependent v a r i a b l e s on the independent v a r i a b l e s : height above ground, dob,  dib, age,  (rings f r o m pith) and mean r a d i a l growth rate  (dib/ (2 x age)) at the point i n the tree where the dependent v a r i a b l e s were measured. A total of 545 specific gravity and m o i s t u r e content m e a s u r e m e n t s f r o m 63 trees were involved.  A v e r a g e tree values for m o i s t u r e content and specific g r a v i t y (converted to a green volume basis) were calculated and used as the dependent v a r i a b l e s i n the analysis of between tree variations.  These  dependent v a r i a b l e s were used i n a multiple r e g r e s s i o n analysis on the independent v a r i a b l e s dbh,  height, crown length, crown width, age,  total tree weight, d r y needle weight, volume (ob), height to l i v e crown, b a s a l area,  crown volume, crown surface area, number of needles,  mean r a d i a l growth rate (bh) and bark per  cent.  Results of A n a l y s i s Within tree v a r i a t i o n i n specific gravity and m o i s t u r e content. The means, standard deviations, and m a x i m u m and m i n i m u m values obtained for sections taken at various height i n t e r v a l s i n the t r e e are p r e s e n t e d i n Table 30. Table 30.  Mean, Standard Deviation, M a x i m u m and M i m i m u m V a l u e s of Specific G r a v i t y and M o i s t u r e Content for 545 D i s c s of Lodgepole Pine. Mean  Standard Deviation  Specific Gravity  0.4805  0. 0426  M o i s t u r e Content(%)  44.97  Characteristic  7. 35  Maximum Value  Minimum Value  0.6367  0.3450  66.67  24.46  110  *Note: s p e c i f i c gravity is based on oven-dry volume. The specific gravity values presented i n Table 30 are based on ovendry volume. The values are higher than the 0.46  shown on page 107  The standard deviation indicates that the v a r i a t i o n i n s p e c i f i c gravity is s m a l l .  M o i s t u r e content i s m o r e v a r i a b l e than s p e c i f i c gravity,  as indicated by the l a r g e r range i n the data and l a r g e r standard deviation for m o i s t u r e content.  Table 31 presents the simple c o r r e l a t i o n coefficients for m o i s t u r e content and s p e c i f i c gravity, and s e v e r a l tree section v a r i a b l e s . Table 31.  The C o r r e l a t i o n of M o i s t u r e Content and S p e c i f i c G r a v i t y to the Height, dob, Dib, Age and Mean R a d i a l Growth Rate of Section Measurements of 63 Lodgepole Pine T r e e s ,  Section Measurement  C o r r e l a t i o n Coefficients (r) Moisture  Height above ground (ft) Dob  (In)  Content  0. 6315  Specific  Gravity  -0. 387 5  -0.3601"  0.1274'  Dib  (in)  -0.3689*"  0.1325'  Section age  (yr)  -0.6090""  0.3645  Section s p e c i f i c gravity  -0. 3534  Mean r a d i a l growth rate (mean ring width)  0.4665  *.*  1, 0000  s  -0.3654  The results i n Table 31 suggest that both moisture content and s p e c i f i c gravity are m o s t strongly c o r r e l a t e d with height above ground. The results indicated that s p e c i f i c gravity decreases and m o i s t u r e tent i n c r e a s e s with i n c r e a s i n g sampling height i n the tree.  con-  Moisture  Ill content i n c r e a s e d and specific gravity d e c r e a s e d with decreasing section age.  The effect of section age i s undoubtedly related to the fact that  section age d e c r e a s e d as the sampling height i n c r e a s e d .  Mean r a d i a l growth rate was p o s i t i v e l y c o r r e l a t e d with m o i s t u r e content and negatively c o r r e l a t e d with specific gravity suggesting that fast growing t r e e s p r o b a b l y have lower specific gravity and higher m o i s t u r e contents than slowly growing  trees.  A s was  expected  m o i s t u r e content and specific gravity were negatively c o r r e l a t e d indicating that as the wood content p e r unit volume i n c r e a s e s the water content d e c r e a s e s .  A multiple r e g r e s s i o n equation of specific g r a v i t y on the section variables, height, dob,  dib, age, and mean r a d i a l growth rate accounted  for 20. 0 per cent of the variation.  Section height, the best independent  variable, accounted for 15. 0 per cent of the v a r i a t i o n with a standard e r r o r of estimate of 0. 039 (8%) i n the relationship:  Sp. Gr. = 0. 503 - 0. 000906 Ht.  S E _ = 0. 039 E  r  = 0. 150"""  T h i s simple l i n e a r relationship i s shown i n F i g u r e 17.  A multiple r e g r e s s i o n analysis of m o i s t u r e content on section height, dob,  dib, age, and mean r a d i a l growth rate accounted for 43.9  per cent of the variation, and the combination of the independent  112  Figure 1 7 .  The R e l a t i o n s h i p between S p e c i f i c  Gravity  and P o s i t i o n i n the T r e e .  i i ii i ii ii ii i ii i •••• •••• I  i iii i iii i  i iii i iii  T  i ii i i  ...  . s*  o o ON O o o o d II  vo  m  r-l  i iii i ii i i ii t ii i ii . ... i i i ..... i i i  LO CM  o lO  O  oII  r  —r  o) *I0A  o o  O  o  VO  '(TO /  'H-M  '(TO)  A*pre-*0  O  dw II  r  o  ON  oTjTostfg  oo'  113  variables height above ground, section age, and mean r a d i a l growth rate accounted for 43. 3 p e r cent of the variation.  The best simple  linear r e g r e s s i o n was:  M. C. (%) = 38. 72 + 0. 2545 Ht.  S E ^ = 5.70% E  t  = 0. 399""  This simple l i n e a r relationship accounted for 39-9 p e r cent of the v a r i a t i o n with a standard e r r o r of 5. 7 0 % (12. 7%), and i s presented i n graphical f o r m i n F i g u r e 18.  Between tree v a r i a t i o n i n s p e c i f i c gravity and m o i s t u r e content A v e r a g e tree values for s p e c i f i c gravity (converted to a green volume basis), and m o i s t u r e content were u s e d to analyse between tree v a r i a t i o n i n m o i s t u r e content and s p e c i f i c gravity.  A v e r a g e tree  specific gravity had a mean of 0. 423 and a range f r o m 0.315 to 0. 540 A v e r a g e tree m o i s t u r e contents ranged f r o m 24.46 p e r cent to 66. 67 p e r cent, with a mean of 44.96 p e r cent.  T a b l e 27 presents the simple  correlations between average tree s p e c i f i c gravity, and m o i s t u r e content, and s e v e r a l tree v a r i a b l e s .  114  Figure 18. \  The R e l a t i o n s h i p between Moisture Content and P o s i t i o n i n the Tree.  \  \ \ \  115  Table 32.  The C o r r e l a t i o n Coefficients Between Specific G r a v i t y and M o i s t u r e Content and S e v e r a l T r e e C h a r a c t e r i s t i c s for 63 Lodgepole Pine T r e e s .  Tree Characteristics  C o r r e l a t i o n Coefficients (r) M o i s t u r e Content  Specific Gravity  0.4026  -0. 3961  Height (ft)  0.4182'  -9. 2986'  C r o w n length (ft)  0.3013"  -0. 2626'  Crown width (ft)  0.5123'  .0. 3264"  Age (yr)  0.4193'  -0. 176l'  T o t a l tree weight (lb)  0.4279'  -0. 3626'  D r y needle weight (lb)  0.4976  •0.3179'  T r e e volume ob (cu. ft. )  0.4055  -0.3869'  Dbh (in)  «.'> 4;l>  Ave.  s p e c i f i c gravity  -0. 2640  i.oooo'  Height to l i v e c r o w n (ft)  0.1786'  -0. 0719"  T r e e b a s a l a r e a (sq. ft. )  0.3915 *T»-P  •0.3827  Crown volume (cu. ft.)  0.4546  •0.3139  C r o w n surface a r e a (sq.ft. )  0,5019'  -0. 3370  Number of needles  0.4450'  .0. 2818  Mean r a d i a l growth (bh)  0.3639  -0. 3942  B a r k p e r cent  -0.0395 ns  0.1488  116 The results presented i n Table 32 suggest that between tree differences i n tree m o i s t u r e content are most c l o s e l y related to c h a r a c t e r i s t i c s of the crown (with the exceptions of crown length and height to l i v e crown) and this i n turn i s probably c l o s e l y r e l a t e d to the influence of crown c h a r a c t e r i s t i c s on evapo-transpiration, synthesis.  and photo-  C r o w n width and crown surface a r e a were the two v a r i a b l e s  most c l o s e l y associated with tree m o i s t u r e content differences.  M e a s u r e s of t r e e size were found to be most c l o s e l y a s s o c i a t e d with tree .specific gravity.  The negative c o r r e l a t i o n coefficients suggest  that as t r e e size i n c r e a s e d t r e e specific gravity decreased.  The r e s u l t s  suggested, as did the analysis of within tree variation, that as tree s p e c i f i c g r a v i t y i n c r e a s e d tree m o i s t u r e content decreased.  Due to  the even-aged nature of the trees analysed t r e e size i s an indication of tree vigor and consequently it is possible to i n d i r e c t l y conclude that tree specific g r a v i t y decreased, and tree m o i s t u r e content i n c r e a s e d with i n c r e a s i n g t r e e vigor.  A multiple l i n e a r r e g r e s s i o n analysis of tree specific g r a v i t y on dbh, height, crown length, crown width, tree weight volume (ob), dry needle weight, height to l i v e crown, b a s a l area, crown volume, crown surface area, number of needles, and mean r a d i a l growth rate (bh) accounted for only 31. 3 per eent of the v a r i a t i o n with a standard e r r o r of 0. 021 (7. 8%).  The best simple l i n e a r r e g r e s s i o n of tree  specific gravity was on dbh.  117  T r e e Sp. Gr. = 0. 458 - 0. 005399 dbh 2  S E _ = 0. 021 E  r  = 0. 157  **  The p r e c e d i n g relationship accounted for 15.7 p e r cent of the variation and had a standard e r r o r of estimate of 0. 021 (7. 8%).  A multiple r e g r e s s i o n analysis of t r e e m o i s t u r e content on the same independent v a r i a b l e s cited i n the p r e c e d i n g paragraph plus specific gravity and bark volume p e r cent accounted for 51.0 per cent of the total variation.  The best simple l i n e a r r e g r e s s i o n was:  T r e e M. C. (%) = 36. 205 + 1. 828 S E _ = 4. 0 8 % E  • r  CW  = 0.262  Crown width accounted for 26. 2 p e r cent of the v a r i a t i o n i n tree m o i s t u r e content, e x p r e s s e d as a percentage of f r e s h weight, with a standard e r r o r of estimate 4.08% (9- 3%).  The equation of the simple l i n e a r r e g r e s s i o n of average tree specific g r a v i t y on b r e a s t height specific gravity was:  Sp. Gr. (ave. tree) = 0. 1456 + 0. 64008 Sp. Gr. (bh)  SE  E  = 0. 013  r  2  = 0. 6 7 5 "  T h i s relationship accounted fof 67. 5 p e r cent of the variation, having a standard e r r o r of estimate of 0. 013 (3. 1%).  F i g u r e 19 presents the  relationship between average t r e e specific gravity and specific g r a v i t y  118  Figure  19.  The  R e l a t i o n s h i p Between Average T r e e S p e c i f i c  Gravity  119  at b r e a s t height on an oven-dry b a s i s .  A simple l i n e a r r e g r e s s i o n of average t r e e m o i s t u r e content on moisture content b r e a s t high accounted for 47. 3 p e r cent of the v a r i a t i o n with a standard e r r o r of 3.45 p e r cent (7.7%).  T h e equation  was:  Ave.  M. C. (%) = 21. 178 + 0. 585 M. C. (bh) O  S E ^ =3.45 E  r  *X**U  = 0.473 ""  The relationship i s presented i n F i g u r e 20.  Summary Where the value of the raw m a t e r i a l i s low, weight s c a l i n g offers s e v e r a l advantages over conventional scaling.  However, as  yet v e r y little study has been directed to analysing factors which influence the weight of wood such as m o i s t u r e content and specific gravity (wood density). The analyses c a r r i e d out i n this thesis point out that easy and accurate conversions can be made between the volume and weight of trees i f data a r e available on the average wood density or volume/weight ratios i s available.  O n the b a s i s of these results i t appears that, when  they are needed, for example, to " c o n t r o l " the rate of forest inventory depletion, accurate estimates of volume can be obtained through weight scaling.  120  o  o o  A v e . M. C.  VD LfN  SE  (i) = 21.178  3,'l+l+8 l b  + ?  0.581+7 2  =  M.C.B.H. ( $ )  0.1+73'  O O  o OJ LfN  —  -p a  -p a O O CD -P •H O  o o o  • CO  o o o  cu cu bD  u  >  o o o* o  o o o vo' ro  O O O CM co  28.000  32.000  36.000  1+0.000  M o i s t u r e Content F i g u r e 20.  1+1+.000  1+8.000  52.000  a t B r e a s t H e i g h t (%)  True R e l a t i o n s h i p Between Average Tree M o i s t u r e Content  and M o i s t u r e Content  ($) a t B r e a s t Height.  {%)  A n a l y s e s of the within and between tree variations i n moisture content and s p e c i f i c gravity were c a r r i e d out.  The results of these  analyses have demonstrated the v a r i a b i l i t y of m o i s t u r e content (C. V. = 16.3%) and s p e c i f i c gravity ( C V . = 8.9%)  i n lodgepole  pine trees. Height within the tree i s the most important factor affecting m o i s t u r e content and s p e c i f i c gravity.  Low s p e c i f i c gravity  and high moisture content are c h a r a c t e r i s t i c of fast growing t r e e s . Between tree variations i n s p e c i f i c gravity and moisture content a r e most c l o s e l y associated with the size of the tree and the properties of the crown, r e s p e c t i v e l y .  It i s apparent that average tree s p e c i f i c gravity and m o i s t u r e content can be a c c u r a t e l y estimated f r o m the combination of m e a s u r e ments of s p e c i f i c gravity and moisture content taken at b r e a s t height and r e g r e s s i o n techniques.  F u r t h e r study should be devoted to  analysing v a r i a t i o n i n specific gravity and m o i s t u r e content due to changes  i n location and season.  122  CONCLUSIONS  The weights of the various components of lodgepole pine i n c r e a s e with t r e e size; however, the p r o p o r t i o n of the total t r e e weight contained i n these components are highly v a r i a b l e and may i n c r e a s e or decrease as tree size i n c r e a s e s , depending upon the component studied.  U s i n g r e g r e s s i o n techniques i t i s p o s s i b l e to  obtain accurate estimates of the component weights of trees f r o m a single m e a s u r e m e n t of dbh, t r e e b a s a l area, or t r e e height.  The  crown and needle c h a r a c t e r i s t i c s of lodgepole pine a r e highly variable.  Double sampling with r e g r e s s i o n offers an easy and r e l i a b l e method of estimating forest t r e e b i o m a s s .  F u r t h e r study should be  devoted to investigate this method m o r e thoroughly.  In most studies  of b i o m a s s i t w i l l probably be d e s i r a b l e to accept a lower degree of a c c u r a c y i n o r d e r to i n c r e a s e the representativeness of the conditions investigated.  V a r i a t i o n s i n specific gravity and m o i s t u r e content, both within and between trees, appear to be r e l a t i v e l y m i n o r p r o b l e m s i n the weight scaling of lodgepole pine.  If data, such as presented herein,  are available on m o i s t u r e content and wood density, conversions can be easily made between volume and weight.  BIBLIOGRAPHY  Alexander,  J . B . 1935. The effect of rate of growth upon the specific gravity and strength of Douglas f i r . Can. Dept. of Inter. , F o r . Serv. , C i r c . 44 (8 pp).  Ando, T. 1965. E s t i m a t i o n of dry-matter and growth analysis of young stand of Japanese black pine (Pinus thunbergii) O r i g i n a l not seen. F o r . A b s t r . , Vol.27. A r t . No. 5609 (page 634). , K. Doi, and H. Fukuda, 1959. E s t i m a t i o n of the amount of leaves, twigs, and branches of Sugi ( C r y p t o m e r i a japonica D.Don) by sampling method. Jour. Jap. F o r . S o c , V o l . 41 (4): 117-125. A t t i w i l l , P.M. 1966. A method of estimating crown weights i n Eucalyptus, and some i m p l i c a t i o n s of relationships between crown weight and stem diameter. Ecology, V o l . 47 (5): 795-804. B a s k e r v i l l e , G . L . 1965. a E s t i m a t i o n of d r y weight of tree components and total standing c r o p i n conifer stands. Ecology, V o l . 46 (6) : 867-869. , 1965 b. D r y - m a t t e r production i n immature b a l s a m for stands. F o r . S c i . Monograph 9. (42 pp). , 1966. D r y - m a t t e r production i n immature b a l s a m fir stands: roots, l e s s e r vegetation, and total stand. F o r . Sci. , V o l 12 (1): 49-53. B a z i l e v i c , N.I. , and L . E . Rodin. 1966. The b i o l o g i c a l cycle of nitrogen and a s h elements i n plant communities of the t r o p i c a l and subtropic zones. F o r . A b s t r . , Leading A r t . S e r i e s No. 38 (12 pages) ( F o r . A b s t r . , V o l . 27 (3): 357-368). B e s l e y , L . 1967. Weight measurement. Importance, v a r i a t i o n , and m e a s u r e m e n t of density and m o i s t u r e . Wood M e a s u r e m e n t Conference P r o c e e d i n g s . E d i t e d by F . Buckingham. Univ. of Toronto F a c . F o r . , Tech. Report No. 7 (112^143).  124  B l a i r , W. M. 1965. Weight scaling pine sawlogs in Texas. Texas F o r . Serv. B u l l . 52 (8 pp). B o y e r , W.D. , and G.R. Fahnestock. 1966. L i t t e r in long leaf pine stands thinned to p r e s c r i b e d densities. U.S.D. A. , F o r . Serv., Res. Note SO-31 (4 pg). B r a y , J.R. , and E . G o r h a m . 1964. L i t t e r production i n the forests of the world. Adv. in E c o l . Res., V o l 2. (101-157). Brown, J.K. 1963. C r o w n weights i n r e d pine plantations. U.S.D. A. , F o r . Serv. R e s . Note L S - 1 9 (4 pp). , 1965. E s t i m a t i n g c r o w n fuel weights of r e d pine and jack pine. U.S.D. A., F o r . Serv. R e s . P a p e r LS-20 (12 pp). B r u c e , D. 1951. F u e l weights on the O s c e o l a National F o r e s t . U.S.D.A., F o r . Serv. F i r e C o n t r o l Notes. V o l . 12 (3): 20-23. B u r n s , G.D. , and E . S. Irwin, 1942. E f f e c t of spacing on the efficiency of white and r e d pine needles as m e a s u r e d by the amount of wood production on the m a i n stem. V e r m o n t A g r i c . E x p . Sta. B u l l . 499, (28 pp). Cable, D. R. 1958. E s t i m a t i n g surface a r e a of ponderosa pine foliage i n c e n t r a l A r i z o n a . F o r . S c i . V o l . 4 (1):'45-49. Can. Dept. N. A. and N. R. 1956. Strength and r e l a t e d p r o p e r t i e s of woods grown in Canada. F o r . B r . F P L . T e c h . Note 3 (7 PP). Cel'niker, J . L . 1963. D e t e r m i n i n g the weight of foliage i n stands without removing the l e a v e s . O r i g i n a l not seen. F o r . A b s t r . , V o l . 24, A r t . 5383. (page 618). Chandler, C. C. I960. Slash weight tables for west side m i x e d c o n i f e r s . U.S.D.A., F o r . Serv. P S W F & RES, Tech. P a p e r . No. 48 (21 pages). C h r i s t o p h e r , J . F . , a n d H . E . Wahlgren. 1964. E s t i m a t i n g the specific gravity of south A r k a n s a s pine. U.S.D. A. , F o r . Serv. S F E S , Res. P a p e r SO-14 (10 pp.)  125  Conway, E . M. and C O . Minor, 1961. Specific gravity of A r i z o n a ponderosa pine pulp wood.. U.S.D.A. , F o r . Serv. R M F & R E S Res. Note No. 54 (3 pp.). Coutts, M.D. 1965. Sir ex noctilio and the physiology of P i n u s radiata. Comm. A u s t r a l i a F o r . Res. Inst. C a n b e r r a , B u l l . 41 (79 pp. ). Dahms, W.G. 1 9 6 6 . The b i o l o g i c a l aspect. How is stand development influenced by density? P r o c e e d i n g s of the I 9 6 6 Annual Meeting of Western R e f o r e s t a t i o n Coordinating Committee, P o r t l a n d , O r e . (15-17). D i e t e r i c h , J.H. 1 9 6 3 . L i t t e r fuels in r e d pine plantations. U.S.D.A., F o r . Serv., Res. Note LS-14 (3 pages). B i m o c k II, E . J . 1958. L i t t e r f a l l in a young stand of Douglas f i r . Northwest Sci. V o l . 32 (1): 19-29. Dobie, J . 1965. F a c t o r s influencing the weight of logs. B . C . L u m b e r m a n . Sept. Issue (36-46). Eggen, R. W. 1967. Weight m e a s u r e m e n t of pulpwood. Wood m e a s u r e m e n t Conference P r o c e e d i n g s . E d i t e d by F . Buckingham. U n i v e r s i t y of Toronto. F a c . of F o r . , Tech. Report No. 7 (157-175). E t h e r i d g e , D . E . 1958. The effect on variations i n decay of m o i s t u r e content and rate of growth of subalpine spruce. C a n . J o u r . Bot. V o l . 36 (187-206). Fahnestock, J. R. 1966. Logging s l a s h f l a m m ability. U.S.D.A. F o r . Serv. I F & R E S Res. P a p e r 58 (67 pp). F i e l d i n g , J . M. and A. G. Brown. I960. V a r i a t i o n s i n the density of the wood of Monterey pine f r o m tree to tree. Comm. Australia F o r . and Timb. B u r . L e a f l e t 77 (28 pp). F o r b e s , R. H. 1966. B u l k scaling logs by weight. B . C . L u m b e r m a n . F e b . Issue (20-22). F r a s e r , A. R. 1964. Scaling by weight. B.C. F . S. 84 (15 pp).  F o r . Serv. M i m e o  F r e e m a n , E . A. 1962. Weight-sealing sawlog volume by truck load. F o r . P r o d . Jour., V o l . 12 (10) 473-475.  126 F r e e s e , F . 1962. E l e m e n t a r y forest sampling. U.S.D.A., F o r . Serv., A g r i c . Hdbk. No. 232 ( 9 1 pp). F r o o d , G.D. 1963. Wood zone and growth zone relationships i n P i n u s contorta (DougL. ) v a r . l a t i f o l i a (Engelm. ). Unpublished B. S. F . thesis, U.B.C. (35 pp). Gibbs, R.D. 1958. P a t t e r n s i n the seasonal water content of t r e e s . (Chapt. 3. of the physiology of f o r e s t t r e e s . E d i ^ t e d b y K . V . Thimann) ( 4 3 - 9 9 ) . Ronald P r e s s , New Y o r k . G i l m o r e , A. R. 1963. M o r e specific gravity of short leaf pine i n southern Illinois. Jour. F o r . V o l . 61 (8): 596-597. , G . E . Metcalf, and W. R. Boggess. 1961. Specific gravity of short leaf pine and loblolly pine in southern I l l i n o i s . Jour. F o r . V o l 59 (12):894-896. Guttenberg, S. , D. F a s s n a c h t , and W. C. Siegel. I960. Weightscaling southern pine sawlogs. U.S.D. A., F o r . Serv., S.F.E.S. O c c a s i o n a l P a p e r 177 (6 pp). H a l l , G. S. 1965. Wood increment and c r o w n distribution relationships in r e d pine. F o r . S c i . V o l . 11 (4): 438-448. H a l l , , O.F. , and R.D. Rudolf. 1957. Weight l o s s of stored jack pine pulpwood. Minn. F o r . Note 57 (2 pp). Harada, H. , and H. Sato I966. On the dry matter and nutrient contents of the stem of mature C r y p t o m e r i a trees, and their distribution to the bark, sapwood and heartwood. Jour. Jap. F o r . S o c , V o l . 8 (8): 315-324. Hardy, S.S. , and G. W. Weiland III. Weight as a b a s i s for the purchase of pulpwood i n Maine. Maine A g r i . E x p . Sta. Univ. of Maine. T e c h . B u l l . 14 (63 pp). Hatiya, K. , T. F u j i m o r i , K. T e c h i c k i , and T. Ando. 1966. Studies on the seasonal variations of leaf and l e a f - f a l l amount i n Japanese r e d pine stands. B u l l . Gov't. Expt. Sta., Tokyo, Japan (101-113). Haygreen, J . 1 9 5 9 . D r y weight of green aspen belts. F o r . P r o d . Jour. , V o l . 9 ( 1 ) : 38-42. Jameson, D. A. 1966. D u i r n a l and seasonal fluctuations i n m o i s t u r e content of pinyon and juniper. U.S.D. A. , F o r . .Serv. Res. Note RM-67 (7 pp).  127 Jensen, R.A. , and J . R. D a v i s . 1953. Seasonal m o i s t u r e variations i n aspen. Minn. F o r . Note 19 ( 2 pp). Johansson, F . 1962. Weight scaling of unbarked conifer pulpwood. O r i g i n a l not seen. F o r . A b s t r . , V o l . 24, A r t . 2541 (page 293). Johnstone, W. D. 1967a. A b s t r a c t s of some of the l i t e r a t u r e dealing with the estimation and m e a s u r e m e n t of f o r e s t tree crown characteristics. Unpublished d i r e c t e d study, U.B.C. (14 pp). 1967 b. A n analysis of some of the v a r i a t i o n i n the specific gravity and m o i s t u r e content of lodgepole pine. Unpublished directed study, U.B.C. ( 3 8 pp). Keen, R. E . 1 9 6 3 . Weights and centres of gravity involvedin handling pulpwood t r e e s . P. & P. Res. Inst. Canada. Woodlands Res. Index 1 4 7 ( 9 3 pp). Keith, C. T. 1 9 6 1 . C h a r a c t e r i s t i c s of annual rings i n r e l a t i o n to wood quality. F o r . P r o d . J o u r . V o l . 1 1 ( 3 ) : 1 2 2 - 1 2 6 . K e r n , K. G. 1 9 6 2 . Relations between some c r o w n v a r i a b l e s and the d r y weight of foliage in Norway spruce and s i l v e r fir O r i g i n a l not seen. F o r . A b s t r . V o l . 2 3 , A r t . 4 0 8 7 (page 4 7 5 ) . K i i l , A. D. 1 9 6 5 . Slash weight and size distribution of white spruce and lodgepole pine. F o r . Chron. V o l . 4 1 ( 4 ) : 4 3 2 - 4 3 7 . , 1 9 6 7 . P e r sonal communications. F o r . and R u r a l D e v e l . , C a l g a r y .  R e s . Off. Can. Dept.  Kittredge, J . 1 9 4 4 . E s t i m a t i o n of the amount of foliage of trees and crowns. Jour. F o r . , V o l . 4 2 ( 9 0 5 - 9 1 2 ) . , 1 9 4 8 . F o r e s t influences. M c G r a w - H i l l Book Co. ( 3 9 4 pp), Knigge, W. 1 9 6 3 . Investigations on the dependency of the average density of N o r t h A m e r i c a n Douglas f i r stems of different growth conditions. U . B . C , F a c . F o r . T r a n s l a t i o n 22 (13 pp). Kozak, A., a n d J . H . G. Smith, 1 9 6 5 . A comprehensive and flexible multiple r e g r e s s i o n p r o g r a m f o r electronic computing. F o r . Chron. V o l . 4 1 ( 4 ) : 4 3 8 r 4 4 3 .  128 K r a m e r , P. J . , and T. T. K o z l o w s k i , I960. P h y s i o l o g y of t r e e s . (Chapt. 12: Internal water r e l a t i o n s . (342-367). M c G r a w - H i l l Book Co. (542 pp.) L a M o i s , L. 1958. F i r e fuels i n r e d pine plantations. U.S.D.A., F o r . Serv. L S F E S , Sta. P a p e r No. 68 ( 1 9 pp). Lange, K.D.  1962. Selling stumpage by weight i n the south: a case study. Jour. F o r . V o l . 60 (II): 816-820.  L a r s o n , P.R. 1957. E f f e c t of environment on the percentage of summerwood and specific gravity of slash, pine. Yale Univ. Sch. F o r . B u l l . 63 (80 pp). L i t t l e f o r d , T.W. 1961. V a r i a t i o n s of the strength p r o p e r t i e s within t r e e s and between trees in a stand of r a p i d growth Douglas F i r . Can. Dept. F o r s . , F P L , V-1028 (20 pp). L o o m i s , R. M. , R.E. P h a r e s , and J . S. C r o s b y . 1966. E s t i m a t i n g foliage and branchwood quantities i n shortleaft pine. F o r . S c i . , V o l . 12(l):30-39. Madgwick, H.A.I. 1963. Nutrient r e s e a r c h : some p r o b l e m s of the total tree approach. P r o c e e d i n g s , Soil S c i . Soc. A m e r . 27:598-600. M a r : M o l l e r , C. 1947. The effect of thinning, age, and site on foliage, increment, and l o s s of dry matter. Jour. F o r . V o l . 45 (393-404). Martin, W. H. , and H. Simard, 1959- Weight as a basis of wood measurement. P & P Res. Inst. Can. , Woodlands Sec. Index 1844 (B-6). Ann. Meeting Rel. No. 1 (294-297). M c K i m m y , M. D. 1959- F a c t o r s related to variations i n specific g r a v i t y i n young growth Douglas f i r . State of Ore. F o r . P r o d . Res. Centre, C o r v a l l i s , B u l l . 8 (52 pp). Metz, L. J. , and C. G. W e l l s . 1965. Weight and nutrient content of above ground parts of some l o b l o l l y pines. U. S.D. A. , F o r . Serv. Res. P a p e r SE-17 (20 pp). Melchanov, A. A. 1949- The r e s e r v e s of needles i n pine t r e e s i n timber stands of different ages. U.S. D. A., F o r . Serv. T r a n s l a t i o n No. 374 (3 pp). Muraro, S.J. 1964. Surface a r e a of f i r e fuel components as a function of weight. Can. Dept. F o r . Publ. No. 1080 (12 pp).  129  , 1966. Lodgepole pine logging slash. Can. Dept. F o r . Publ. No. 1153 (14 pp). Nylinder, P. 1967. Weight m e a s u r e m e n t of pulpwood. Wood M e a s u r e m e n t Conference P r o c e e d i n g s . E d i t e d b y F. Buckingham. Univ. of Toronto. , F a c . F o r . , Tech. Report No. 7 (157-176). Odum, E . P . 1959- Fundamentals (546 pp).  of ecology. W.B. Saunders Co.  Ovington, J. D. 1956. The form, weights, and productivity of t r e e species grown i n close stands. New Phytol. V o l . 55 (289-304). , 1957. D r y matter production b y Pinus s y l v e s t r i s L . Ann. Bot. , Lond. N. S. 21 (287-314). , 1962. Quantitative ecology and the woodland e c o s y s t e m concept. Adv. i n E c o l . Res., V o l . 1 (103-192). , and H. A. I. Madgwick 1959- Distribution of organic matter and plant nutrients i n a plantation of Scots pine. F o r . Sci. V o l . 5 (4): 344-355. Page, R. H. 1961. Weight as a m e a s u r e of volume F o r . P r o d . Jour. , V o l . 11 (7): 300-302 , and P. J. B o i s . 1961. Buying and selling southern yellow pine sawlogs b y weight. Ga. F o r . Res. Council, Report 7 ( 9 pp). Poljakova-Mincenko, N. F. 1961. The foliage of b r o a d - l e a v e d stands i n the steppe zone. O r i g i n a l not seen. F o r . A b s t r . V o l 23, A r t . 999 (page 112). Raber, O. 1937. Water utilization b y trees, with s p e c i a l r e f e r e n c e to the economic forest species of the north temperate zone. ( U.S.D. A., F o r . Serv. M i s c . P u b l . 527 )97 pp). Rennie, P. J. 1966. A forest sampling prodedure for nutrient uptake studies. Comm. F o r . Rev. V o l . 45 (a): 119-127. Reukema, D. L . 1964. L i t t e r f a l l i n a young Douglas f i r stand as influenced b y thinning. U.S.D. A., F o r . Serv. Res. P a p e r PNW-14 (8 pp).  130  1966. The y i e l d and density aspect. Does dense spacing r e a l l y produce the most v o l u m e ? Proceedings of the 1966 Annual Meeting of Western Reforestation Coordinating Committee. Portland, O r e . (23-26). R i s i , J. , and E . ZeUer, I960. Specific g r a v i t y of the wood of black spruce ( P i c e a m a r i a n a M i l l . B. S. R. ) grown on a H y l a c a m i u m - C p r n u s site type. L a v a l Univ. F o r . Res. Found. Contrib. 6 (70 pp). Rodin, L. E. , of of 38  and N. I. B a z i l e v i c , 1966. The b i o l o g i c a l p r o d u c t i v i t y the m a i n vegetation types i n the northern h e m i s p h e r e the old world. F o r . A b s t r . , L e a d i n g A r t . S e r i e s No. (3 pages) ( F o r . A b s t r . V o l . 27 (3): 369-372).  Rogerson, T. L. 1964. E s t i m a t i n g foliage on l o b l o l l y pine. U.S.D.A. F o r . Serv. Res. Note SO-16 (3 pp). Romancier, R. M. 1961. Weight and volume of plantation-grown l o b l o l l y pine. U.S.D.A., F o r . Serv., S E F E S . Res. Note 161 (2 pp). Row, C. , and S. Guttenberg. 1966. Determining weight-volume relationships for sawlogs. F o r . P r o d . Jour. V o l . 16 (5): 39-47. Samset, I. 1962. The weight of a complete Norway spruce t r e e : a p r e l i m i n a r y study at Sildevika. O r i g i n a l not seen. F o r . A b s t r . V o l 24. A r t 4037 (page 465). . Satoo, T. 1962. Notes on Kittredge's method of estimation of amount of leaves of forest stands. Jour. Jap. F o r . Soc. V o l 44 (10): 267-273. , 1965. F u r t h e r notes on the method of estimation of amount of leaves of forest stands. Jour. Jap. F o r . Soc. V o l . 47 (5): 185-190. , and M. Senda. 1966. M a t e r i a l s for studies of growth i n stand (VI) Tokyo Univ. Publ. 62, (116-146). Schopfer,  W. 1961. Quantitative determination of the a s s i m i l a t i n g organs of Norway spruce. O r i g i n a l not seen. F o r . Abstr. V o l . 21 A r t . 955 (page 102).  131  Schultz, C. D. , 1964. Wood chips measurement and valuation. Schultz T i m b e r B u l l . 95 (4 pp). Scott, D. R. M. 1955. Amount and c h e m i c a l composition of the organic matter contributed by o v e r s t o r y and u n d e r s t o r y vegetation to forest s o i l . Yale,Univ. Sch. F o r . B u l l . 62 (73 pp). Smirnov, V. V. 1961. The foliage and the weight of a e r i a l parts of trees i n b i r c h stands of the coniferous/broadleaved forest subzone. O r i g i n a l not seen. F o r . A b s t r . V o l . 23, A r t . 998 (page 112). Smith, J.H. G. 1966a. Studies of crown development are i m p r o v i n g Canadian forest management. P a p e r p r e s e n t e d at the 6th W o r l d F o r e s t r y Congress, M a d r i d . (16 pp). , 1966 b. The financial aspect. E a r l y stocking control? P r o c e e d i n g s of the 1966 Annual Meeting of W e s t e r n Reforestation Coordinating Committee. Portland, Ore. (17-23). , J . W. Ker, and J.' C s i z m a z i a . 1961. E c o n o m i c s of r e f o r e s t a t i o n of Douglas f i r , western hemlock, and western r e d cedar i n the Vancouver F o r e s t D i s t r i c t . U . B . C , F a c . F o r . , B u l l . No. 3. (144 pp). , and D. D. Munro. 1965. Point sampling and m e r c h a n table volume factors for the c o m m e r c i a l trees of B. C. U . B . C , Fac. F o r . M i m e o (39 pp). , and A. Kozak. 1967. T h i c k n e s s and percentage of b a r k of the c o m m e r c i a l t r e e s of B. C. U. B. C , F a c . M i m e o (33 pp). Society of A m e r i c a n F o r e s t e r s (SAF) 1961. Ronald P r e s s , New Y o r k .  For.  F o r e s t r y Handbook.  Spurr, S.H. , and W. Hsuing. 1954. Growth rate and specific g r a v i t y i n c o n i f e r s . Jour. F o r . V o l . 52(3)': 191-200. Srivastava, L. M. 1964. Anatomy, chemistry, and physiology of bark. Intern. Rev. of F o r . Res. V o l 1. (203-277). Stage, A. R.  1963. S p e c i f i c gravity and tree weight of single tree samples of grand f i r . U.S. D. A. , F o r . Serv. Res. P a p e r INT-4(llpp).  132  Steinlin, H. , and P. Dietz, 1962. Scaling and selling wood b y weight. O r i g i n a l not seen. F o r . A b s t r . V o l . 24, A r t . 2540 (page 293). Stemsrud, F. , and A. Gudim. 1962. T h e distribution of b a r k and wood, water and dry matter, density etc. at different heights i n b i r c h stems. O r i g i n a l not seen. F o r . A b s t r . V o l . 24. A r t . 929 (page 101). Stiell, W. M. 1962. C r o w n structure i n plantation r e d pine. Can. Dept. F o r . Tech. Note 122 (36 pp). , 1966. R e d pine crown development i n r e l a t i o n to spacing. Can. Dept. F o r . , Publ. No. 1145 (44 pp). Stonecypher, R. , F. C. Cech, and B. J . Zobal. 1964. Inheritance of s p e c i f i c g r a v i t y i n two and three year o l d seedlings, of l o b l o l l y pine. Tappi 47 (7): 405-407. Sundahl, W. E. 1966. Crown and tree weights of madrone, black oak, and tanoak. U.S.D.A., F o r . Serv. Res. Note PSW-101 (4pp). Tackle, D. 1962. Specific g r a v i t y of lodgepole pine i n the i n t e r mountain region. U.S.D.A., F o r . Serv., I M F & R E S Publ. 100 (4 pp). Tadaki, Y. 1965. Studies on the production structure of forest VIII. P r o d u c t i v i t y of an A c a c i a m o l l i s s i m a stand i n higher stand density. Jour. Jap. F o r . Soc. V o l . 47 (II): 384-391. , 1966. Some d i s c u s s i o n s on the leaf b i o m a s s of forest stands and t r e e s . B u l l . Gov't F o r . Exp. Sta. No. 184. Tokyo (135-161). , and T. Shidei, 1960. Studies on production structure of F o r e s t I. The seasonal v a r i a t i o n of leaf amount and the d r y matter production, of deciduous sapling stand. Jour. Jap. F o r . Soc. V o l . 42 (12): 427-434. , and F. Kawasaki. 1966. P r i m a r y p r o d u c t i v i t y of a young C r y p t o m e r i a plantation with e x c e s s i v e l y high stand density. Jour. Jap. F o r . Soc. V o l . 48 (2): 55-62.  133 , T. Shidei, T. Sakasegawa, and K. Ogino. 1961. Studies on production structure of forest II. E s t i m a t i o n of standing crop and some analysis on productivity of young b i r c h stand. (Betula platyphyla). Jour. Jap. F o r . Soc. V o l . 43 (1): 19-26. , N. Ogata, and T. Tadagi. 1962. Studies on production structure of forest III. E s t i m a t i o n of standing crop and some analyses on productivity of young stand of gastanopsis caspioata. Jour. Jap. F o r . Soc. V o l . 44 (12): 350-360. , N. Ogata and Y. Nagamoto, 1963. Studies on production of forest V. Some analyses on productivity of a r t i f i c i a l stand. ( A c a c i a m e l l i s s i m a ) Jour. Jap. F o r . Soc. V o l . 45 (9): 293-301. T a r a s , M. A. 1956. Buying pulpwood b y weight as compared with volume measure. U. S. D. A. , F o r . Serv. S F E S , Sta. P a p e r 74. (11 pp). , 1967. Weight scaling: its past-present-future. Wood M e a s u r e m e n t Conference P r o c e e d i n g s . Edited b y F. Buckingham. Univ. of Toronto. , F a c . F o r . Tech. Report No. 7 (143-156). Turnbull, K. J. , L . V. Pienaar, and I. E. B e l l a . 1965. Report on a study of log weight estimation. Univ. of Wash. , Sch. F o r . M i m e o (20 pp). U.S.D. A.,  1955. Wood Handbook. U.S.D. A., F o r . Serv., A g r . Bdbk. 72 (528 pp). , 1965a. Southern wood density survey. U.S. D. A. , F o r . Serv., Res. P a p e r F P L - 2 6 (38 pp). , 1965 b. W e s t e r n wood density survey. U. S. D. A. , F o r . Serv., Res. P a p e r F P L - 2 7 (58 pp).  Vaidya, M. S. L . 1963. D r y matter production and nutrient accumulation i n plantations of shortleaf pine. O r i g i n a l not seen. F o r . A b s t r . V o l . 25, A r t . I860 (page 211). Wahlgren, H. E. 1967. P e r s o n a l communications. U. S. D. A. , F o r . Serv. F o r . P r o d . L a b . Madison.  134 and D. L . Fassnacht. 1959. E s t i m a t i n g tree specific g r a v i t y f r o m a single i n c r e m e n t care. U. S.D. A. , F o r . Serv. F P L 2146. Madison (9 pp). , A. C. Hart, and R. R. Maeglin. 1966. E s t i m a t i n g tree specific gravity of Maine conifers. U.S.D. A. , F o r . Serv. Res. P a p e r F P L 61 (22 pp). Wakefield, W. E . 1957. Determination of the strength p r o p e r t i e s and p h y s i c a l c h a r a c t e r i s t i c s of Canadian woods. Can. Dept. N. A. and N. R. , F o r . B r . 119 (64 pp). Weetman, G. F. , and R. Harland. 1964. F o l i a g e and wood production in unthinned black spruce i n northern Quebec. F o r . Sci. V o l . 10 (1): 80-88. Wellwood, R. W. , and J.H. G. Smith. 1962. V a r i a t i o n s i n some important qualities of wood f r o m young Douglas f i r and hemlock trees. U.B.C., F a c . F o r . , Res. P a p e r 50 (15 pp). , and J. W. Wilson. 1965. The growth i n c r e m e n t as a guide to p r o p e r t i e s i n conffer wood. P a p e r presented at Meeting of I U F R O , Sec. 41. (25 pp). Wendel, G. W. I960. F u e l weights of pond pine crowns. F o r . Serv., .SEFES., P a p e r 149 (2 pp).  U.S.D. A.,  , T. G. Storey, and G. M. B y r a m . 1962. F o r e s t fuels on organic and a s s o c i a t e d soils i n the coastal plain of N o r t h C a r o l i n a . U. S. D. A. , F o r . Serv. S E F E S , Sta. P a p e r 144 (46 pp). Wheeler^ P. R. , and H. L. Mitchell, 1962. Specific gravity v a r i a t i o n i n M i s s i s s i p p i pines. U.S. D. A. , F o r . Serv. F L P - 2 2 5 0 (4 pp). Whittaker, R. H. 1966. F o r e s t dimensions and production i n the G r e a t Smoky Mountains. Ecology, V o l . 47(1): 103-121. Wilde, S.A. , and B.H. P a u l . 1959Growth, specific gravity, and c h e m i c a l composition of quaking aspen on different s o i l types. U.S.D. A., F o r . Serv., F P L . M a d i s o n 2144 (4 pp). Wile, B. C. 1964. C r o w n size and s t e m diameter i n r e d spruce and b a l s a m f i r . Can. Dept. F o r . Publ. 1056 (9 pp).  135 Wilfong, J. G. 1966. Specific gravity of wood substance. F o r . P r o d . Jour. V o l . 16(1) 5 5 - 6 l . :  Williston, H. L . 1965. F o r e s t floor i n l o b l o l l y pine plantations as related to stand c h a r a c t e r i s t i c s . U.S.D.A. F o r . S e r v . , Res. Note SO-26 (93 pp). Witkamp, M. 1966. M a c r o f l o r a , m i c r o f l o r a , and soil r e l a t i o n ships i n a pine plantation. Ecology, V o l . 47 (2): 238-244. Woods, F. W. I960. E n e r g y flow s i l v i c u l t u r e - a new concept for f o r e s t r y . Proceedings of S.A. F. , Wash. (25-27). Yamamoto, T. 1965. Amount of nutrients i n the leaves and growth of t r e e s . Inorganic components i n the leaves of white b i r c h trees (Betula platyphylla var. japonica) B u l l . Gov't. F o r . Exp. Sta. No 182 (43-65). Young, H. E . , 1964. The complete t r e e concept - a challenge and an opportunity. Proceedings S. A. F. Ann. Meeting (11 PP), and A. Chase, 1965. F i b e r weight and pulping c h a r a c t e r i s t i c s of the logging residue of seven tree species i n Maine. Tech. B u l l . No. 17, Maine A g r . Exp. Sta. (44 pp). , L . Strand, and R. Attenberger, 1964. P r e l i m i n a r y f r e s h and d r y weight tables for seven t r e e species i n Maine. Tech. B u l l . 12, Maine Agr. Exp. Sta. (76 pp).  136 A P P E N D I X I.  Investigator  A S u m m a r y of P r e v i o u s Investigations of B i o m a s s , Foliage, and Slash.  .. ,_  Location.. ,  Plant. Community.  Characteristics Investigated  Japan  L e a v e s & twigs  Ando  (1965)  Japan  C r y p t o m e r i a japonica Pinus thumb e r g i i  Attiwill  (1966)  Australia  Eucalyptus  Crown weight  B a s k e r v i l l e (1965a)  Canada  Abies b a l s a m e a  S e v e r a l components  B a s k e r v i l l e (1965b)  Canada  B a k s e r v i l l e (1966)  Canada  B o y e r and F a h n e s t a c k (1966) B r o w n (1963)  U.S.  A'.balsamea & _P. glauca A. b a l s a m e a & P. glauca Pinus p a l u s t r i s  Ando et a l (1959)  B r o w n (1965) B r u c e (1951) B u r n s & Irwin (1942)  Branch, s t e m  S e v e r a l components Roots, and l e s s e r veg. litter & flash fuels  u. s.  Pinus r e s i n o s a  U.S.  P. r e s i n o s a & P. banksiana P. p a l u s t r i s & P. serotina P. strobus & P. resinosa  needle wt. needle surf, a r e a  U.S. U.S.  crown wt. crown wt.  Variables  Best Variable  Suggested a method of sampling Site Index and density dbh & B A  BA  Density Density Stand B A dbh  In c l o s e d stands site index and density had little affect. Objected to use of mean tree sampling method Ave. diameter depends upon component measured D i s c u s s e d the affect of stand density on d r y matter production. T o t a l i n c r e a s e d and l e s s e r d e c r e a s e d with i n c . density. Increased with i n c r e a s e d stand B A Investigated influence of site index and density  dbh & c r . length  dbh  Studied influence of stand density T a b l e s for open and closed stands.  crown wt. vol. i n c .  Needles m o r e efficient at wider spacing  Cable (19 58)  u. s.  Pinus ponderosa  Cel'niker (1963) Chandler (I960)  U. S.S.R.  u. s.  B r o a d - l e a v e d trees number of needles slash conifers  D i e t e r i c h (1963) Fahnestack (I960)  u. s. u. s.  Pinus r e s i n o s a many species  surface fuel crown wt.  H a l l (1965)  U.S.  Pinus resinosa  stem growth  H a r a d a & Satoo (1966)  Japan  H a t i y a et a l (1966)  Japan  C r y p t o m e r i a japonica Pinus densiflora  K e r n (1962)  Germany  P. abies &: A. alba  several variables cr. surf, area  K i i l |19 6 5)  Canada  dbh  Kittredge (1944)  U.S.  P. glauca & P. contorta foliage wt. Pinus ponderosa  dbh dbh  density &; age dbh & c r . length dbh  height foliage wt.  Other Comments  season  vol. i n c r . & dbh  Relationship unchanged for different sizes, densities, and ages. C l o s e relationship o b s e r v e d s l a s h amount affected b y t r e e size and species B A good and age i m p r o v e d prediction Developed r e g r e s s i o n equations to predict crown weight S t e m growth related to amount of foliage above i t V a r i e d with stand age and region Site quality and density had little effect on seasonal v a r i a t i o n Differences between the two species s m a l l SI. wt. /merch. cu.ft. v a r i e s with dbh  BA  Relationship undhanged b y age, density and tree size  A P P E N D I X I (Cont'd) 137 Pinus resinosa P i n u s echinata  needle wt. foliage & b r a n c h wt.  density &: site several variables  L a M o i s (1958) L o o m i s et al.(1966)  U.S. U.S.  Madgwick (1963) Mar: M o l l e r (1947) Molchanov (1949)  U.S. Denmark U.S.S.R.  M u r a r o (1964)  Canada  P i n u s contorta  s l a s h wt.  M u r a r o (1966) Ovington (1956)  Canada U. K.  Pinus contorta S e v e r a l species  s l a s h wt. biomas s  dbh many v a r i a b l e s  Ovington (1957) Ovington (1962) Ovington Ik Madgwick (1959) Pojakova-Mincenko (1961) Rennie (1966) R o g e r s o n (1964) Satoo (1962) Satoo (19 65) Satoo & Senda (1966)  U. K. U. K.  P. s y l v e s t r i s M a n y species P. s y l v e s t r i s  biomass  several variables  U. K. U.S.S.R. Canada U.S. Japan Japan Japan  Schopfer (1961) S m i r n o v (1961)  Germany U.S. S. R.  S t i e l l (19 62) Stiell (1966) Sundahl (1966) T a d a k i (1965) T a d a k i (1966) T a d a k i & K a w a s a k i (1966) T a d a k i & Shidie (I960)  Canada Canada U.S. Japan Japan Japan Japan  T a d a k i et al.(196l) T a d a k i et al.(1962)  Japan Japan  T a d a k i et al-(1963) V a i d y a (1963) Weetman &a H a r l a n d (1964)  Japan U.S. Canada  P. abies & Q. rofclur litter Pine (presumably needle wt. Pdnus s y l v e s t r i s )  C r y p t o m e n a japonica P i c e a abies Broad-leaved trees  Pinus resunosa Pinus resinosa Broad-leaved trees Acacia mollissima Several C r y p t o m e r i a japonica V/lmus p a r v i f o l i a Betula p l a t y p h y l l a Castanopsis c u s pidata Acacia mollis sima Pinus palustris Picea mariana  density  biomass  B r o a d - l e a v e d t r e e s foliage Pinus reginosa P i n u s taeda  diam. cr. base  biomass foliage wt. foliage wt. foliage wt. biomass s l a s h &: foliage wt. crown wt. etc. ,  dbh &: vol. i n c r -  dbh & dbh  BA  dbh  foliage wt. foliage wt. crown & tree wt. foliage wt. foliage b i o m a s s  Both v a r i a b l e s affect amount of fuels C r . length/height adjusts for density & bole f o r m Suggested sampling method Thinning reduced amount of organic matter Needle weight was d i r e c t l y p r o p o r t i o n a l to volume i n c r e m e n t r e g a r d l e s s of age and density Height & SI didn't s i g n i f i c a n t l y affect b r a n c h litter d i s t r i b . Wt. / cu. ft. v o l . v a r i e d i n v e r l y with dbh cr. wt. i n c r e a s e d with age; bole wt/unit canopy i n c r e a s e d with age and height Studied changes i n t r e e weight distribution D i s c u s s i o n of b i o m a s s and quantitative ecology D i s c u s s need to consider each component separately. C l o s e r e l a t i o n s h i p o b s e r v e d between foliage wt. and volume and dbh i n c r e m e n t s P r o p o s e d sampling method O b s e r v e d a close r e l a t i o n s h i p Sampling Sampling Studied m e a n tree and f o r m u l a stand table methods U s e d double l o g a r i t h m i c t r a n s f o r m a t i o n L i n e a r r e l a t i o n s h i p between leaf wt. and s t e m wt. leaf wt. and b r a n c h wt. , and b r a n c h wt. and s t e m wt. F o l i a g e wt. /tree i n c r e a s e d with wider spacing Studied influence of spacing on crown wt. Weight tables p r e p a r e d * Studied b i o m a s s and leaf a r e a index D i s c u s s i o n of leaf b i o m a s s of stands and trees Max. production - pole stage  -  foliage wt. biomass  season BA  D i s c u s s e d seasonal v a r i a t i o n s Studied influences of stand density  biomass biomass biomass biomass  B A & dbh BA dbh & height dbh & volume  D i s c u s s e d stand s t r u c t u r e and productivity Studied p r o d u c t i v i t y Influence of site quality d i s c u s s e d  A P P E N D I X I (Cont'd)  138  Wendal (196.0) Wendel et aL(1962) Whittaker (1966)  U.S. U.S. U.S.  Wile (1964)  U.S.  Whitkamp (1966) Y a m a m o t o (1965) Young et al.(1964) Z y i j a e v (1964)  U.S. Japan U.S. U.S.S.R.  Pinus serotina F u e l wt. Pinus serotina F o r e s t fuels Q. alba & S. s e m p e r v i r o n s biomass P. rub ens & A. balsamea crown'wt. Pinus sylvestris biomass Betula platyphylla foliage S e v e r a l species biomass jLarix s i b i r i e a foliage wt.  F u e l weight tables Weight of u n d e r s t o r y vegetation &: l i t t e r Influence of site and l o c a t i o n on b i o m a s s  dbh & stocking  dbh & c r . 1. & CW  dbh  height & age many variables  vol. cai  U s e d double l o g a r i t h m i c t r a n s f o r m a t i o n Soil-biomass relations discussed Wt. i n c r e a s e d with height and age Weight tables b y dbh and height Several relationships  139 A P P E N D I X II  L o g a r i t h m i c Relationships of T r e e and T r e e Component F r e s h Weight (lb) on Dbh (in)  The following formulae are based on data obtained f r o m 63 lodgepole pine t r e e s ranging i n diameter at b r e a s t height f r o m 4. 3 inches to 10.9 inches (ob). 1.  T o t a l T r e e Weight (above a 1 foot stump): Y (lb.) = 2524. 49 l o g SE  2.  E  = 76. 27 l b . (17. 42%) r  SE  E  dbh (in.) - 1335. 16  = 65.92 lb. (17.01%) r  dbh (in.) - 1485. 97  S E „ = 64. 51 l b . (19. 58%) r E  SE  E  dbh (in.) - 242. 84  = 18. 08 lb. (35. 90%) r  = 0. 826  2  T r e e Slash Weight (needles plus branches plus non-merchantable top): Y (lb.) = 251. 17 l o g SE  6.  = 0. 934  2  T r e e C r o w n Weight (needles plus branches): Y (lb.) = 367. 17 l o g  5.  = 0.925  2  Merchantable Stem Weight (1 foot stump to 4 inch top (ob): Y (lb.) = 2273. 33 log  4.  = 0. 926  2  T o t a l Stem Weight (above a 1 foot stump): Y (lb.) = 2157. 32 log  3.  dbh (in.) - 1578. 0  E  dbh (in.) - 92. 03  = 25. 61 lb. (23. 59%) r  2  = 0. 525  D r y Needle Weight: Y (lb.) = 72. 08 log  dbh (in.) = 46. 51  S E „ = 3.93 lb. (35. 57%) r E  2  = 0.795  s o  CJ  O -I  C3 O o  Appendix III - .1. o o  The Relationship Between F r e s h T o t a l Stem P r o p o r t i o n (%) and Crown Width (ft. ).  Q CO  o o o  C? X  c o  • (-*  a a O ru _  !-<  o cx o ^1 PH  a a a a  co  07  o H  a  X _ . rt X K  1—1  CO CJ  X  o  to _ CP  o o o CO CO  o a o  co  O a a  co O  o  8 o CO  2.U0Q  3.200  u. 00Q  4.800  5.600 iAr^  6.f0Q Ji-l,  I ft-  \  i 7.200  —I——  8. 000  8.800  o o  §-4  o o o  07  A p p e n d i x III - 2.  The R e l a t i o n s h i p B e t w e e n D r y T o t a l S t e m P r o p o r t i o n (%) and C r o w n W i d t h (ft.).  o o o  o o  0  4-> .  X  u  'o .o PM  O  o o  ra.  X  X x  x  CO  11 u Q  O)'  a o  *  o  x *  o  o o CO _j  CO  o a o CO  o o o ra . CO  2.400  1  3.200  1  M.000  1  4.800  — ,  ,  5.600  6.1400  ' C r o w n W i d t h (ft. 1  —I  (  7.200  8.000  8.800  A p p e n d i x III - 3 .  The Relationship Between'Fresh Merchantable Stem P r o p o r t i o n (%) and Dbh (in; ).  x XX  *  x*x  X X X  x X X  *  X X  X  "i. 000  ~1 4.800  1  5.600  6. WO  1  7.200  8.000 6hh  (in.  )  I 8.QO0  "1 9.600  o o O  CO . C P  Appendix III - 4 .  The Relationship Between Dry. Merchantable Stem P r o p o r t i o n (%) and Dbh (in..).  o  •O O  CO, VO  X X  X  a  a o  a". co  o  x  X X  X  *  '  x X  0 ^ u  o CL o u  X  o  O  &°.  X  =*•. CD  CO  'a>  i—i ,Q rt C3 rt CD. X. LD  O  X ' X  U M  x x  X  ll)  to. 3*  o o a  X  o a o  X  ro  a a o .  rvr  4-  4.000  I  4.800  1  5.600  1—:  6.400  1  7.200  1  .  8,000  dbh (in. )  1  8.800  1  9.60Q  1  10.400  a o a  CD —  o o o  cn  Appendix III - 5.  T h e Relationship Between F r e s h Bole Wood P r o p o r t i o n (%) and Dbh. (in.).  o o o  X x X  o o o  X X  o.  O o o :CD. -co  x  Xx  o • I-l  X  o° 0-o  o• ,  u  to. OH CO • O  o. O  CD  ^  CO  X-  X  co  CO  o o o  X  CNJ.  oo  o a a a -\ co  o o o  o Q o CD .  4.000  ~1  4.800  I  5.600  I 6.400  1  1  7.200  8. ODD dbh  fin \  ,  . 8.8D0  1  9.600  1D.HQD  o o o CO  o o a 0>  Appendix III - 6.  The Relationship Between D r y Bole Wood P r o p o r t i o n (%) and Dbh (in.).  o a o oj. a>  *  x  *  O. 0?  a o o co. ^ co 5^  XX  X  C 0  x  • f-l  x  ^ a o o o. • o to.  X *  X  PH  X  T3 O 0  > o ? o o  x  X  CO  O  a o  <\i. co  X X  X  X  a o a  X  x  cd.  CO  o a o  ed. 4^  o O CO .  r-  t  4.. OOQ  ~1  4.800  I  5.600  I  o\40D  7.2DD  8.000  ~ T —  8.800  9.600  10.40D  o  a  oo CO  Appendix III - 7.  o o  The Relationship Between F r e s h Needle P r o p o r t i o n (%) and Crown Length (ft.).  CO  o o  3 co'  x  o a CD  eft  X  1 0 "  X  o X  o ® rH  X  -f. '  X  CD  X  r—I  CU 0  <H  r-,  a  r—i  CU  X  X  X  & X  ,  X  3  X X X  a a CM CT)'  a =r  cvi'  x X  • a LO  ON  CD  r-.  !  8.000  12.000  I  16.ODD  1  :  SO.000  i  2»i. 000  1  .  28.000  Crown Length (ft. )  1  ...  ZZ. 000  36.000  40.000  ra o co CO ' A p p e n d i x III  - 8.  The Relationship Between D r y Needle P r o p o r t i o n (%)  a n d C r o w n W i d t h (ft.).  a o a op  E3 O  co"  X X  C3  o  CO  fl o o O PH  o  o  X X  0 3  ^  X X  X  x x  .—i  T3 <U 0 £ C3  X X  ^ a Xx  Q *  x  x  X  a  a ca ro"  X  x  a a cvi"  a a to  4^  -a  cn  tn  r- .  2.400  I  3.SOD  1  4.ODD  1  4.80D  1  1  5.BOD  6.400  C r o w n W i d t h (ft. )  !  7.30D  J  Q.QDO  \  B.80Q  0  o o  •'. CM  a a a  cd.J  o C3 O  Appendix III - 9 .  The Relationship Between F r e s h B r a n c h P r o p o r t i o n (%) and T r e e B a s a l A r e a (sq. ft. ).  a a a  a C3  a o  u d rH  CP CJ ' co co  CO  u h •  o a  X  co  X X  a o a  * X  X  x x  x  X X X  *x  x  X  X  *X  v  * x  a a  00  a a .079  .159  32Q  I ,^00  1 .180  B a s a l A r e a (sq. ft. )  I .560  .640  ,72D  a a. CM  a a a coj  a a  <P-J  Appendix III - 10.  The Relationship Between D r y B r a n c h (%) and Crown Width (ft. ).  Proportion  a a  a a  CM_J  o o  5  CM  .  2 °• U <—' PH  •u CQ  a  f-i  CO  x X  Q  a CD  X X  o a X X. X  X  X  *x  y  X  a CNJ  sO  a CD a  S.ljaa  ,  O.2Q0  ,  4.Q0D  ,  4.800  ( 5.600  ,  6. UOO  Crown Width (ft. )  7. £00  8.000  I  a. B O O  a a CO.  Q  o a  d. oj  Appendix III - 11.  The Relationship Between F r e s h C r o w n P r o p o r t i o n (%) and C r o w n Width (ft.).  a a O  ca.  a o o co_J  o Q  O  '  • rH  to C M  0  H  X  X  2 oi.  X  X  ' .-HI  o tH U a a  a  X X  rH  X  X  x  CJ D  x *  a CD X X  a a a  * X  CO'  a a • o C3  a  1=3  C\i"  2.100  3.2DO  ~1 4. ODD  4.800  T  T  5.600 6.100 Crown Width (ft. )  7.2DD  I  8.000  f 8.800  a O  • a  Appendix III - 12.  The Relationship Between D r y C r o w n P r o p o r t i o n (%) and C r o w n Width (ft. ).  a  a co J  a  • a  fi  r-.  .2 §  •K °  O OJ. PH -r-l O PH  a  o a u o U d_J >^ Q  o o a  X  ed'  x  tn • a  x X  X X  x *  x X  X  to'  D • a  o o o I  2.100  3.2Q0  |  4.000  1  4.800  [  1  5.600  6.400  . C r o w n Width (ft. )  1  7.EDO  J  8.000  8.80D  o o  o  CO . CO  o o a  *  a . CO  a a o  Appendix III - 13.  The Relationship Between F r e s h Slash P r o p o r t i o n {%) and T r e e Height (ft.).  o a  o co  o a a  i  CO. 1/7  a  —-  X  S CD.  .2 =r-  X.  rH  O O >H  *  a  D  rt CO D  rH  a a a  cvi ro X  *  a a  X *  *  X  CM  X  a a a  x*  cd  o-1 3 41.000 aS  *  X  < X  X X  X  —,  48.000  ,  52.ODD  ,  5S.00D  ,  6D.Q0D  X X  ,  61.000.  T r e e Height (ft.)  x  X  X  ,  6B.0Q0  j  72.000  7G.0D0  o  CD  o  CO . CO  o  a a dt.  CD  A p p e n d i x III - 14. The Relationship-Between D r y Slash P r o p o r t i o n (%) and T r e e Height (ft. ).  CO  a a  a o a  a • a — a c  CO . LP  O :  o P- a o a PH  CO.  CO  ' rt . r—i  CO  Q  a a'.  3*  •  a •  X  'X X  c J . r o  x* X  a a CD  Xx X X  -r. CO  x X X XX x  • a a CO  x  4  a ca a  .  cb 4H.QQ&  , 4,8:000  , .  52.000  , 56. ODD  —,  ,  6D.000 6t.QDP Tvr.o. T-Tei rrht ( f t . )  ,  J  68.0DQ  72,. ODD  76-000  

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