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Yield and volume tables for aspen in central and northern Alberta MacLeod, William Kenneth 1952

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YIELD M D  VOLUME TABLES FOR ASPEN IN  CENTRAL AND NORTHERN ALBERTA  by WILLIAM KENNETH MACLEOD  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE  REQUIREMENTS FOR THE DEGREE OF MASTER in  OF FORESTRY  the F a c u l t y of  GRADUATE STUDIES  We  accept  standard  this  t h e s i s as c o n f o r m i n g  required  degree  from c a n d i d a t e s f o r the  o f MASTER  Members o f t h e F a c u l t y  THE  OF FORESTRY  of F o r e s t r y  UNIVERSITY OF B R I T I S H COLUMBIA April,  t o the  1952  ABSTRACT Even-aged w e l l stocked aspen stands A l b e r t a were  sampled i n o r d e r t o d e r i v e  a c r e f o r number and s i z e measures  of volume.  qualities  of  site  of  trees,  The s t a n d s  i n Northern  "normal" y i e l d s  basal  area,  occur c h i e f l y  and v a r i o u s on  three  w h i c h have been c l a s s i f i e d i n t o  Medium and Good by t h e  average h e i g h t  E x c e p t i o n a l l y h i g h m o r t a l i t y p e r decade  acteristic  in fully  s t o c k e d young aspen s t a n d s  o f number o f  markedly d i f f e r e n t other species.,  t r e e s p e r acre  from the  A table  of  Pair,  of dominant t r e e s  80 y e a r s .  relation  per  is  at  char-  and t h e  to average diameter  is  t r e n d s f o u n d by i n v e s t i g a t o r s s t a n d d e n s i t y u n i t s was  t o p e r m i t the, r a p i d . c a l c u l a t i o n of  for  constructed  s t a n d - d e n s i t y i n d e x when  a v e r a g e d i a m e t e r and number o f t r e e s p e r a c r e  have been  deter-  mined . The mean a n n u a l c u b i c v o l u m e g r o w t h on medium i s maximum a t  age I4.O.  growth reaches  a peak  F o r merchantable at  f r o m two o t h e r r e g i o n s aspen t r e e s  above  85 and 130 y e a r s  show t h a t  80 y e a r s  wood s h o u l d be u t i l i z e d  of  before  the  age,  aspen stands  respectively.  amount o f  cull  a stand-age  show s i g n s  of  130 y e a r s  volume i s  feet, Data  is high in  t h i s indicates that  r e a c h e d i f maximum r e t u r n i n b o a r d f o o t By lij.0 y e a r s  c u b i c and b o a r d  sites  the is  desired.  of b r e a k i n g up.  The of  hardwood  s t a n d s m e a s u r e d were composed m a i n l y  aspen b u t b o t h w h i t e b i r c h  many o f t h e p l o t s . slightly  less  The g r o w t h o f t h e b l a c k p o p l a r i s o n l y  than that  l o w e r volumes p e r t r e e volume t a b l e s  and b l a c k p o p l a r o c c u r r e d on  f o r t h e aspen.  I t has c o n s i s t e n t l y  which p e r m i t s the use o f aspen  when c o r r e c t i o n f a c t o r s  are a p p l i e d . '  ACKNOWLEDGMENT  The his  a u t h o r ' would l i k e  appreciation  Resources Branch,  t o t h e Department o f  and D e v e l o p m e n t ,  Ottawa,  the tables  Forestry  f o r permission  t h e d a t a employed of  to express  to use  i n the development  presented.  TABLE OP CONTENTS -''  ' Page' 1  INTRODUCTION THE POPLAR FOREST. SAMPLED.-..  .:  ASPEN Y I E L D TABLES  ' '  Height  Growth and S i t e "Index  Number  and S i z e  '  '  ••  '  '  -•  l± 11.  llj.  Volume Y i e l d s  . ll|.  Cubic Feet  Merchantable Increment  '  13  of Trees  Basal Area Y i e l d s  Total  2  llj.  C u b i c and B o a r d F e e t  II4. 2I4.  and R o t a t i o n Age  Cull  25  Density  28  BLACK POPLAR,  PERCENTAGE COMPOSITION  VOLUME TABLES FOR ASPEN AND  CHANGE  33 36  BLACK POPLAR  Measurements and C o m p u t a t i o n s  36  Total  37  Cubic Feet  Merchantable  Cubic Feet  38  Merchantable  Board F e e t , Scribn'er R u l e  39.  VOLUME TABLES FOR WHITE BIRCH Total  Cubic Peet  Merchantable  '  C u b i c and B o a r d P e e t  i|4 '  kk' • )|)|  '  53  Basic Data F i e l d Work  53  Office  56  APPENDIX  Computations.  Method o f A n a l y s i s • BIBLIOGRAPHY  .  56 65  ILLUSTRATIONS Table 1.  Page Stand c o m p o s i t i o n species  on  and  frequency  sample p l o t s  .  2..  Total.height  3.  T o t a l number o f t r e e s p e r  Jj..  and l a r g e r Diameter of site  of  of occurrence  ..  average dominant  0 . 6 - i n c h d.b.h.  acre  6 the  a v e r a g e t r e e by  age  class  and  T o t a l basal area per acre i n c l u d i n g a l l t r e e s 0 . 6 - i n c h ' d . b . h . and l a r g e r  6.  Yield  9.  10.  11.  12.  13.  acre  i n cubic  feet, excluding  . f o r a l l t r e e s 0 . 6 - i n c h d.b.h. and  7  bark,  l a r g e r .......  7  Y i e l d p e r a c r e i n c u b i c f e e t o f m e r c h a n t a b l e stem, e x c l u d i n g b a r k , f r o m a 1 - f o o t stump t o a [(.-inch t o p i n s i d e b a r k ; f o r a l l t r e e s Jj.-incb.es d.b.h. and  8.  6  • • ••  5.  7.  \x 5  aspen  index  per  of  larger  ••••  •  ••  16  Y i e l d s p e r acre i n c u b i c f e e t of m e r c h a n t a b l e stem, e x c l u d i n g b a r k , f r o m a 1 - f o o t stump t o a ij.-inch t o p i n s i d e b a r k ; f o r t r e e s J4.-II i n c h e s d.b.h. i n c l u s i v e ,,  16  Y i e l d s per acre i n c u b i c f e e t of merchantable stem, e x c l u d i n g b a r k , f r o m a 1 - f o o t stump t o a ij.-inch t o p i n s i d e b a r k ; f o r t r e e s 12-inches d.b.h. and l a r g e r  17  Y i e l d s per acre i n board f e e t , S c r i b n e r l o g r u l e , f r o m a 1 - f o o t stump t o a 6 - i n c h t o p i n s i d e ,bark; f o r a l l t r e e s 7 - i n c h e s d.b.h. and l a r g e r  17  Y i e l d s per a c r e . i n board f e e t , S c r i b n e r l o g r u l e , f r o m a 1 - f o o t stump t o a 6 - i n c h t o p i n s i d e b a r k ; f o r a l l t r e e s 12-inches d.b.h., and l a r g e r •  18  C o n v e r s i o n u n i t s a p p l i e d t o t o t a l c u b i c volume "of w e l l s t o c k e d a s p e n s t a n d s t o o b t a i n merc h a n t a b l e c u b i c volume o f a l l t r e e s JL-inches d.b.h. and l a r g e r ......... ^ ...  20  C o n v e r s i o n u n i t s a p p l i e d t o t o t a l c u b i c volume o f w e l l s t o c k e d aspen s t a n d s t o o b t a i n m e r c h a n t a b l e c u b i c volume of a l l t r e e s 12-inches d.b.h.. and l a r g e r  21  ILLUSTRATIONS Table 111.  15.  16.  17.  18.  19.  20.  21. 22. 23. 2I4.. 25.  (  Page. Conversion u n i t s applied to t o t a l cubic volume o f w e l l s t o c k e d , aspen s t a n d s t o o b t a i n m e r c h a n t a b l e board f o o t volumes, S c r i b n e r r u l e , o f a l l t r e e s 7 - i n c h e s d.b.h. and l a r g e r  21  C o n v e r s i o n u n i t s a p p l i e d t o t o t a l c u b i c volume o f w e l l s t o c k e d a s p e n s t a n d s t o o b t a i n merc h a n t a b l e board f o o t volumes, S c r i b n e r r u l e , of a l l t r e e s 1 2 - i n c h e s d.b.h. and l a r g e r  22  Mean and p e r i o d i c a n n u a l aspen g r o w t h p e r a c r e i n c u b i c f e e t , e n t i r e stem, e x c l u d i n g b a r k , a l l t r e e s 0 . 6 - i n c h d.b.h. and l a r g e r  22  Mean and p e r i o d i c a n n u a l aspen g r o w t h p e r a c r e i n cubic f e e t , merchantable stand, e x c l u d i n g b a r k , f r o m a 1 - f o o t stump t o . a 1 | - i n c h t o p i n s i d e b a r k ; f o r a l l t r e e s [(.-inches d.b.h. and l a r g e r  23  Mean, and p e r i o d i c , a n n u a l a s p e n g r o w t h p e r a c r e i n board f e e t , S c r i b n e r r u l e , from a 1 - f o o t stump t o a 6 - i n c h t o p i n s i d e b a r k ; f o r a l l t r e e s 7 - i n c h e s d.b.h. and l a r g e r  23  R o t a t i o n age t o t h e n e a r e s t h a l f d e c a d e f o r maximum wood p r o d u c t i o n , a c c o r d i n g t o p o r t i o n o f s t a n d and u n i t o f volume c o n s i d e r e d , f o r three s i t e c l a s s e s  25  C u l l p e r c e n t , f o r t r e e s li-inches l a r g e r , r e l a t e d t o aspen t o t a l medium s i t e s ..  26  d.b.h. age f o r  and  S t a n d d e n s i t y u n i t s f o r aspen c o r r e s p o n d i n g average stand.diameters i n i n c h e s Percentage t o age  composition  of b l a c k p o p l a r  to '  31  related  35  Volume t a b l e f o r aspen and t o t a l cubic feet  black poplar '  Volume t a b l e f o r a s p e n and merchantable cubic f e e t  black poplar i n  Volume t a b l e f o r a s p e n and merchantable board f e e t  black poplar i n  '  in J4.9 50 5l  ILLUSTRATIONS  Table  Page  26.  Volume  27.  Plot  '28.  Correction i n years to from increment b o r i n g s a s p e n t o t a l age  29.  30.  t a b l e s f o r white  distribution  by  birch  age  and  be or  52  .... site  index  53  classes  added, t o a g e stump c o u n t s ,  determined to obtain 55  F r e q u e n c y d i s t r i b u t i o n o f . r e s i d u a l s and the probits corresponding to their cumulative frequency percentStatistics illustrating reliability t a b l e s , and e f f e c t o f age, and s i t e  59  =. ...  of.yield and age,  6I4.  Figur,e 1.  Map showing l o c a t i o n of sample p l o t s ; e a c h d o t m a r k s a l o c a l i t y w h e r e one o r m o r e p l o t s w e r e taken .. .  2  2.  Height  curves  5  3«  Number  of  and I4..  site  5»  Total  6.  Yield  8.  9.  site  acre  classification  showing  trends  '  with  age 8  of  tree  showing  acre  trends  of  average  trends  area  showing  per  showing 7.  trees per  basal  d.b.h.,  for  index  Diameter height,  used  per  with  acre  trends  age  breast  site  f o r trees  over  0.6-inch  site  index  with  and  age  area' at  and  i n cubic feet with  basal  age  and  excluding site  9  index  9  bark, 10  index  Y i e l d p e r acre i n c u b i c f e e t of merchantable stem, e x c l u d i n g b a r k ( t o a [(.-inch t o p i n s i d e b a r k ) , s h o w i n g t r e n d s w i t h age and s i t e i n d e x  18  Y i e l d p e r acre i n - b o a r d .feet, S c r i b n e r l o g r u l e (to a 6 - i n c h top i n s i d e b a r k ) , showing t r e n d s w i t h age a n d s i t e i n d e x ••••  19  The r e l a t i o n s h i p b e t w e e n t h e m e r c h a n t a b l e c u b i c f o o t - t o t a l c u b i c f o o t volume r a t i o , t o average s t a n d d.b.h., where the m e r c h a n t a b l e s t a n d i n c l u d e s t r e e s I 4 . - i n c h e s and l a r g e r  .  19  t  ILLUSTRATIONS  Figure 10.  :  11.  12.  ' The r e l a t i o n s h i p between b o a r d f o o t - t o t a l c u b i c f o o t volume r a t i o , t o a v e r a g e s t a n d d.b.h., where t h e m e r c h a n t a b l e s t a n d i n c l u d e s t r e e s 7 - i n c h e s d.b.h. and l a r g e r  20  The r e l a t i o n o f t o t a l number o f t r e e s p e r a c r e t o average, s t a n d d.b.h., f o r .78 f u l l y s t o c k e d aspen sample p l o t s  30  The r e l a t i o n o f p e r c e n t a g e c o m p o s i t i o n , by b a s a l a r e a , t o t o t a l age f o r b l a c k p o p l a r on 61 sample p l o t s  35  1 3 . ' The t r e n d o f h e i g h t foot height class Iij.. 15.  16.  17. 18.  19.  20. 21. 22.  23. :  •Page  on d.b.h. w i t h i n e a c h  10I4.5  The- r e l a t i o n o f b o a r d f o o t volume ( S c r i b n e r r u l e ) on d.b.h. by 1 0 - f o o t h e i g h t c l a s s e s  l\$  The r e l a t i o n o f b o a r d r u l e ) on t o t a l h e i g h t classes  I4.6  f o o t volume ( S c r i b n e r by 2 - i n c h d i a m e t e r  S l o p e c o e f f i c i e n t s "b" f o r t r e n d o f S c r i b n e r b o a r d f o o t volume on t o t a l h e i g h t , p l o t t e d on d i a m e t e r a t b r e a s t h e i g h t  ij.7  A d j u s t e d volume r a t i o s ( b a s i s = 80 f e e t ) p l o t t e d over diameter at b r e a s t h e i g h t  Itf  I n t e r c e p t c o e f f i c i e n t s "a" f o r trend of S c r i b n e r b o a r d f o o t volume on t o t a l h e i g h t , p l o t t e d on d i a m e t e r a t b r e a s t h e i g h t  I4.8  The r e l a t i o n o f t h e c o e f f i c i e n t s o f v a r i a t i o n . .. and s t a n d a r d d e v i a t i o n s o f d o m i n a n t h e i g h t r e s i d u a l s t o t o t a l age  57  The r e l a t i o n o f t h e l o g a r i t h m t r e e s t o a v e r a g e d.b.h  58-  The r e l a t i o n o f s i t e r e l a t i o n i s shown'-.:  index  o f number o f  t o age; no  cor-  60  F r e e h a n d c u r v e s s h o w i n g i n (a) t h e a v e r a g e r e l a t i o n o f volume t o age; i n (b) t h e r e l a t i o n o f t h e s t a n d a r d d e v i a t i o n o f volume t o age; and i n ( c ) t h e c o e f f i c i e n t o f v a r i a t i o n o f volume t o age  63  The r e l a t i o n between the f i r s t r e s i d u a l s o f t o t a l c u b i c volume ( e x p r e s s e d i n s t a n d a r d u n i t s f o r i t s age) and 'site -index'  61|  Y I E L D AltfD VOLUME TABLES FOR ASPEN IN CENTRAL AND NORTHERN ALBERTA  INTRODUCTION  .  /  Aspen"'" ( P o p u l u s t r e m u l o i d e s abundant but  of the f o o t h i l l  at present  Locally, stock, This  tree  important  rough lumber,  situation  ones b e i n g ,  and p l a i n s r e g i o n  i t i s of general  it'is  M l c h x . ) i s t h e most  value  only  as a c o v e r  f o r fuelwood, fenceposts,  and l o g s f o r l o g c a b i n  e x i s t s f o r many r e a s o n s ,  adequate  c o n i f e r o u s woods on t h i s  supplies,  continent  construction.  t h e most  (2) t h e more  are s t i l l  plentiful,  (3) t h e p r e v a l e n c e  of heart  unsuitable  t o an i n d u s t r y w h i c h i s g e a r e d  significant that  out-  valuable  relatively  r o t i n a s p e n makes i t to the production  only. The  future p o s s i b i l i t i e s  fore  subject  wood  and i t s b y - p r o d u c t s  f o r this  t o s p e c u l a t i o n , but the ever  a question  o f time b e f o r e  provincial  forest  species  utilization  are t h e r e -  i n c r e a s i n g v a l u e of  strongly i n d i c a t e s that i t i s only aspen w i l l  be i m p o r t a n t  i n the  economy.  I t was i n a n t i c i p a t i o n o f an i n c r e a s e d and  crop.  wagon  (1) t h e r a n g e o f a s p e n i s so e x t e n s i v e  s i d e m a r k e t s have  o f lumber  of A l b e r t a ,  o f aspen t h a t  this  study  was  interest i n  undertaken.  O t h e r names i n u s e a r e : w h i t e p o p l a r , p o p l a r , p o p p l e , a s p , a s p e n p o p l a r , q u a k i n g aspen, and s m o o t h - b a r k e d p o p l a r .  -2-  THE POPLAR FOREST SAMPLED The constructed described  area f o r which the p r e s e n t  i s contained  by H a l l i d a y ( 5 ) .  w i t h i n the l i m i t s The b u l k  m e a s u r e d , however, a r e c o n c e n t r a t e d Lesser  Slave  development. in  yield  Lake sub-drainage  o f t h e B 18  region  o f t h e sample p l o t s i n the v i c i n i t y  where p o p l a r a t t a i n s  A d d i t i o n a l d a t a were c o l l e c t e d  l o c a t i o n s .shown  t a b l e s were  i n r e d i n t h e s k e t c h map,  o f the optimum  west o f Edmonton Figure  1.  FIGURE 1 - Map s h o w i n g l o c a t i o n o f sample p l o t s ; e a c h d o t marks a l o c a l i t y where one o r more p l o t s were t a k e n .  -3Only  a few  entire side  of the  rivers  r e g i o n are  and  streams  shown and,  i s a f e a t u r e of the  although  topography,  of r a t h e r deep U - s h a p e d v a l l e y s , otherwise  i n part  forest  to the  the heterogeneous glauca  lodgepole pine Banksiana  Of  cover  destruction mixtures  Lamb.).  birch  The  former  existing  flats,  or  the degree  caused  relief  stands  such  occurrences  aspen w i t h white  to  an  i n pure  to t h i s  stands  are not as  with  (L.)  of occurrence  value  are  of these  Mills),  (Pinus  (Picea  patchiness.  seldom  and  entirely  alluvial  aspen  found  as  soil  i n moist  soils  of  moisture in  almost  localities  of r e l a t i v e l y  percentage  deciduous  as r e p r e s e n t a t i v e o f t h e  rule  but  I t most f r e q u e n t l y e x i s t s tree  shown i n T a b l e  and  the The  a general  growing  i n a few  a twisted spindly  frequency  the p l o t s measured  be  average  (Picea  along creek margins.  v e r y , common.  The  to  b a l s a m i f e r a L.)  the  individuals  W h i t e b i r c h may  importance.  taken  on  and  jack pine  apparent  (Populus  successfully  commercial  population  1  nature  spruce  f i r (Abies balsamea  add  of h i g h marketable  the m i x t u r e s  a patchy  by p a s t f i r e s  o f i t s success depends upon  pure  be  abrupt  i s t h e more common p a r t i c u l a r l y  as l a r g e  characteristics.  not  provide  many swamps o f b l a c k s p r u c e  B.S.P.) b u t  s b l a c k p o p l a r competes but  country-  larger.streams, centres  ( B e t u l a p a p y r i f e r a M a r s h . )•• a r e  The  habitats, river  the  ( P i n u s c o n t o r t a D o u g l . ) and  (Mill.)  absent.  in  of  t h e hardwoods b l a c k p o p l a r  white  the  a gently rolling  i n g e n e r a l i s of  (Moench.) V o s s ) , b a l s a m  mariana  through  r e g u l a r landscape. The  due  which wind  1,  little  composition  and  species included i n These f i g u r e s  entire  r e g i o n but  should of  the  sampled.  "^"Other names i n u s e p o p l a r , tacamahac,  a r e : tealsam p o p l a r , b a l m , b a l m o f and r o u g h - b a r k e d p o p l a r .  Gilead,  -kTABLE 1 STAND COMPOSITION AND  FREQUENCY OF OCCURRENCE OF ON SAMPLE PLOTS  '  Composition by S c i e n t i f i c name basal area ~ — — % Aspen P o p u l u s t r e m u l o l d e s M i c h x . 93.92 B l a c k p o p l a r . P.opulus b a l s a m i f e r a L. 5.16 White b i r c h B e t u l a p a p y r i f e r a Marsh. 0.92 Common name  SPECIES Frequency of occurrence  %  :  100.0 71.8 28.2  ASPEN Y I E L D TABLES The  yield  estimated  t o be  land.  such  In  canopy except H e r e the is  utilizing stands  i n the  fully  the  are d e r i v e d from  a s p e n crowns f o r m  case  of t h o s e  Yields  obtained  are commonly r e f e r r e d  t o as  an  o f the  g e n e r a l l y agreed  that normal y i e l d  u s e f u l d u r i n g e a r l y phases of f o r e s t r y Tables average  d o m i n a n t s , number of  area,  and  ities  of  completed fully  2 to 6 i n c l u s i v e ,  volume o f wood p e r site.  They are  d u r i n g the  stocked  stands  trees,  summer o f 1950.  89  overlapping stocked are  sampling  t a b l e s but  i t will are  development.  show t o t a l h e i g h t average  of  There  t a b l e s h a v e b e e n and  size  of.the  of t r e e , ages and  a p r o j e c t begun In  c o n t a i n i n g even-aged  II4.O y e a r s were m e a s u r e d on  age.  the b a s i s of  acre f o r d i f f e r e n t  the r e s u l t  of  such f u l l y  resulting yield  the  complete  "normal" y i e l d s .  and be  apparent  from  o b j e c t i o n s to b o t h  application  a fairly  u n d e r 30 y e a r s  a number o f o b v i o u s the  stands  the growing c a p a c i t y of  crowns become n a r r o w e r and  characteristic.  stands  tables presented  this  basal qual-  and  study y i e l d s  a s p e n between 10  small' temporary  sample  areas  of and  -5TABLE 2 TOTAL HEIGHT OP AVERAGE DOMINANT ASPEN  T o t a l T o t a l h t . by s i t e i n d e x age 50 • 60 70 80 90 years  10 20 30 ko  ft.  ft.  10  l  20  26  28 3k 39 k3  60  1  total  k  35 U2 k7 52  Total age  Total  $0  60 70  80  Index 90  ft.  ft.  ft.  ft.  ft  kl  56 60 63 65 67 69  66  75 85 80 90 8k 9k 86 97 89 90 91 102  ft.  ft.  ft.  years  17 31 kl k9 56 61  20 36 1*8 57 6k 10  23 42 55 65 73 79  70 80 9.0 100 110 120  h e i g h t o f average  FIGURE 2 - 'Height  curves used  50 52 5k 56 58  dominant  f o r site  h t . by s i t e  70  73 76 78 80  aspen o f 80 y e a r s  classification.  -6TABLE 3 TOTAL NUMBER OP TREES PER ACRE • 0 . 6 - INCH D.B.H. AND LARGER Trees p e r acre by s i t e index:  Total age  5o  ;,  60  10,000 4 6900 ' 14.700 3250 2200  50  60 70 80 90 100 110 120  90  Number  (years) 10 20 • 30 ll-O  80  70  1550 1100 790 610  U95  [j.20 370  8500  7700  5000  $800 3900 2650 I8I4.O 1300 930 690 535 1*35 . 365 , 315  :  3300 22^0 1550 1100 800 600 1*65 380 320 276  6700 144.00 2800 1900 1350 960 705  6050 3750 2500 1680 1180 850 630  I4IO 330 280 224.0  370 295 214.5 210  525  kio  • TABLE; h DIAMETER OP THE AVERAGE TREE .BY AGE CLASS AND S I T E INDEX Total age  \  , 50  (years) 10 20 30  k-0  50 60 70 80 90 1°° }\% ° 1 2  .  "  ;  60 \ .  0.6 1.3 1.9 2.5 3.2 ,3.8 . lj.,6  S-k  6.2 -9 I' 8.0  6  Diameter at b r e a s t h e i g h t .-. ' by s i t e 'index: . 70 :  0.7 1.5 2.2 2.9 . 3.6 I4..I4. ' 5.2 6.1 6.9 7.7 '  5  9.0  89 7~~  Inches 0.8 1.7 .2.5 3.3 ' I4..I k-9 5.9 6.8 7.8 , 8.6 9.14. 10.1  . •  90  ~'  1.0 2.0 2.9 '3.8 ' I4..6 - 5-5 ' 6.5 7.6 8.6 9.6 10.14. 11..2 •  1.3 2.3 3.2 I4..2 5.1 6.1 7.1 8.3 9.1|. 10.5 11.5 12.14.  .-7. TABLE 5 TOTAL BASAL AREA PER ACRE INCLUDING ALL TREES 0.6-INCH D.B.H., AND LARGER Total age  Basal 50  area per 60  70  index: 80  . 90  50 103 130 11*7 155 160 162 16k 165 166 166 166  .61 Ilk 11*1 158 168 172 176 177 178 178 178 178.  Square f e e t  (years) 10, 20 30 ko 50 60 70 80 90 100) 110 120  acre by s i t e  lk 66 9k 111 118 122 12k 126 128 128 128 128 .  26 78 106 122 . 130 131* 137 139 llj.0 llj.0 llj.0 llj.0  38 91 119 136 11*3 lk8 150 152 15k 151+ .151* 15k  TABLE 6 YIELD PER ACRE IN CUBIC FEET, EXCLUDING BARK, FOR ALL TREES 0*6-INCH D.B.H., AND LARGER Total age  . 50  Y i e l d p e r acre by s i t e t  6b  (years) 10 20 30 ko 50 60 70 80 90 100 110 120  70 Cubic  80 620 llk5 1605 1970 2270 2525 2735 2910 3050 3165 , 3255  1-80 ' 855 lk80 2030 2k80 2850 3180 3l*k0 3650 3805 3920 .k030  index: ; 80  90  feet  280 1120 1890 2575 3115 3560 3925 k2k0 k5io 1*730 lj.900 ' 5035  k20 11*152315 311*5 3800 1*31*5 k790 5160 51*60 5700 . 5900 • 6080  570 1715 2775 3775 • k555 5155 5685 6115 6k75 6760 6980 7170  -8-  PIGTTRE 3 - Number o f and s i t e i n d e x .  trees per  acre  showing t r e n d s w i t h  age  ¥  •  M-oi-  -  J.0  ZO  •  •  30  40  J  ...... .1. _  SO  - ...  40  70  gC  _  <?£>  - ., .. ..  100  Aspen total age - ijecrs  110 ' LZO  j  j  ;  FIGURE li - - d i a m e t e r of t r e e of a v e r a g e b a s a l a r e a a t b r e a h e i g h t , showing t r e n d s w i t h age and s i t e i n d e x . !—-•<•>-;  i  II ;  20O|  "  "  "  !  '  —  '  !  '  1  (-r- -+  ¥  {  20  so  40  \o  0  "  |  "  I•  so  1  -  "' :  &o  1  "  1  —  '  '"  —  -. - -  70  —  —  —  &c  90  no  too  —  S*r !  tw\  Aspen toto; ^. s-^ears —  —  —  «  —  —  ' . ,  —  ,  „  L  5 - T o t a l b a s a l area p e r acre f o r t r e e s over 0,6i n c h d.b.h., showing t r e n d s w i t h age and s i t e i n d e x .  FIGURE  FIGURE 6 - Y i e l d p e r a c r e i a c u b i c f e e t e x c l u d i n g showing t r e n d s w i t h age and s i t e i n d e x .  bark,  scattered  throughout  plot  site  age,  the  quality,  o f wood were c a r e f u l l y  r e g i o n 3hown i n F i g u r e 1. number and  and methods o f measurement  The  variables  to  age  and  and  site  shown i n t h e  sampled b u t  assurance  over  the  a scrubby  appearance  the h e i g h t - d i a m e t e r evidence  and  from  in  o t h e r p a r t s of A l b e r t a may  that  according will  be  Height  Appendix.  and  related  stands with  shown i n t h e  age  only a p p l i c a b l e to be  used  with  S o u t h o f Edmonton the  the  few m e a s u r e m e n t s a different permit  tables,  not  be  limiting  degree  poplar  available  shape.  comparable w i t h  a different  some  Peace  This  the  I t does i n d i c a t e however, t h a t p o p l a r  For  the  area growth yield  of s t o c k i n g  p r e d i c t e d v a l u e s must be c o r r e c t e d  to standard procedures.  Growth and  Site  The  amount of  this  correction  Index  The  height  a t t a i n e d by  used  as t h e  index  chosen because  aspen  because t h i s  white  analy-  d e s c r i b e d l a t e r under " d e n s i t y . "  y e a r s was  and  of the  Grande P r a i r i e ,  does not  applicability.  from  strictly  r e l a t i o n s h i p s have  i s i n c o n c l u s i v e and  values.  are  La Biche,  of  table  quantity  obtained.  r e g i o n i n c l u d e d by Lac  each  a c r e f o r e a c h o f the  i t i s b e l i e v e d t h e y may  R i v e r , A t h a b a s k a and has  details  are d e s c r i b e d i n the  s i t e from'which y i e l d s per  c l a s s e s shown were  area  Full  t a b l e s were a n a l y s e d  These y i e l d ? t a b l e s the  siz,© o f t r e e s and  determined.  sis  -For  spruce  age  the  average  of  site  quality.  s t a n d s by  this  time  has  been u s e d  (6) w h i c h i s commonly  dominant T h i s age  at  80  was  have a t t a i n e d m a t u r i t y ,  to develop  site  associated with  curves f o r the  poplar.  -12The  following illustrates  between p l o t principal  frequency  site  the  occurrence  percent  similarities  f o r the  three  classes.  Site classes a t 80  (height  rather striking  Frequency of p l o t occurrence aspen white spruce (percent) (percent)  years)  70 70-80 60-70-80 2 p o r t r a y s the  Figure height with The  use  age  of t h i s  from  trend.of  which the v a l u e s  height age  are known.  height  the  to r e c o g n i z e .  of f r o m  stand has  larger  stands  above 100  and  taken.  and  likely  the  In t h i s  of  an  dominant  age,  the  aver-  s i n c e dominants  study,  f o r each p l o t  average  be u n i m p o r t a n t  m e c h a n i c s of e s t i m a t i n g s i t e an  average  For varied  the h e i g h t - d i a m e t e r  estimate  will  years  be u s e d  appearance.  s h o u l d be  dominant h e i g h t from between t h i s  and  of  average  l\. t o 8 d o m i n a n t s i s a d e q u a t e , p a r t i c u l a r y i f a uniform  samples  quality  F o r y o u n g e r ages the  o f t h e d o m i n a n t s were a v e r a g e d  small  when age  o f t h e u p p e r canopy may  are d i f f i c u l t height  In  site  dominant  2 were d e r i v e d .  i n Table  information to estimate  area f o l l o w s standard procedures  average  of  types the  to obtain  difference  actual heights i s  i n p r a c t i c a l work.  i n d e x may  stands,  diameters  and u s e d  c u r v e . The  of  b e s t be  The  illustrated  by  example. If be be  Referring axis,  t h e c r u i s e i n f o r m a t i o n shows t h e age o f the s t a n d t o 60 y e a r s and t h e a v e r a g e h e i g h t o f t h e d o m i n a n t s t o 65 f e e t , what i s the s i t e i n d e x ? t o F i g u r e 1,  a height  of 65  opposite  feet  falls  an  age  between  o f 60 site  on  the  class  horizontal 70  and  80,  -'13w h i c h may be  be  interpolated  o b t a i n e d f r o m the 70  between t h e  i s , 70  cisely broad  site  scriptive  use  80  and  by  ( l | / 9 x 10)  /  index c l a s s e s title  has  T a b l e 2.  of  site  as. 7I4..  eye  The  same r e s u l t of- 6 5  A height  feet  Number and  pre-  or  only  are  7k'k'  I  used,  been g i v e n  to  practice usually  n  so  f o r convenience  ,  the  t o t a l number o f  f r o m w h i c h T a b l e 3 was trees  Prom 10  t r e e s per  a c r e d e c r e a s e s f r o m 7700 t o 1 5 0 0 ,  per  decade of l 5 0 0  mortality in 36O  the and  to 50  Pacific  y e a r s on mediiim s i t e s  trees.  N o r t h w e s t by  per  comparison,  decade r e s p e c t i v e l y f o r the f o r a s p e n has  Lake S t a t e s ;  (20)  Zehngraff  rate  of  the  r e a s o n s e a r l i e r Lake S t a t e s f o u n d t o be  too  The age  classes  100  mortal-  years  the  Douglas f i r  mortality same  of  is  only  periods. in  the  "the'exceptionally  ( a s p e n ) as  one  of  the  high  underlyin  e s t i m a t e s o f volume y i e l d s were  high.  large  are  average  For  age  number  a l s o been found  r e f e r s to  species"  the  an  the  depicts  l a r g e r by  Prom ages 5 0 t o  Similar high mortality  mortality  and  decade d e c r e a s e s t o 23I4. t r e e s . .  per  60  derived,  0 , 6 - i n c h d.b.h.,  classes.  ity  Index  Trees  3>  Figure  de-  90 80 70 60 50  ' of  a  each.  or e x c e l l e n t ' ••  Size  fall  index c l a s s , which c a l c u l a t e d  Site Very best Good Medium Pair Poor  may  number of  trees per  r e f l e c t e d i n the  small  a c r e i n the average stand  young diameters  -II].-  ' ( F i g u r e I4. arid T a b l e I4.). effect  on d i a m e t e r  This  increment  years i t i s s l i g h t l y  situation  l e a d s t o an  unexpected  p e r d e c a d e s i n c e f r o m $0 ages 10  g r e a t e r than from  100  to  t o £0 y e a r s .  Basal Area Y i e l d s The  trend  of b a s a l  shown i n F i g u r e 5.  square  feet  by  100.  age  Volume  of b a s a l  Figure ing.age,  site  age  and  5>0,  age  II4.3  this. increases  t o iSk-  6 p o r t r a y s the t o t a l stump and  wood p r o d u c e d  with  top, i n a l l t r e e s 0.6-inch site  and  age  class  increas d.b.h.,  are g i v e n i n  6. Cubic  Yields  and B o a r d  sites,  and b o a r d f o o t  f o r portions  a t v a r i o u s ages by  were computed f r o m obtained from  total  the r a t i o  volume, p l o t t e d  d.b.h. and  the r a t i o  site  The  trends f o r cubic  classes i n and  i n board  merchantable  volume t o t o t a l  stand diameter. feet  differFigures  v a l u e s by means o f  of merchantable  over average  inclusive.  larger,  over.  cubic y i e l d  volume,  o f s t a n d s on t h e  f o r t r e e s [(.-inches d.b.h. and  f e e t f o r trees 7-inches  illustrate  cubic  a r e p r e s e n t e d i n T a b l e s 7 t o 11  8 show t h e y i e l d s  cubic feet  Feet  i n merchantable  the S c r i b n e r l o g r u l e ,  and  On medium s i t e s ,  a r e a are. p r o d u c e d ;  Volumes f o r e a c h  Merchantable  7  v a l u e s f o r each  sites i s  Peet  including  and l a r g e r .  ent  for five  Yields  T o t a l Cubic  by  average  a r e shown i n T a b l e . - 5 .  class  Table  The  a r e a w i t h age  table  factors cubic  - F i g u r e s 9 and  i n t r e e s I|.-inches  10 d.b  -15and  larger,  above,  and f o r b o a r d  the d e s i r e d u n i t s total  1  converted  are o f v a l u e f o r r a p i d  o f measure.  After  d.b.h.,  be o b t a i n e d r e a d i l y . .  volumes w i l l  the d i s t r i b u t i o n  and  presented  The  o f t h e stem d i a m e t e r s .  should  result.  i n T a b l e s 12  other  accuracy  into  diameter volume of  these  depend on t h e d e g r e e o f s t o c k i n g and  and t h e l a t t e r m o r e ' o r l e s s  inaccuracies  conversion  the average  c u b i c volume, have b e e n computed  m e a s u r e s may  average  in. t r e e s 7 - l n c h e s  respectively. The r a t i o s  and  feet  t o 15  I f the former i s  r e g u l a r , no  serious  The c o n v e r s i o n u n i t s u s e d inclusive.  are  -16TABLE 7 YIELD PER ACRE IN CUBIC FEET OF MERCHANTABLE STEM, EXCLUDING BARK, FROM A l - F O O T STUMP TO A'k-INCH TOP'INSIDE BARK; FOR ALL TREES' k-INCHES. D.B.H. AND LARGER t  Total age  Yield  4  50  ko  50 -60 70 80 90  100 110 120  p e r acre by s i t e  60'  7.0; ,  _  _  -  185 k95 890 1375 1795 2125 2370 2555 2690  95 385 • ' 860 Ik55 2010 2k85 2835 3100 3290 3k55  _  -  . 220' 710 • Ikl5 • 2105 2770 3270 3695  kho  1230 2070 2900 3600 ki85 . k620 k975 5255 5520  J4.OOO  k255  1  :  90  feet  _  -  20  index:  80  Merchantable cubic  (years)  10 20 30  r  v  _ IkO  695 1790 2825 3725 ' kk80 5110 5620 6ok5 6370 6655  TABLE 8 Y I E L D S PER ACRE IN CUBIC F E E T OF MERCHANTABLE STEM, EXCLUDING' BARK, FROM A 1-FOOT STUMP TO A k-INCH TOP INSIDE BARK; FOR TREES k-11 INCHES D.B.H. INCLUSIVE : . Total age  Yield  20 30  ho  5o 60 70 .80 90  100 110 120  site  ^5  ^  index:  80  MeTcl^nTable c u b i c  (years)  10  p e r a c r e by  feet  -  -  -  -  20 185 k95 890 1375 1795 2125: 2370 2370 23k5  95 385 860 ik55 2010 . 2k85 . 2835 2880 2815 2725  220 710 11*15 2105 2770 3270 3395 33kO 3155 2875  kko  -  90  1230 2070 2900 . 3600 3925 3855 . 3560 31k5 25k5  IkO  695 1790 2825 3725 kk20 kk25 kl70 3525 2585 1550  -17TABLE 9  •  1  YIELDS PER ACRE IN CUBIC PEET OP MERCHANTABLE STEM, EXCLUDING BARK, PROM A 1-FOOT STUMP TO A I4.-INCH TOP INSIDE BARK; FOR TREES 12 INCHES D.B.H. AND LARGER  i  Total a  S  ;  ;  Yields  50  e  90  100 110 120  ;  60  (Years)  10 20 30 1+.0 50 60 70 80  ;  :  :  p e r a c r e by s i t e  70  -  -  135 275  -  -  —  14-75  730  TABLE  69  260 765 11*15 2110 2975  300 660 1100 1580  220  90  feet  -  -  1—  80  Merchantable cubic  -  ;  Index:  685  ii*5o  2520 3785 5105  10  Y I E L D S PER ACRE IN BOARD FEET, SCRIBNER LOG RULE, FROM A 1-FOOT STUMP TO A 6-INCH TOP INSIDE BARK; FOR A L L TREES 7-INCHES D.B.H. AND LARGER ~  i  Total age  i  20 30 1*0 50 60 70 80 90  100 110 120  -  Y i e l d p e r a c r e by s i t e  50  60  rears) 10  i  70 Board  .  index:  80  90  feet  —  1*0  270 770 151*5 2705 1*150 5825 7260  200-  725 1560 3010 1*965 7610 9880 11725  90  560 11*05 3060  51*70  9380 12580 151*35 17825  —  375 1160 2630 5270 9905 11*525  I86I4.O  21770 21;320  55 755 2070 1*510 8640 11+980 20395 25215 28550 3101*5  -1811  TA.BLE  YIELDS PER ACRE IN BOARD FEET, SCRIBNER LOG RULE, FROM A l-FOOT STUMP TO A 6-INCH TOP INSIDE BARK; FOR A L L TREES 12-INCHES D.B.H. AND LARGER Y i e l d p e r a c r e by s i t e  Total age  60  5o  70  (years)  Board  10  --  30 5o 60 70 80 90  90  —  --  feet  120  —  330  275 585 960  100  110  -  ' 80  _  20  —1  index:  --  -— -  —  190 1060 2565 • 5815 99io 1I1650  -  320 1130 2225 1*265 7150  855 1590 25ko  —  \  9000  655 229< 5635 11965 l88k5 25310 .  1—&gj  1 —  >  _3 -  1  ^  ^ ^^^^  ^^y^  '  —--"1 j  8  0  4000  Q  ^^"^ - -t;  V  2.000  S  .  x  ___L———'  6 0  r  / / / ^ ^ 0  10  ZC  30  40  SO  60  70  80  1  90  too  110 120  Mp&r rota! oge-yeors ' FIGURE 7 - Y i e l d p e r a c r e i n c u b i c f e e t o f m e r c h a n t a b l e s t em, excluding bark (to a k - i n c h top i n s i d e bark),showing trend s w i t h age and s i t e i n d e x .  -19%•  "  1  "  •  n  "~  .90 « v. /  Z4000  - 7 2oooo  7  -*§ L ^ o o o  On  J  _ 60  -  .  $ L 1  _  /  is  -j-  ;  •  fr / /  /  " T5Q%  - 4ooo»  . c  LO  23  30  .  ..  :  .  40 So bo 70 80 Aspen total, age-years  <90  LOO  110 1 2 0  FIGURE 8 - Y i e l d p e r a c r e i n b o a r d f e e t , S c r l b n e r rule ( t o a 6 - i n c h t o p i n s i d e b a r k ) , showing t r e n d s w i t h age and s i t e ' i n d e x .  Average p.Q.H. ofptots-mches  FIGURE 9 - The r e l a t i o n s h i p between t h e merchantable cubic f o o t - t o t a l cubic foot volume r a t i o , t o a v e r a g e s t a n d d.b.h., where t h e m e r c h a n t a b l e s t a n d includes t r e e s [{.-inches and l a r g e r .  FIGURE 10 - The r e l a t i o n s h i p between board f o o t - t o t a l c u b i c f o o t volume r a t i o , to average stand d.b.h., where the merchantable stand i n c l u d e s t r e e s 7-inches d.b.h. and l a r g e r . TABLE 12 CONVERSION UNITS APPLIED TO TOTAL CUBIC VOLUME OF WELL STOCKED ASPEN STANDS TO OBTAIN MERCHANTABLE CUBIC VOLUME OF ALL TREES 4-INCHES D.B.H. AND LARGER Average Average stand diameter,tenths of an i n c h stand 0.0 0.1 0.2 0.3 O-.lj. 0.5 0.6 0.7 O.B 0.9 ~ d.b.h. Conversion u n i t s , t o t a l cubic to mer. c u b i c v o l . , t r e e s IL"J. 1  inches  1.0 2.0 3-0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11,0 12.0  .033 .049 .210  435  .606 .715 .783 .826 .857 .883 .904 .922  .230 • 455 ,620  .723 .788 .830 .860 .885 .906 .924  .065 .251 .474 .633 .731 .794 .833  .862  .887 .908 .925  -  .082 .275 • 493 .645 .738 .799 .836 .865 .889 .910 .926  .099  .298 .511 .656 .745 .803 .839 .868 .891 .911 .928  -  ,116 .322 .528 .667 -752 .807 -843 .870 .8^4 .913 .930  .0)17  -21TABLE  13  CONVERSION UNITS APPLIED TO TOTAL CUBIC VOLUME OP WELL STOCKED ASPEN STANDS TO OBTAIN MERCHANTABLE CUBIC VOLUME OP A L L TREES 12-INCHES D.B.H.AND LARGER Average A v e r a g e s t a n d d i a m e t e r , t e n t h s o f an i n c h stand 0.0 0.1 0.2 0.3 O.U 0.5 0.6 0.7 O.b 0.9 d.b.h. Conversion u n i t s , t o t a l cubic t o mer.cubic v o l . t r e e s 1  (inches)  6.0 7.0 8.0 9.0 10.0 11.0 12.0  12"+  " '  .004 .084 .818 .300 .454 .637  .011 .094 .191 .314 .472 .656  .019 .103 .202 .328 .489 .675  .026  .112 .213 .343 .506 .694  .034 .121 .224 .358 .524 .712  TABLE  .042 .131 .236 .373 .542 .729  .050 .140 .248 .389 .561 .747  .058 .150 .260 .405 .580 .764  .066 .160 .273 .421 .599 .780  .075 .170 .286 .437 .618 .796  14  CONVERSION UNITS APPLIED TO TOTAL CUBIC VOLUME OP WELL STOCKED ASPEN STANDS TO OBTAIN MERCHANTABLE BOARD FOOT VOLUMES SCRIBNER RULE, OF A L L TREES 7-INCHES D.B.H. AND LARGER Average A v e r a g e s t a n d d i a m e t e r , t e n t h s o f an i n c h stand 0.0 0.1 0.2 0.3 0.4 6.5 0.6 0.7 0.8 0.9 d.b.h. Conversion u n i t s , t o t a l cubic v o l . to board f t . , t r e e s (inches)  3.0 4.0 5.0  6.0  7.0 8.0  9.0 10.0  11.0 12.0  " -  .16 .42  .82  -  .18 .k6  .88  I . 4 4 1.52 2.23 2.31 2.91 2.97  3.49 3.54 3.93 3.97 4.23 4.26  .02 .20 .49 .93 1.60 2.38 3.03 3.59 4.00 4.29  .04 .23 .53  .05  .06  .26  .28  .08 .10 .12 .14 .30 .34 .36 .40 .56 .60 .64' .69 .73 .78 .98 1.04 1.10 1.16 1.22 1.29 I . 3 6 1.68 1.76 1.84 1.92 2.00 2.08 2.16  2.45 2.52 2.59 2.66 2.72 2.79 2.85  3.09 3.64 4.03 4.31  3.15 3.69 4.06 4.33  3.21 3.73 4.09 4.35  3.27 3.78 4.12 4.38  3.32 3.38 3.43 3.86 3.90 4.15,4.18 4.21 4.40 4.42 4.44. 3.82  7"^  -22-  TABLE 15 CONVERSION UNITS APPLIED TO TOTAL CUBIC VOLUME OP WELL STOCKED ASPEN STANDS TO OBTAIN MERCHANTABLE BOARD FOOT VOLUMES, SCRIBNER RULE, OP ALL TREES 12-INCHES D.B.H., AND LARGER Average Average stand diameter, tenths of an i n c h stand 0.0 0.1 0.2 0.3 O.k 0.5 0.6 0.7 0.8 0.9 d.b.h. Conversion u n i t s , t o t a l cubic v o l . to board ft,,trees (inches) 6.0  7.0 8.0 9.0 10.0 11.0 12.0  ' -  0.01  0.10 0.12 0.30 0.32 O.63 0.68 1.35- 1.1+2 2.23 2.32 3.17 3.26  0.02  0.13 0.35 0.74 1.50  0.02  0.15 O.38 0.80 1.59 2.kl 2.51 3.35 3.44  0.03 O.Oij. 0.05  0.16 0.18 0.20 O.I4.O O.I4J4. 0.it7 O.87 0.95 1.02 1.68 1.77 1.86 2.61 2.70 2.80 3.53 3.61 3.70  0.06  0.22 0.40 1.10 1.95 2.89 3.78  0.05  0.09  0.25 0.27 0.54 0.58 1.18 1.26 2.0i+ 2.Ik 2.99 3.O8 3.86 3.9k  TABLE 16 MEAN AND PERIODIC ANNUAL ASPEN GROWTH PER ACRE IN CUBIC PEET, ENTIRE STEM, EXCLUDING BARK, ALL TREES 0.6^INCH D.B.H., AND LARGER /  j  /  (years)  1  Total age  P a i r 60 m.a.1. p. a. 1  1  ,  Mean and p e r i o d i c  1  annual growth  Medium 70 m.a.1. p . a . i .  '  Good 80 m.a.1. p . a . i .  T o t a l cubic f e e t  10 20 30 4o 50 60 70 80 90 100 110  18.0 k2.8 49.3 50.8 49.6 47.5 45.4 43.0 4o.6 38.0 35.6  _  65.5 59.0 50.0 41.0 35.0 29.5 23.0 18.0 13.5 11.0  28.0  56.0  63.O  64.4 62.3  59.3 56.1 53.0. 50.1 47.3 44.5  _  80.5 73.5 62.0 49.0 39.5 34-0 29.0 24.5 20.0 15.0  42.0 70.8 77.2 78.6 76.0 72.4 68.4 64.5 60.7 57.0 53.6  —  94.0  87.O  75.0 59.5 49.0 40.5 33.5 26.5 22.0 18.5  ~ 12 H J  -2kIncrement  and  rotation  T a b l e s 16,  1?  Medium and  Good s i t e s  increment.  T a b l e s 16  feet The  f o r the e n t i r e  and  g r o w t h i t may  of  and  no  age  tables site  i s usually  be  a l l be alone  that  yield  included. and  stands  In c u b i c  portion. f o r the t r e e s  type  taken  i s an  into  a new  the p r o p e r  in this  study  aspen  years  of t h i s  age  at  practice,  produces  of p r o l i f i c  crop w i l l added.  coppice  come I n A  stand  o f a number o f  age  desired,  silvicultural  account.  important  In  age  cut  t h e maximum volume r e t u r n p e r  of product the  same.  the f i n a n c i a l  f e a t u r e s of the  It will  be n o t e d  The  rotation  are  shown i n T a b l e  are i n d i c a t e d .  ages i n d i c a t e d  S i n c e most of  are below k - i n c h e s  forpro-  from  growth i s i n f l u e n c e d  a  aspects  N e v e r t h e l e s s , volume  item.  fact-  at which to cut  the  by by  the  19.  F o r maximum p r o d u c t i o n o f wood p e r a c r e , of kO  annual  t o as t h e  Since  i s capable  t h e p e a k o f mean a n n u a l  data collected  the  of g r o w t h i s o n l y one  and measure o f v o l u m e .  tions  Pair,  required to obtain regeneration  assumed t h a t  will  Rate  The  referred  growth are be  abundantly  evaluated i n f i x i n g  stand.  duction  i n board f e e t  a d d i t i o n a l y e a r s n e e d be  age  of g r o w t h .  must  mean  f o r the merchantable  are e x p r e s s e d  f o r e s t management and  est  and  c u t , s h o u l d be  safely  the r o t a t i o n  given  and  on  show t h e s e g r o w t h v a l u e s  that w i l l  s e e d f r e q u e n t l y and  t o be  17  and mean a n n u a l  a f t e r the f i n a l  ors  and  18  t h e number o f y e a r s  year  i n terms o f p e r i o d i c  rotation  which p e r i o d i c  at  show r a t e s o f g r o w t h  over.  The  immediately  18  and  stand  values i n Table  7-inches  age  short  the  i n diameter,  rota-  trees i n a  kC—year  -25 rotation period  -  i s of r a t h e r t h e o r e t i c a l i n t e r e s t at p r e s e n t .  T h i s low r o t a t i o n age, however, i t i s i n t e r e s t i n g to note, i s the same as t h a t suggested by MacLeod (6) f o r aspen i n mixedwood stands growing i n the same g e n e r a l  area.  k-inches d.b.h. and l a r g e r are considered, i s lengthened t o 85 y e a r s . inches  When only  trees  the r o t a t i o n p e r i o d  F o r board f o o t measure, t r e e s 7-  and above, a r o t a t i o n i n t e r v a l of 130 y e a r s i s i n d i c a t e d . TABLE 19  ROTATION AGE TO THE NEAREST HALF DECADE FOR MAXIMUM WOOD PRODUCTION,ACCORDING TO PORTION OF STAND AND UNIT OF VOLUME CONSIDERED,FOR THREE SITE CLASSES  When u n i t of volume and p:&rt o f stand  Is  T o t a l cubic volume, a l l t r e e s l " + i n c l u d e d Merchantable cubic  feet,all  t r e e s k" + i n c l u d e d  Merchantable board f e e t , a l l (Scrib.rule)  t r e e s 7" + i n c l u d e d  F a i r Med. Good 60 70 80 T o t a l age i n y r s . kO ij.0 35 90  85  - (130)  80 (125)  ( ) - bracketed f i g u r e s are e x t r a p o l a t e d . Cull Unfortunately  there  i s no i n f o r m a t i o n  on the amount  of wood r o t p e r t r e e f o r the area n o r were any d a t a taken i n t h i s study.  Some c o n s i d e r a t i o n must be g i v e n to t h i s  important f a c t o r , however, which i n other s i n g l e cause f o r c u l l  i n aspen.  very  areas i s the g r e a t e s t  Although i t i s o b v i o u s l y  unwise  to apply  c u l l percentages d e r i v e d from s t u d i e s made i n o t h e r  regions,  some of the dangers i n doing so may be more apparent  than r e a l , p a r t i c u l a r l y when one pathogen, Fomes i g n i a r i u s , i s  -26-  th© most important  r o t causing agent  throughout  the e n t i r e  range of p o p l a r . Prom Black's d a t a  (1),  f o r aspen i n Northern  O n t a r i o , f i g u r e s on percentage were used  of c u l l r e l a t e d to diameter  to estimate t o t a l r o t i n percent f o r each p l o t The v a l u e s shown i n Table 20  measured i n Northern A l b e r t a .  were read from a graph where these percentages  were c o r -  r e l a t e d with age. TABLE 20 CULL PERCENT, FOR TREES k-INCHES D.B.H. AND LARGER, RELATED TO ASPEN TOTAL AGE FOR MEDIUM SITES 1  T o t a l age (years)  1.0 1.0 2.0 k.0 6.0  30 LL0 50 60 70 Meineke 1929.  «  Cull (percent)  f  T o t a l age (years)  Cull (percent)  9.0 13.0 18.0 22.0 27.0  80 90  100 110 120  (8) s t u d i e d the pathology of aspen i n Utah i n  The c u l l percentages  shown i n h i s p u b l i c a t i o n are s i m i l a r ,  when c o r r e l a t e d w i t h age, to the v a l u e s i n Table 2 0 .  The per-  centages d e r i v e d i n both r e g i o n s are g i v e n below f o r comparison: Age  30 60 90  120 It  C u l l as a percentage Northern O n t a r i o 1.0%  k.0# 13.0^ 27.0$  of merchantable volume f o r : Utah 1,0% l.% 9.0^  30.0$  should be noted that the c u l l percentages  r e g i o n s do not have a s t r i c t l y  shown f o r the two  comparable b a s i s .  In B l a c k ' s  A l l p o r t i o n s of the merchantable stem having a r o t diameter g r e a t e r than 1-inch; based on B l a c k ' s data (1) f o r aspen i n Northern O n t a r i o .  study, merchantable l e n g t h f r o m a 1 - f o o t stump t o  included  a 3«5-inch top;  this  the  total  able He  culled  p o r t i o n was  then expressed  each t r e e .  clear.  For  increasing  large the  the  ages shown above are percentages  Alberta great  not  are n o t  f o r that  applied  years,  estimates  are  employ t h e  cull  as  of  merchant-  a 2-inch  top.  a percentage  of  only  that  not  i n method a r e  similarity  applicable the  is  of  the  Although to  small,  percentthese  Northern  error incurred  w i l l not  a c o r r e c t i o n t o volume  be  estimates  an  f i g u r e s i n d i c a t e a l s o that f o r stands  t o be  o f much v a l u e ,  and  that  i t may  be  estimated deductions than to d i s r e g a r d  t o volume y i e l d s , little  s t a n d s 120  the  cull  changes the  and  i n lowering these  of  f o r both t o t a l years  older  a l l o w a n c e f o r r o t i s n e c e s s a r y i f volume  Application  adjusted  volume  employed  to chance a l o n e .  as  The  region. The  t h a n 80  are  the  strictly  aspen, i t i s l i k e l y  i f they  result  due  stem  a l t h o u g h Meineke measured  samples t h e s e d i f f e r e n c e s that  of t h e  Black considered  lower diameter l i m i t  possibility  stem  a percentage  mass o f d e c a y as  above 6 - i n c h e s d.b.h., and  merchantable t r e e s ,  Since  as  a 1 - f o o t stump and  volume o f t h e  the  culled.  stem t h a t p o r t i o n between  trees  very  portion  Meinecke i n c l u d e d  m e r c h a n t a b l e volume o f  cull  of  volume of e a c h t r e e .  e x p r e s s e d the  the  any  t h a n 1 - i n c h was  with a r o t diameter greater of  that portion  older,  the  ages a r e  r o t a t i o n age  them  percentages given  and  merchantable cubic  amount of  the  c a n n o t be  cull  given  r a n g e c o v e r e d by determined.  For  which  f o r board the  20  suggested  feet.  i s high  to  entirely.  i n Table  r o t a t i o n ages p r e v i o u s l y  rotation period  beyond  better  should  feet.  data  an  -28Density Basal  area  of normal y i e l d than  any  as  t a b l e s was  other y i e l d  from f i e l d f r o m the  data  yield  a measure o f d e n s i t y  and  compared  a stocking value  expressed  i n percent.  of a s t a n d  as 130 160  square f e e t x  100  is usual  t h u s a t age feet.  8l  or  Table  100  the  and  The  For  this  be  obtained  site The  of  ratio  aspen, 60  age  index) i n  has  stocking  figure will 166  be  i f the been  basal  computed  a density  of  therefore, i s  remain the x  order  is usually  f u t u r e p r e d i c t i o n s of  basal area w i l l  towards n o r m a l i t y  stocked  stands.  Use  conservative  stands  takes  of the  overstocked.  upon s t o c k i n g ,  age  the p a r t i c u l a r  species  The  o f the in  Although basal measure t o be the y i e l d greater  above  .81  growth same;  o r 134  i n overstocked  assumption,  stand  of  and  square  under-  t h e r e f o r e , i s to  f o r understocked  this  error will  stands depend  growth c h a r a c t e r i s t i c s  a r e a has  been suggested h e r e density  trees per  area.  a c r e has  Reineke  (16)  as  i n conjunction  of  the with  been r e c e i v i n g  f o r e s t e r s when r e l a t e d t o t h e  average b a s a l  a  question.  u s e d when e s t i m a t i n g  a t t e n t i o n by  and  optimistic forecasts for extent  t a b l e s , number o f  t r e e of  place  f u t u r e growth estimates  ( t h e most common) and  which are  the  $).  that  can  i t i s compared w i t h  percent.  t o assume  and  i n the case  acre,  area  better  Growth i n f o r m a t i o n f r o m p e r m a n e n t p l o t s i n d i c a t e t h a t  trend  give  (from  t o age  q u a l i t y 80  site  t o be  t a b u l a r value, . ( i n t e r p o l a t e d  for a forest.  Thus,  square f e e t per  130/160 it  of  Basal  to the  tables according  (10)  Meyer  t a b l e measure.  to o b t a i n  area  f o u n d by  i n the a p p l i c a t i o n  has  diameter  of  shown t h a t f o r  -29a number o f s p e c i e s  this  r e l a t i o n s h i p assumed a s t r a i g h t l i n e  f o r m when p l o t t e d on d o u b l e l o g a r i t h m i c p a p e r . species same.  t h a t were t e s t e d Employing  f o r 12 o f t h e s e were t h e  the s l o p e s  an a v e r a g e d.b.h. o f 10 i n c h e s  d i a m e t e r and a s h e a f o f l i n e s p a r a l l e l he  was a b l e  to ascribe  This  stand  (13) h a s b r o u g h t  and t h e a v e r a g e s t a n d  density  index i s therefore  the stand  density  possibilities.  Although  employed t o d e v e l o p  other  stand  the slope  of  t r e e s on a v e r a g e d i a m e t e r  be  quite different  aspen growing i n  shown i n F i g u r e  i s used.  of the regression  i n Eastern  i n each 2-inch  and a s t r a i g h t l i n e  average d i a m e t e r c l a s s These p o i n t s a r e  obviously  k.257,  where N e q u a l s t h e number o f t r e e s p e r a c r e o f the a v e r a g e t r e e  were a l l c o n v e r t e d method o f l e a s t  i n inches.  to logarithmic  squares,  a slope  fits  as l o g N = - I . 7 6 7  The e q u a t i o n  area  was d e t e r m i n e d  by Reineke  the average of the  best.  basal  o f number  Canada.  a v e r a g e d.b.h. on l o g p a p e r . 11,  line  It will  (on d o u b l e l o g a r i t h m i c p a p e r ) may  the r e g r e s s i o n l i n e ,  number o f t r e e s p e r a c r e was p l o t t e d o v e r  t o the a t t e n -  f o r a s p e n t h a n t h e one d e r i v e d  determine  (12)  Mulloy  t a b l e s , they are  comparison with  u s e d by M u l l o y f o r s p e c i e s To  t h e number o f  i n d i c e s have n o t been  where t h i s m e a s u r e o f s t o c k i n g  a l s o be shown t h a t  and  density  where t h e  a l s o has explored i t s  any p o r t i o n o f t h e y i e l d  here to f a c i l i t a t e  regions  (19)  line,  d i a m e t e r were  index concept  o f C a n a d i a n f o r e s t e r s and S p u r r  presented  t o the main guide  a t an i n d e x d i a m e t e r o f 10 i n c h e s .  t r e e s p e r acre  tion  as h i s i n d e x  a d e n s i t y number t o any s t a n d  number o f t r e e s p e r a c r e known.  Out o f t h e 111  values  the data  log D +  and D t h e  When t h e p l o t and f i t t e d  o f -I.6I4.6 was  data  by t h e  obtained,  a  FIG-TTRE 11 - The, r e l a t i o n o f t o t a l number o f t r e e s p e r a c r e t o a v e r a g e s t a n d d.b.h., f o r ?3 f u l l y s t o c k e d a s p e n sample p l o t s . The s l o p e o f t h e f i t t e d r e g r e s s i o n l i n e i s compared w i t h " t h a t o b t a i n e d by R e i n e k e f o r a number o f o t h e r s p e c i e s .  -31-  TAELE 21  STAND DENSITY UNITS FOR ASPEN CORRESPONDING TO AVERAGE STAND DIAMETERS IN INCHES  Average stand  0 . 0 - '0-1  Average stand d.b.h..' tenths of an inch <K2 0^3 0i4 0.5 0^6 0.7 0.8  * (inches)  d  1.0 2.0 3.0 4.0 5.0  0.9  Stand density u n i t s  T ) , t u  0.017 0.020 0.023 0-027 0.031 0.035 O.O39 0.043 0.048 0.053 0.058 O.O63 0.068 0.074 0.080 0.086 0.092 O.O98 0.105 0.112 0.119 0.126 O.I33 0.140 0.148 O.156 0.164 0.172 0.180 0.189 0.198 0.20? 0.216 0.225 0.234 0.244 0.254 0.264 0.274 0.284 0.294 O.305 O.316 O.327 0.338 O.349 O.360 O.371 O.382 0.394 0.406 O.532 0.673 0.830 1.000  0.418 O.545 0.688 0.847 1.018  O.43O 0.442 0.573 0.703 0.718 O.863 0.880 I.O36 I.O56  O.454 0.587 O.734 0.897 1.074  U.0 12.0 13.0 14.0 15.0  I.I83 I.378 1.587 1.811 2.044  1.202 1.498 1.609 1.834 2.068  1.221 1.418 I.631 1.857 2.092  1.259 1.278 1.298 1.460 1.481 1.502 1.675 1.697 1.719 I.903 1.926 1.949 2.140 2.164 2.188  16.0  2.288 2.313 2.388 2.363 2.389 2.415 2.441 2.467 2.493  O.559  1.240 1.439 I.653 1.880 2.116  0.467 0.601 0.750 0.914 1.092  0.480 0.493 O.506 O.519 0.615 0.628 0.643 O.658 0.766 0.782 0.798 0.814 O.93I 0.948 O.965 0.982 1.110 1.128 1.146 1.164  6.0 7.0 8.0 9.0 10.0  I.3I8 I.523 1.742 1.972 2.213  I.338 I.358 1.5^ 1.565 1.765 1.788 1.996 2.020 2.238 2.263 2.519  -32somewhat l o w e r reason (9)  by  o f n a t u r a l numbers.  This error  i s a systematic  be c o r r e c t e d by u s e o f t h e s t a n d a r d t h e method  the  of l e a s t  squares  error.  standard e r r o r decreased The l i n e  methods, was  with  or whether the wealth  fitted  the  t h e d a t a by l e a s t  analyzed  methods.  Schnur  s l o p e t o be somewhat f l a t t e r  Reineke,  freehand  I t i s n o t c l e a r whether  than  squares  revealed the slope of  -1.605 p r e s e n t e d i n h i s p a p e r by s t a n d a r d p r o c e d u r e s i n g d a t a by f r e e h a n d  by  (18)  of balanc-  f o r Upland  Oak  the slope obtained  w h i l e f o r a s p e n t h e s l o p e a p p e a r s much s t e e p e r  t o F i g u r e 11).  If this  last  stand  t o be t h e b e s t f i t and.employed  by f i t t i n g  of d a t a  fitted  an i n c r e a s e i n a v e r a g e  described later.  Reineke obtained h i s curve  The l i n e  awkward t o make when  i n F i g u r e 11,  illustrated  t h e r e f o r e assumed  the computations  one and  d i d n o t conform t o the p l o t t e d  o f t h e d a t a , b u t c o r r e c t i o n s were  diameter.  in  The  f o r t h i s d i f f e r e n c e h a s been e x p l a i n e d by H. A. Meyer  averages  in  methods.  as due t o e r r o r s i n c u r r e d by t h e u s e o f l o g a r i t h m s i n t h e  place may  s l o p e t h a n d e r i v e d by f r e e h a n d  found by  (refer  i s t r u e t h e e x p l a n a t i o n must l i e  the r a t h e r e x c e s s i v e m o r t a l i t y of the aspen i n t h e e a r l y  y e a r s . •To be c o n s i s t e n t w i t h o u t l i n e d by R e i n e k e , was  converted  10-Inches.  1.767  the stand d e n s i t y index  the r e g r e s s i o n l o g N =  t o t h e 1000  tree level  The r e s u l t i n g f o r m u l a  -I.767 l o g D + k.257  a t an a v e r a g e d.b.h. o f  i s expressed  by, L o g F =  l o g D + k.767. I n o r d e r t h a t s t a n d d e n s i t y i n d i c e s may  rapidly,  a t a b l e of stand d e n s i t y u n i t s  t e d f o r aspen s i m i l a r Reineke s 1  is  concept  formula.  as f o l l o w s .  ( T a b l e 21)  t o t h e one d e r i v e d by M u l l o y  The p r o c e d u r e  adopted  be  calculated  was  construc-  using  t o d e r i v e these  tables  -33The to  r e q u i r e d average diameter v a l u e s were  l o g a r i t h m i c numbers and  l a t e d from the formula k.767.  The  5  stand d e n s i t y u n i t s were obtained by d i v i d i n g  be computed q u i c k l y .  determined as 6.1 index w i l l  acre calcut -  g i v e n above, l o g N = - 1 . 7 6 7 l o g D +  values f o r N i n t o 1 0 0 0 . may  the number of t r e e s per  converted  Prom these the  I f the average diameter has  w i t h 200 t r e e s per acre, the stand  0 . k l 8 x 200 or 8k.  be  stand d e n s i t y  g r e s s i o n of number of t r e e s over steep e i t h e r as a r e s u l t  I t i s admitted  index been density  t h a t the r e -  average diameter may  be  too  of b i a s i n the sample or as a r e s u l t  of below-normal s t o c k i n g of the o l d e r stands.  Since f i r e  a major problem i n the area, i t i s c o n c e i v a b l e  that older  i n the l a r g e r diameters have been subjected t o f i r e p e r i o d i n the  the  is stands  at some  past.  BLACK POPLAR, PERCENTAGE COMPOSITION CHANGE P l o t s were chosen i n pure hardwood stands mainly cent  of aspen, and  although b l a c k p o p l a r o c c u r r e d on 7 1 . 8  of them, i t never exceeded 30 p e r c e n t  sition.  composed  of the stand  per-  compo-  Since no r e s t r i c t i o n s were imposed to govern the number  of stems a l l o w a b l e ,  s i g n i f i c a n t changes i n the amount of b l a c k  p o p l a r throughout the age  c l a s s e s can be mainly  d i f f e r e n c e s i n growth between t h i s  s p e c i e s and  c o n c e i v a b l e , however, t h a t the c o l o u r and p o p l a r bark, which i s almost black some e f f e c t on be presented  t h e r e f o r e be  aspen.  It is  t e x t u r e of the  i n o l d e r stands,  the choice of p l o t s made.  may  c r e d i t e d to  The  black  would have  r e s u l t s which  will  i n f l u e n c e d by p e r s o n a l b i a s .  Only those p l o t s c o n t a i n i n g b l a c k p o p l a r were used to  -34determine the r e g r e s s i o n of percentage composition by the method of l e a s t squares. each age An  c l a s s and  average percentage w i t h i n 12.  made to t e s t the r e l i a b i l i t y of the  The f i g u r e s obtained are given b&low: Degrees of ' Sum Freedom Squares  Source V a r i a t i o n due regression  age  the r e g r e s s i o n l i n e are shown i n F i g u r e  a n a l y s i s of v a r i a n c e was  relationship.  The  and  to  1  221.71  Residual v a r i a t i o n  59  2877.25  Total variation  60  3098.96 (3),  From t a b l e s shown by F i s h e r and Yates  Mean Squares  ' Variance Ratio  221.71  4.55  48.76  the v a r i a n c e  ratio  at the 5 percent l e v e l i s 3*97 compared with the 4*55 value determined.  The  r e g r e s s i o n , t h e r e f o r e of the two v a r i a b l e s  employed i s s i g n i f i c a n t at the 5 percent p r o b a b i l i t y The percentage composition  level.  of b l a c k p o p l a r at ©ach  20-year age  c l a s s i s g i v e n i n Table 22.  small (0.65  percent per decade) and w i l l not be i n t r o d u c e d  The  average change i s as  c o r r e c t i o n i n the p r e d i c t i o n of black p o p l a r growth from the yield tables. The  r e l a t i o n s h i p shown i n F i g u r e 12  i n d i c a t e s the  s i m i l a r i t y i n b a s a l area growth of aspen and b l a c k p o p l a r where they e x i s t i n c l o s e a s s o c i a t i o n .  This j u s t i f i e s ,  somewhat,  t r e a t i n g a l l s p e c i e s i n the hardwood mixture as one u n i t .  This  procedure has been f o l l o w e d i n the development of p o p l a r y i e l d s described i n this  thesis.  -35-  g  70  A*  5  10  20  30  40  SO  &0  70  80  90  UX  110 120  Totol aye- years  FIGURE 12" - The r e l a t i o n o f p e r c e n t a g e c o m p o s i t i o n , b y b a s a l a r e a , t o t o t a l age f o r b l a c k p o p l a r on 61 s a n p i e p l o t s .  TABLE 22 PERCENTAGE COMPOSITION OF BLACK POPLAR RELATED TO AGE  Total  age  (years)  20  kO  60 80 100  Composition by b a s a l a r e ; (percent)  9.3 8.1 6.7 5-4 4.1  -36VOLUME TABLES FOR Measurements and Aspen during y i e l d pure p o p l a r diameters points: and  BLACK POPLAR  Computations  and b l a c k p o p l a r  t r e e s were f e l l e d  s t u d i e s c o n d u c t e d by stands growing  a t a stump h e i g h t  a t t h e end  the w r i t e r f o r mixedwood  i n Northern Alberta.  o f 1 - f o o t , a t k.5  F o r each  p o i n t measured i n s i d e bark.  and  t h e t i p o f the t r e e .  was By  and t h i s  plotted  joining  g r a p h f o r e a c h t r e e was  Lengths  and tree,  following  above  ground  between  o f stem  accumulated h e i g h t  were  at  each  over the c o r r e s p o n d i n g d i a m e t e r  t h e p o i n t s w i t h a smoothed l i n e , o b t a i n e d from which  r e a d measurements f o r t h e u t i l i z a t i o n  measures used  feet  of each e q u a l - l e n g t h e d l / 1 0 - s e c t i o n  accumulated f r o m the base  cubic  and m e a s u r e d  and b a r k t h i c k n e s s e s were r e c o r d e d a t t h e  breast height  to  ASPEN AND  i n A l b e r t a were t o t a l  i t was  desired.  a  possible The  volume  cubic feet,merchantable  feet  (1-foot  stump t o a k - i n c h  top i n s i d e bark)  board f e e t  (l-foot  stump t o a 6 - i n c h t o p i n s i d e  and  bark,Scribner  rule). Total  cubic foot  calculated using  volume i n s i d e b a r k f o r e a c h t r e e  S m a l i a n ' s f o r m u l a ; t h e p o r t i o n between  and 1 - f o o t stump h e i g h t was c h a n t a b l e volume was stump and t o p .  treated  o b t a i n e d by  subtracting  i n board f o o t volume.  10.3,  14»3,  or 16.3  stem w h i c h r e m a i n e d  feet  The  mer-  t h e volume o f logs  t o p l o g c o u l d be  8.3,  long depending  f r o m the l a s t  The  ground  16.3-foot  From the graphs o f each t r e e ,  were s c a l e d 12.3,  as a c y l i n d e r .  was  on the l e n g t h o f  16.3-foot l o g .  -37Por a n a l y s i s of volume, the measurements used f o r each aspen and b l a c k p o p l a r t r e e were: 1.  Diameter at b r e a s t h e i g h t i n inches o u t s i d e bark,  2.  T o t a l height i n feet,  3.  Volume i n (a) t o t a l cubic f e e t , (b) merchantable cubic f e e t , (c) and merchantable board  T o t a l Cubic  feet, Scribner rule.  Feet  The  t o t a l c u b i c volume f o r each aspen t r e e was  com-  pared with volumes given i n a t a b l e c o n s t r u c t e d f o r t h i s  1 s p e c i e s i n e a s t e r n Canada . consistently high.  The  t a b l e gave v a l u e s which were  Adjusted volumes were obtained from a  graph d e r i v e d by p l o t t i n g a c t u a l volumes over t a b u l a r volumes on double l o g a r i t h m i c paper (Table  23).  From a comparison made p r e v i o u s l y by the w r i t e r , i t was  found  t h a t b l a c k p o p l a r had  a characteristically thicker  bark and poorer form than the aspen.  The volumes  obtained  t h e r e f o r e , when the b l a c k p o p l a r t r e e s were i n t e r p o l a t e d i n Table  23,  were too h i g h .  determined and  applied.  A c o r r e c t i o n f a c t o r of 0.8L2 The  which r e s u l t e d proved to be erence was  estimate  of the a c t u a l volumes  satisfactory.  The  aggregate  small and the average d e v i a t i o n d i d not  beyond t h a t obtained f o r the aspen.  1  was  Dominion Form C l a s s Volume T a b l e s , page 182,  19k8.  diff  increase  -38'Merchantable No l i m i t s used fore,  Cubic  Feet  a s p e n volume t a b l e s a p p l i c a b l e i n A l b e r t a were l o c a t e d .  t o c o n s t r u c t a new  a n a l y s i s was  essentially  table.  height this  by p l o t t i n g  F o r the  straight  Although  into  account.  are f i t t e d  The  intervals.  From t h e s e  techniques each  group of curves i n  by h e i g h t  are  next  a common  origin.  the  by h e i g h t  r e a d i n g o f volume f o r 1 - i n c h curves the v a l u e s  diameter  t o be' a f a m i l y  i n t h i s p a r t of  over diameter  ob-  classes.  2-inch class  curves proved  be h a r m o n i z e d  replotted  order to f a c i l i t a t e  This  o f volume t o h e i g h t by  aspen d a t a these  c u r v e s may  (2).  by D w i g h t  l i n e s , most o f them r a d i a t i n g f r o m  the  i n the  c o n c u r r e n t l y w i t h those  volume o v e r d i a m e t e r  a n a l y s i s , volume was in  method employed  there-  of h e i g h t - t o - d i a m e t e r w i t h i n  t o d e r i v e the r e l a t i o n s h i p  classes.  merchantable  necessary  standard g r a p h i c a l  v o l u m e s and h e i g h t s r e a d f o r e a c h  used  of  i s taken  ( F i g u r e 13)  step  tained The  class  I t was  that suggested  method i s an improvement on because the r e l a t i o n s h i p  The  t o the  classes  diameter  shown i n T a b l e  2k  were o b t a i n e d . The  b l a c k p o p l a r t r e e data f o r merchantable  f e e t were now  compared w i t h v o l u m e s i n t e r p o l a t e d  and h e i g h t i n T a b l e a g a i n too h i g h . resulted in  the  aspen.  2k.  The  average  diameter  t a b u l a r v a l u e s o b t a i n e d were  M u l t i p l y i n g by  i n a much i m p r o v e d  for  cubic  a correction factor  estimate with but  deviation percent  of  a slight  0.817 increase  over t h a t o b t a i n e d f o r the  -39Merchantable  Board F e e t , S c r i b n e r  A similar f o o t volume was  Rule  a n a l y s i s f o r d i a m e t e r , h e i g h t and  carried  o u t f o r the a s p e n up  t o and  t h e s t e p o f p l o t t i n g volume o v e r h e i g h t by d.b.h. F i g u r e s 13  and  of t r e e s used Figure to  15  lk illustrate to weight  the f i r s t  each p o i n t  The  diameter c l a s s  s p a c i n g and  by  are o m i t t e d ) .  of s t r a i g h t  lines  fitted  f o r each  (11).  related  the f o l l o w i n g  ( t h e number  an a d a p t a t i o n o f a method  S i n c e volume i n b o a r d f e e t directly  including  classes.  s l o p e s of these l i n e s  are harmonized  o u t l i n e d by Meyer  is  steps  on t h e g r a p h s  shows t h e p r e l i m i n a r y g r o u p  the d a t a .  two  board  to t o t a l  f o r any one  h e i g h t , i t may  be  diameter expressed  class by  formula: V = a + where  bH  V = board f o o t a -  intercept,  b =  slope,  volume,  H = total height i n feet. The determined.  slope of the l i n e  These v a l u e s p l o t t e d  a freehand curve  (Figure 16).  f o r 13-inch diameters  line  -5.65 + 0.612D.  and  For  t h e p r e s e n t i t may  may  be  and  read from 12-inches.  and l a r g e r ,  the r e l a t i o n  that  straight  of slope t o i s required-  individual  t h e c u r v e i n F i g u r e 16  is a  by  w i t h a s l o p e of b" =  a d i f f e r e n t procedure be n o t e d  was  o v e r d i a m e t e r were f i t t e d  This relationship  Below 1 3 - i n c h e s  diameter i s curved,  7  f o r each d i a m e t e r c l a s s  slope values  f o r diameters  between  -koIn the next  where t h e a d j u s t e d - b" (average  = -5.65  b"  an a d j u s t e d  obtained  standard  a curve  fitted  proved  height  The a v e r a g e v o l u m e s and h e i g h t s averages f o r each  v o l u m e s were t h e n  as shown i n F i g u r e  t o be a s t r a i g h t  larger,  f o r t h e d.b,h. c l a s s ) - 80, and  by c a l c u l a t i n g weighted Adjusted  the r e s u l t i n g  line  p l o t t e d over 17.  f o r diameters  -236  a standard  1.  A d j . volume  height  -bH by  V-bH  equation  13-inches and by t h e e q u a t i o n ,  and a d j u s t e d  =  adjusted  volume  equation  -236.0 f 28.5D -5.65+ 0.612D) 80 o r k52.0 - I4.9.OD  adding  -  since V  that  o f 80-feet t h e f o l l o w i n g i s t r u e :  (1)  (2)  and  + 216.0 - 20.5D  =  a  d i a m e t e r and  + 28.5D.  (V) =  2.  2-inch  f o r any d.b.h. f r o m t h e c u r v e .  From t h e s l o p e for  were  the regression  b e l o w 1 3 - i n c h e s , i t may be n o t e d  volume may be r e a d  4- 216.0 - 20.5D  = a + bH and a = V - bH.  e s t i m a t i n g volumes o f t r e e s w i t h  above, t h e r e  Again  r e g r e s s i o n i s expressed  adj. v o l . = For diameters  diameter,  volume = t h e a v e r a g e volume f o r t h e d.b.h.  + 0.612D.  class.  For  volume f o r a  c l a s s o f 80-feet was computed f o r e a c h 2 - i n c h  height  class  step,  a r e now t h r e e  diameters  13-inches and  equations;  A  General  expression  B  The s l o p e  C  The i n t e r c e p t e x p r e s s i o n  expression  V* =  a  + bH  b =  _ 5,65  a =  +  + 0.612D  216.0 - 20.5D  -kl'Since  slope  "b" and i n t e r c e p t " a " a r e c h a n g i n g  manner f o r d i a m e t e r s applicable obtained are  t o the smaller diameters.  calculating  values  While  corresponding  required i n order  each 1-inch diameter  class.  s l o p e v a l u e s may be  to derive individual  equations f o r  T h i s d i f f i c u l t y was overcome, b y these  over diameter  as  The c o m p u t a t i o n s f o r 'a' were made f r o m  expression, a = volume a t c h o s e n h e i g h t  - b x (chosen  where volume may be r e a d f r o m F i g u r e 17 F i g u r e 16. for  B and G a r e n o t  f i g u r e s f o r the i n t e r c e p t  o f ' a ' and p l o t t i n g  shown i n F i g u r e 18. the  below 13-inches, e q u a t i o n s  f r o m F i g u r e 16,  still  i n a curvilinear  An i n d i v i d u a l  the diameters  equation  required.  v a l u e s f o r the board  and s l o p e v a l u e s  t h e r e f o r e , was  From the e q u a t i o n s  -  9" 10" 11" 12"  -  Group I I - D i a m e t e r s larger.  V V V V V V  =: =• :: =: =: =:  - 8.8 - 13.6 - 18.5  +  0.22H  +  - 31.0  i T  0.79H 1.12H  +  l.k6H  - 2k.1 - kO.O  from  determined  shown b e l o w t h e  f o o t v o l u m e s shown i n T a b l e  Group I - D i a m e t e r s a t b r e a s t h e i g h t f r o m 7-12  7" 8"  height)  25 were  inches  obtained.  inclusive  0.50H  1.87H  a t b r e a s t h e i g h t f o r t r e e s 1 3 - i n c h e s and  General expression V The s l o p e e x p r e s s i o n b The i n t e r c e p t e x p r e s sion a  = =  a + bH -5.65 *  =  + 216.0 - 20.5D  0.612D  -1+2 Examples o f For  application clarity,  examples o c c u r r i n g 1.  volumes i n board f e e t  are c a l c u l a t e d f o r  i n Group I and Group I I .  Wanted: t o d e t e r m i n e t h e volume i n b o a r d f e e t f o r a i n c h t r e e o f h e i g h t 63 f e e t .  10-  From Group I t h e e q u a t i o n i s : - 2k.l  V =  +  Substituting  - 2k.1  V z  k6.5  V = 2.  1.12H for H  +  1.12  board  63  x  feet.  Wanted: t o d e t e r m i n e t h e b o a r d f o o t t r e e o f h e i g h t 9k f e e t .  volume f o r a 1 9 - i n c h  From Group I I t h e g e n e r a l e q u a t i o n i s : V = to determine the slope  a  +  bH  19 f o r D i n b =  substitute  -  5»65 + 0.612D  b =  -5.65  =  +5.98  to determine the i n t e r c e p t  +  substitute  216.0 = - 173.5  f o r b, a, and H i n t h e g e n e r a l  V = -173.5 «*• 388.6  +  p o p l a r volumes the t a b u l a r  O.787.  equation  5.98 x 9k  board  feet.  To a p p l y t h e v a l u e s i n T a b l e  them by  19 f o r D i n a = +216.020.5D  - 20.5 x 19  a = +  substituting  0.612 x 19  figures  25  to estimate  were r e d u c e d b y  black  multiplying  -43The method employed above to harmonize a f a m i l y of s t r a i g h t l i n e s was  o r i g i n a l l y suggested by W.H.  Meyer to  develop volume t a b l e s i n board f e e t where the r a t i o of volume/ diameter p l o t t e d over diameter by h e i g h t c l a s s e s , form a s e r i e s of s t r a i g h t l i n e s .  The  aspen d a t a p l o t t e d t h i s  way  i n d i c a t e d c u r v i l i n e a r i t y f o r diameters above 20-inches. e x p l a n a t i o n may understocked was  The  be t h a t l a r g e r diameters are found mainly i n  stands and are u s u a l l y t r e e s of poorer form.  It  f e l t t h e r e f o r e , t h a t Meyer's method c o u l d not be j u s t i f i -  ably employed. Adapting the method d e s c r i b e d , o f f e r s l i t t l e to  those who  are f a m i l i a r w i t h the systems of c r o s s c u r v i n g ,  but f o r those who mathematical  are not, the i n t r o d u c t i o n of t h i s  system may  slope and spacing. may  advantage  facilitate  semi-  the h a r m o n i z a t i o n of both  Another f e a t u r e of the method i s t h a t i t  be employed f o r o t h e r r e l a t i o n s h i p s where a system of  straight lines i s applicable. may be gained by a mathematical  In c e r t a i n cases, some c o n t r o l of t a b u l a r and  advantage inter-  mediate v a l u e s . The weakness l i e s i n the manner o r i g i n a l have been obscured by p r e v i o u s c u r v i n g .  averages  T h i s would seem to  be no more s e r i o u s however, than the weaknesses i n v o l v e d i n any m u l t i c u r v i l i n e a r method.  -kk-  VOLUME TABLES FOR  Total  Cubic  WHITE BIRCH  Feet  H e i g h t measurements f o r 93 b i r c h by MacLeod out the  (6) as t h e y o c c u r r e d i n mixedwood  same r e g i o n as t h i s  shown i n T a b l e 26  Merchantable  study.  and  Cubic  board  and  Board  d.b.h. c l a s s ,  the r a t i o  f o r b i r c h was  applied  tables,  To  of aspen  as a  s t a n d s m e a s u r e d was  seriously  incorrect affect  c u b i c volumes  total  the  volumes i n  f o r the d i a m e t e r s shown f o r  each  c u b i c volume t o  volume r a t i o s  measures p r o v i d e d the o n l y  The  and  that  correction.  p o s s i b l e under the c i r c u m s t a n c e s measured f o r volume.  aspen  t h e volume  assume a s p e n - b i r c h t o t a l  same f o r m e r c h a n t a b l e  a r i s e from  total  through-  Feet  f e e t were i n t e r p o l a t e d  h e i g h t s g i v e n i n T a b l e 26,  To  The  stands  taken  are taken from h i s r e p o r t .  To d e r i v e m e r c h a n t a b l e cubic  t r e e s were  s i n c e no  birch  were  the  basis trees  were  amount o f b i r c h p r e s e n t i n t h e  s m a l l however,  and  any  volume t a b l e s f o r t h i s results.  errors  that  might  s p e c i e s cannot  -45-120  -WO  IOO  90  t£ 80  Sol —  V  \  \ eo  -20  8  12  Di'ometer;  I  16 Breast  Vir?ches)__  20  24  28  Height, 1  FIGURE 13 - The t r e n d o f h e i g h t on d.b.h, w i t h i n each 1 0 - f o o t h e i g h t c l a s s .  FIGURE - ll). The r e l a t i o n o f board f o o t volume ( S c r i b n e r r u l e ) on d.b.h. by 1 0 - f o o t h e i g h t classes.  -1+6-  l^Mal on t^hlilhl o t a l height  0f hCl d ^f 5'°\ by 2 - i,. n c hl d i a m e t e r °c l a s s e s . f  o  t  V  o  l  u  r  a  s  (Scribner  rule)  -hi-  top  of  •  — 2-o  0  A \  i6 I2 Diameter.Qreat 8  20  1  iht-  z4  26 I  1J  1  1  FIGURE 16 - S l o p e c o e f f i c i e n t s "b" f o r t r e n d o f S c r i b n e r b o a r d f o o t volume on t o t a l h e i g h t , p l o t t e d on d i a m e t e r a t b r e a s t h e i g h t .  — 600 <-> 500 tQ  4O0  1  -v§ Zoo  -\Zoo  / 0  4  Iz 2 16 Diameter. E.breast Heiqh 1, 6  •  fi  FIGURE 17 - A d j u s t e d volume r a t i o s ( b a s i s = 80 f e e t ) p l o t t e d over diameter at b r e a s t h e i g h t .  160 WO  $  1 ^  oo  £o —  -40  — •10  0  2  1  4  <  >  I 8  0  i2  1Height-,  eter, Breast l  in.)  14  I  i  \  FIGURE 18 - I n t e r c e p t c o e f f i c i e n t s " a " f o r t r e n d o f S c r i b n e r b o a r d f o o t volume on t o t a l h e i g h t , p l o t t e d on d i a m e t e r a t b r e a s t h e i g h t .  TABLE 23 VOLUME TABLE Aspen (P. tremuloides Michx.) and Black Poplar (P.balsamifera L.) Total Cubic foot Volume Central and Northern Alberta Total Height - feet  d. b.h. in. 1 2 3 4 5 6  20  10  0.04 0.06 0.13 0.21 0.28 0.47 0.85 I.36  7  8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 2?  Basis number 70 80 90 100 110 30 40 50 60 of Total peeled volume i n cubic feet trees 2 0.07, 0-.45 4 0.29 I 0»37 J_04 0.66 0.85 9 1.19 1.53 1.871 2.21 13 1.90 I 2.44 2.98 13 3.52 6 5.15 _____ 2.75 3.55 *-35 9 4.86 5.97 7.09 8.20 1 9 0 1 10 6.38 7.84 9.30 10.76 12.22 13.7 5 8.10 10.00 11.8 13.6 17.3 15.5 6 16.7 12.3 21.1 18.9 14. 8 20.0 14.8 22.6 25.2 17. 5 29.8 32.9 20.5 23.6 26.7 17.5 7 20.4 34.8 38.4 31.2 24.0 27.6 8 40.1 44.2 36.0 27.8 31.9 23.5 7 36.3 45.8 50.5 41.1 31.6 26.9 11 51.6 46.3 62.2 _ _ _ 40.9 30.3 70.2 11 64.2 _____ 46.1 52.2 58.2 _£__ 64.8 ____. 58.1 78.2 8 44.6 64.4 5 86.7 ^9.5 _±_L 56T9 71.9__2_i 4 71.0 95.5 5^.7 62.9 79.2 87.3 6 77.6 104.2 68.8 86.5 95.3 4 84.2 112.9 74.7 93.8 103.3 90.8 101.11111.3 121.6 1 97.4 _________ 130.3 2 104.0 115.7 127.3 139.0 1 110.6 -23T0I135.3 147.7 130.3 145; 3 156.4 117.2  Basis num28 ber of «g 8 15 18 16 29 I65 39 trees f o r Black Poplar multiply tabular volumes by 0.842 - basis, 46 trees. Heavy line indicates the extent of the original data. Volumes include entire stem inside bark. Table was prepared by adjusting aspen volume table, page 196, Dominion Form Class Volume Tables, 1948. Aspen i Aggregate difference, table 0.267 percent high • Average deviation 4 6.15 percent 1  Black Poplar  : Aggregate difference, table 0.023 percent low : Average deviation  4  6.09 percent  -50TABLE 24 VOLUME TABLE Aspen (P.tremuloides Michx.) and Black P o p l a r ' (P.balsamifera L.) Merchantable Cubic Peet Central and Northern A l b e r t a d.b.h. in.  1  Total Height F t .  30  4 5 6 7 8 9 10 11 12 13  40  0.15 1.05  2.40  90 60 ' 70 50 Merchantable volume i n cubic' feet 80  0.45 1.50 3.05  1.93  3.70 5.70  14.6  18.2  18.6  24.1 27.1  16.6  15 16 17  21.1  30.5 33.6 37.9  18  19 20 21 22 23 24 25 26 27  40.2  43.9  2.40  ^•35 6.60 7.50 9.00 10.1 11.90 13.55 15.2 17.5 18.4 21.3 21.9 25.5 25.6 30.1 29.6 35.1 33.5 39.9 37.7 44.9 41.8 50.0 46.0 55.1 50.2 60.2 54.7 65.5 58.8 70.5 63.O 75.6 80.6  85.6 90.6 95.6  28  Basis,number of trees -  10  18  110  0.75  3.90 4.80 7.80 5.50 6.70 6.95 8.60 10.25 8.20 10.50 12.9 12.5 15.4  14  100  16  29  39  11.2 15.2 19.8  24.3  29.4 3^7  40.6  46.3 52.1 58.2  64.2  70.2 76.2  39.2 46.1 52.7 59.3 66.£ 73.3 80.2  87.0 82.3 94.0 88.2 100.7 94.2 107.7 100.2 114.8 106.2 121.7 112.2 1 128.7 118.2 135.7 28  66.5 74.6  82.4  90.2 97.8 105.7 113.3 121.3 129.4 137.3  145.2  142.7  153.2 161.2  7  -  Basis number of trees  10 13 6 9 10 5 6 8 5 7 8 7 11 11 8 5 4 6 4 1  -  2 1  147  for Black Poplar multiply tabular volumes by 0.817 - basis,number of trees 46. Heavy l i n e indicates the extent of the o r i g i n a l data. Volumes include stem from l«foot stump to a 4-inch top, i n s i d e bark. Table was prepared f o r aspen by mult-curvilinear methods. Correction term 0.817 was applied to table values f o r estimating Black Poplar volumes. Aspen : Aggregate difference, table 0.462 percent low. : Average deviation + 6.18 percent Black Poplar  : Aggregate difference, table 0.114 percent high : Average deviation + 6.49 percent.  -51-  TABLE 25 VOLUME TABLE * Aspen (P.tremuloides Michx.) and Black Poplar' (P. balsamif era L.) Merchantable Board (Scrib.) inside bark-Central and Northern Alberta  d.b.h. • in.  Total Height Peet 40  50 ' 60 Merchantable  2 11 21 32  7  8 9  10 11 12 13  42  4 16  29 43 57 72  88  14  104 120  15 16 17  136  1 152  169  18  19 20 21 22 23  185 201  70  '  80  '  90  ' 100  1  110  volume i n board feet .(Scribe) 7  21 37  54 71 91  Ul  133 156 178  200 223 245 267  290 312  9  26 45  66 86 109 134 I63 191 219 248  277 305 333 362  390 419  447  24  25 26  476 504  3 9  31  5 6  53 77  100  8  128  157 192 226 261  295 330 365 399 434  468 1503 538 1572  606  641  27 28  1  Basis - Number of trees  5 7  180  221  262 302 342 384 424 465  506 546  588 628 669 709  8 7  390 438 434 531  578 624 672 718 765 812  750 791  858 906  7  -  11 11 8 5  4 6  4 1 2 1  -  Basis number of trees  -  -  9  28  39  28  f o r Black Poplar multiply tabular volumes by 0.787 - basis 46 trees. Heavy l i n e indicates the extent of the o r i g i n a l data. Volumes include stem from 1-foot stump to a 6-inch top inside bark. Table prepared for aspen by m u l t i - c u r v i l i n e a r methods. Correction term 0.787 was applied to tabular values to estimate Black Poplar volumes. Aspen : Aggregate difference, table 0.126 percent high : Average deviation + 12.65 percent Black Poplar  : Aggregate difference,table 0,029 percent low : Average deviation + 14.84 percent  111  -52TABLE 26 VOLUME TABLES White B i r c h (B. P a p y r i f e r a Marsh.) C e n t r a l and Northern A l b e r t a .  /  d.b.h. (inches)  1  2 3  k  5 6 7 8 9  10 11  12 13  /  Total Height (feet)  .  i  Volumes i n s i d e bark Total Merch. cubic cubic feet feet  13  0.07 0.35  22 30 38  0.88 1.76 3.00 k.6l 6.63 9.12 11.9 .  k$  51 56 61  65 69 73 76 78 80  '  ,  Based on a h e i g h t /d.b.h.  15.1  18.9 22.9 27.1 31.7  • -  0.11 l.k6  3.25  5.33  7.6k  10.k  13.7 17.5 21.6 25.9 30.9  Merch. Board f e e t (Scrib.) -  3  15 31  k9 68 92  115 U3  curve f o r 93 t r e e s .  T o t a l cubic volume i n t e r p o l a t e d from volume t a b l e f o r white b i r c h , i n Quebec (Dominion Form C l a s s Volume T a b l e s , page  I82,19k8).  Volumes i n merchantable cubic and merchantable board f e e t ( S c r i b . ) obtained by a d j u s t i n g c o r r e s p o n d i n g aspen volumes f o r these measures by a r a t i o equal t o : t o t a l c u b i c volume f o r aspen d i v i d e d by c o r r e s p o n d i n g white b i r c h t o t a l cubic volume. Merchantable cubic volumes i n c l u d e stem from 1 - f o o t stump t o a k-inch top i n s i d e b a r k . Merchantable board f o o t volumes i n c l u d e stem from 1 - f o o t stump to a 6 - i n c h top i n s i d e bark.  APPENDIX  Basic  Data It  every the of  age  and  sample age  Table  is difficult site  a fair  and  site  27.  The  q u a l i t y , but distribution  q u a l i t y was  stands  considering among t h e  obtained.  f i e l d method f o l l o w e d  or normal p l o t s from the of  t o o b t a i n measurements i n f o r e s t s f o r  o f each  age  where a r a n g e i n s i t e  best,  class. existed.  Some s t a n d s  c o n d i t i o n were m e a s u r e d .  Forests  s o u g h t out  average guide curve prepared offered  by  the  during  the  progress  of dominant h e i g h t  w r i t e r f o r the  distribution  of the  site  qualities TABLE  PLOT DISTRIBUTION BY  AGE  AND  stocked  portions  however, were  site  o f the  o v e r age  a record  in  satisfactory  the  very  average  qualities study.  then,  An  previously  aspen i n mixedwood  some a s s i s t a n c e i n k e e p i n g  fully  the p o o r  plots representing of other  of  combinations  select  T h i s p r o c e d u r e was  two  t o be  to  size  is illustrated  the medium and  uniform-and i n such cases  had  small  possible  This was  the  stands  of the  approximate  sampled.  27 S I T E INDEX CLASSES .Totals  5 8 11 9 9 9  Totals  3  13  32  23  7  7 8 9 3 78  -5V Fleld  Work F o r t h e most p a r t , ' aspen  not n a t u r a l l y over  occur  t h e r e f o r e had  plots  such  steel with  acute  from  angles never  varied  recorded  from  by  80 y e a r s  of  ing  than  groups,  age  of  an  r e q u i r e d on  than  by  total  except  h e i g h t was  Two  each 2 - i n c h d i a m e t e r  and  h e i g h t s o f d o m i n a n t s were r e c o r d e d  o b t a i n e d by  calipered  found  counting  rings  above  Those m e a s u r height  These  stands  smaller  steel  where t r e e s 1-  b e l o w 80 y e a r s  i n o l d e r stands.  and  Diameters  s e p a r a t e l y ; they  varied  plot. counting  that consistent estimates the  Small  h e i g h t s f o r each  d e t e r m i n a t i o n s were made by  I t was  Size  measured w i t h  i n dense young  If. t o 8 t r e e s p e r  taken  computations.  for  Age  each p l o t .  i n two  3 feet plus.  class  and  A minimum of  inch classes.  i n c h were r e c o r d e d and  were  i n some s t a n d s  c l a s s were t a k e n f o r s t a n d s  i n number f r o m  a few  t r e e s were  w h i c h were f o u n d  and m e a s u r e d d i r e c t l y .  i n c h diameter  a compass  to over l / 2 acre  l / l O acre  i n c l u d e d i n the y i e l d  Abney l e v e l  were f e l l e d  rings.  with  60 d e g r e e s .  A l l living  6 inches to 3 f e e t  F o r each p l o t , and  composite  inch c l a s s e s according to species.  0.6  t r e e s were n o t  Individual  r a t h e r than  surveyed  than  were r e c o r d e d  extending  (7).  were  less  less  o f the u n d e r s t o r y  less  stands  Most p l o t s were r e c t a n g u l a r b u t  young t o o l d s t a n d s .  trees  tape  selected  t r e e s i n the m a i n s t a n d was  therefore  and  t o be  p l o t boundaries  tape.  A l b e r t a does  r a t h e r i n small patches.  as t a k e n by M c A r d l e  The  100  i n uniform w e l l stocked  l a r g e areas but  plots  i n Northern  on  the  annual  could only  the b u t t of the  tree  be  after  -55felling. sharp  I t was n e c e s s a r y  axe i n o r d e r  t o make a v e r y  sloping cut with  t h a t m i n u t e r i n g s c o u l d be d i s c e r n e d .  Though t h e a v e r a g e  age o f t h e d o m i n a n t s was t a k e n  age,  adopted f o r each  age  the procedure counts  considered erally  throughout even-aged.  Such  species.  values ant  Since  age d e t e r m i n a t i o n s  a t these  r e q u i r e d to reach the height  i n Table  t o make  t o be g e n -  above t h e g r o u n d l e v e l ,  t o add t h e ages o b t a i n e d  of years  s t a n d was f i r s t  a c o n d i t i o n was f o u n d  u s u a l l y made a t s e v e r a l f e e t  ber  as p l o t  t o a s c e r t a i n i f a l l t r e e s c o u l d be  true f o r t h i s  necessary  were  i t was  h e i g h t s t h e num-  o f t h e stump.  The  28 b a s e d on some 300 m e a s u r e m e n t s o f d o m i n -  a s p e n s e e d l i n g s were u s e d  to convert  the r i n g  count t o  t o t a l age. TABLE 28 CORRECTION-IN YEARS TO BE ADDED TO AGE DETERMINED PROM INCREMENT BORINGS OR STUMP COUNTS, TO OBTAIN ASPEN TOTAL AGE Distance from average ground level to boring o r t o p o f stump  S Correction A  e  (inches)  (years)  1  1  2 3  k  5 6 7  8  9  a  1 1 1 1 2  2  2  2  D i s t a n c e from average ground l e v e l to boring o r t o p o f stump (inches)  10  12 18 2k 30 36  k2  Age Correction (years)  2  3 3 k k  5 5  k8  5  Skr  5  -56Office  Computations The  now  computed  height ed.  basal area per p l o t and  a height diameter  of e a c h d.b.h. c l a s s  In t h i s  last  corresponding recorded.  case,  t o the  This  tables for  each of f i v e  by  number o f t r e e s .  in  the l a t e r  class  The  from  average  the  curve  diameters  by b a s a l a r e a .  S c r i b n e r board computed w i t h  foot  the  Total  volumes f o r  a i d of  volume  T o t a l s were t h e n  taken  (number o f t r e e s , b a s a l a r e a and t o an  dividing A ratio  the  total  (total  a cross-check  a n a l y s i s was  acre  average  also  was.  d o m i n a n t were o b t a i n -  dominant  inclusive).  converted  to provide  drawn.  read  calculated  c u b i c and  items  average  of the  b a s a l a r e a o f the  calculated  adopted  was  t o 26  t h r e e v o l u m e s ) and  was  average  c l a s s were now  ( T a b l e s 23  The  and  curve  t h e h e i g h t was  average  cubic, merchantable each d i a m e t e r  f o r each diameter  the  basis. t r e e s f o r each  b a s a l a r e a by  plot  the  volume d i v i d e d by  total  basal  b e t w e e n volume and  area)  basal  area  computed.  Method o f A n a l y s i s The described of  average  the  the  age  age,  Osborne  and  F i g u r e 19, of  of t h i s graph  employed was  Schumacher  d e v i a t i o n and  c l a s s was  sheaf  analysis  dominant h e i g h t  standard  each on  by  method o f  over  age  (15). by  calculated  first.  To site  coefficient  essentially obtain  index  that  curves  classes,  of v a r i a t i o n w i t h i n These  statistics  plotted  p r o v i d e d the b a s i s w i t h which to c o n s t r u c t  curves a site  Illustrated index value  earlier  i n F i g u r e 2,  c o u l d be  By  given to each  means plot  -57Coefficient of \'ariafion of Dominant Height Residuals to Age  c 30  93  s  O  I"  §20 *o ^  1  <i  C o e f f i c i e n t of  >  i  )  e  Age - )'ears  10  20  30  40  50  60 ' 70  80  90  100 11o  120 \iJO 1'10 IJ  Standard Deviations of Dominant Height Residuals to Age  Q  Age - Years -'  iir-  i  10  20  30  40  50  60  70  8C  90  100 II 0  120  130  140 150  PIGfURE. 19 - The r e l a t i o n o f t h e c o e f f i c i e n t s o f v a r i a t i o n and s t a n d a r d d e v i a t i o n s o f d o m i n a n t h e i g h t r e s i d u a l s t o t o t a l age.  -58according  t o i t s age Next,  the  IkO y e a r  considered The  aspen  truly  a n d doxJiFhant  age g r o u p .  stands found stocked  be and  to develop n o r m a l  of l i t t l e  To  plotted  the p l o t t e d  action  was  of f i e l d observations.  age c o u l d n o t be c o n s i d e r e d  Inclusion  evidence  of such  of  breakup  unsatisfactory to  y i e l d s was t h e r e f o r e c o n s i d e r e d  w h e n no s t a n d s i n t h e 120 located.  o f number o f t r e e s  the data.  average  t o average  diameter  The number o f t r e e s p e r a c r e was  to logarithms, grouped  over  arbitrary  ensure u n i f o r m i t y of d e n s i t y i n the r e m a i n i n g  to test  converted  at t h i s  age c l a s s e s were  the r e l a t i o n  was u s e d  the result  value, p a r t i c u l a r l y  t h e 130 y e a r  plots  This r a t h e r  and i n many c a s e s  was o b v i o u s l y a p p a r e n t . plots  6 plots i n  i t was f o u n d n e c e s s a r y t o r e j e c t  expedient from  fully  height.  into  stand diameter.  points i s illustrated  2 - i n c h c l a s s e s and The c u r v e f i t t e d  i n Figure 20.  Average D.B.fir of plot$~'wcfte$ FIGURE 20 - The r e l a t i o n o f t h e l o g a r i t h m o f number o f t r e e s t o a v e r a g e d.b.h.  to  -59To  test  uals to  f o r normality  from  the curve  cumulative  riate  probit  the frequency  was  first  frequency values  distribution  obtained.  percentages  were  These  f o r each  extracted from  Yates  (3).  The  the  upper  class  limits  shown  i n the f i r s t  the p r o b i t  values  given  i n the l a s t  over  sigmoidal enough  curve  distribution  indicated,  to affect  was  now  column  TABLE  by  approp-  by  Pisher  plotting  of Table  column.  of the procedure  resid-  converted  given  checked  revealed kurtosis,  the balance  were  of which,  tables  and  of the  29  The  slightly  but not  strongly  t o any  extent.  29  F R E Q U E N C Y D I S T R I B U T I O N OP R E S I D U A L S AND T H E P R O B I T S C O R R E S P O N D I N G TO T H E I R C U M U L A T I V E F R E Q U E N C Y PERCENT Class interval logarithms  40.14-0.16  +0.11-0.13 +0.08-0.10 +0.05-0.07 +0.02-0.04 -0.01-0.01 -0.04-0.02 -o.07-0.05 -0.10-0.08 -0.13-0.11 -0.16-0.14 -0.19-0.17 -0.22-0.20 -0.34-0.32  standard  lated  and  outside This and  1  f o l l o w i n g5 t h e a c c e p t e d  o f two  meant  o f 0.089 l o g  deviation  a  overstocked.  of  5  The  plots  -  number  of trees  procedure,  standard devi ations  total  2.74 3.02 3.20 3.70 3.99 4.33 4.80 5.26 5.63 5-92 6.17 6.66 6„79 6.98 7.26 8.72 +  -  83  Total  Probits units  1.2 2.4 3.6 9.6 15.7 25.3 42.2 60.2 73-5 82.0 87.9 95.2 96.3 97.6 98.8 100.0  1 1 1 5 5 8 14 15 11 7 5 6 1 1 1 1  •0.20-0.22 +0.17-0.19  The  Cumulative frequency percent  Plots number  remaining  a l l plots  (2 x 0.089)  were r e j e c t e d , 78  were  was  were  calcu-  falling  discarded.  4 understocked  employed  i n the  -60-  analysis  site  described  below.  To e n s u r e  that  the i n d e p e n d e n t  were n o t c o r r e l a t e d ,  t h e i r i n t e r r e l a t i o n was  means o f a s c a t t e r d i a g r a m , of A s s o c i a t i o n " significant  described  variables,  Figure  by  21,  Olmstead  and  and  tested  the "Corner  and Tukey  c o r r e l a t i o n b e t w e e n them was  age  (Ik).  by  test No  found.  000^' —  "  inn  — w  go  0  c o o  o <  —  r 1_  •  o o  0  0  o o  O  0 o  0  O  rt  o  O  0 0  Q  o  O 2  o  60  o  -+ O O  1  0  •  -  5o  An  0  1£>  20  3o  4o  50  (iO  \Aspen fotol  FIGURE 21 - The i s shown.  r e l a t i o n of s i t e  "70  80  90  1.00  uo  u0  age-years  i n d e x t o age;  no  correlation  -61The year the  age  classes.  basic guide  basal  area,  volume. by  data  this  age,  corresponding  the  per tree.  volume/basal  cubic  into  curves  coefficient  Prom  provided average.  to derive The  other  curves  the cross-checking  23  a r e shown  site for  index,  different  age  and  were  two  were  guide  and  into  read  from of  average  basal  area  the standard f o r each age  age,  total  age  as  Figures  cubic  class. was  the before 22  and  deviation  standard  Similar  deviation  about  standard  and  from  a basis  coincidence  of  total  process.  the residuals  quality  and  were a l l  cross-checking  values.  the trends  classes.  provided  and t h e  curves  computed  of interrelated  site  cubic  the corresponding  index  when d e r i v i n g  formed  the product  of this  of site  with  10-  diameter"*",  total  per acre  measures with  brought  of v a r i a t i o n  obtained  site  curves  to i l l u s t r a t e  coefficient  of  age  average  equal  of this  obtained  of these  by  and  were  give  average  of v a r i a t i o n  the r e l a t i o n  should  will  The  obtain curves  average  area  the product  ratio  into  i s conveniently  basal  a g r e e m e n t by means  To  and  area  on  and  of trees per acre  Also  volume p e r a c r e .  brought  these  number  sorted  plotted  area  of cross-checking  f o r a given  now  of trees,  volume/basal  The  the  were  values  of curves.  mean  area  plot  f o r number  cubic  A method system  each  average  curves  the  basal  The  total  curve  from  units  volume  curves  with  yield  were  ''"average d i a m e t e r = a v e r a g e b a s a l f o r e a c h a g e c l a s s d i v i d e d by t h e c o r r e s p o n d i n g a v e r a g e number o f t r e e s . These v a l u e s d i d n o t c o i n c i d e w i t h t h e mean o f t h e a v e r a g e d i a m e t e r s themselves. T h e r e f o r e the c o r r e s p o n d i n g v a l u e s were p l o t t e d on d o u b l e l o g p a p e r and a l i n e f i t t e d . T h i s r e g r e s s i o n was used as a b a s i s t o a d j u s t t h e a v e r a g e d i a m e t e r ( s q . f t . ) f o r each plot.  -62constructed  f o r each  The checked The  against  statistics  noted tion is  that  taken in  were  the  are  age  of  smaller  age  class.  trees when for  of  groups,  f o r by  they  younger.  effect  site  The  of  10-30  now  results  of  the  least  the  influence  tables  for  of  the  site to  other  the  by  be  varia-  found  plots  k0-110,  increased of  the  these,  and  Age  the  9.1  percent  computations  only  67.2  age c l a s s k0-110 years accounted for,percent  80.  trees  In  those  was  When  §ge c l a s s 10-30 years accounted for,percent  trees  Variation  with  does  affect  this In  It will  below:  Variation Number  item  were  constructed.  30.  the  above.  curves  were  site.  Item Number  these  i n Table  reason  and  the  two  accounted  older  given  into  given  The  years  from  which  number  account.  variables described  derived  from  f o r become  30  five  are  the  overweigh  divided  variation  data  for  stands  influences  tables  the  only  into  the  obtained  accounted  exist  in  yield  of  Site  53»5  -  30  the  s e n s i t i v e and site.  obtained other  and  -  Table  of  Age  by  figures  total The  show  volume  results  are  89.k-  that  the  i n v e s t i g a t o r s who  species.  3  basal  most  area  sensitive  in general, have  is to  comparable  presented  yield  -63-  oC  __•  :  '  i ' iiT«iri_ii :  :  'O—  ~> ZO  3  0  to  *  io  30  40  So  _o  70  8o  go  LOO  no* j2o  FIGURE 22 - Freehand c u r v e s showing i n (a) t h e average r e l a t i o n of volume t o age; i n (b) the r e l a t i o n of the s t a n d a r d d e v i a t i o n of volume t o age; and i n (c) the c o e f f i c i e n t of v a r i a t i o n of volume t o age.  -6k-  +t6  FIGURE 23 - The r e l a t i o n between t h e f i r s t r e s i d u a l s o f t o t a l c u b i c volume (expressed i n s t a n d a r d u n i t s f o r i t s age) and s i t e i n d e x . TABLE 30 STATISTICS ILLUSTRATING RELIABILITY OF YIELD TABLES, AND EFFECT OF AGE, AND SITE AND AGE Item  Age o n l y  Age and S i t e  NUMBER OF TREES Aggregate d i f f e r e n c e , p e r c e n t Standard e r r o r , number V a r i a t i o n accounted f o r , p e r c e n t  +0.776 691 88.3  +  0.953 785 84.6  AVERAGE DIAMETER (Inches) Aggregate d i f f e r e n c e , p e r c e n t Standard e r r o r , i n c h e s V a r i a t i o n accounted f o r , p e r c e n t  + 0.563' 3.7 81,7  +  0.687 2.8 93-7  BASAL AREA ( S q u a r e - f e e t ) Aggregate d i f f e r e n c e , p e r c e n t Standard e r r o r , square f e e t V a r i a t i o n accounted f o r , p e r c e n t  -0.311 23 69.4  TOTAL CUBIC VOLUME Aggregate d i f f e r e n c e , p e r c e n t Standard e r r o r , c u b i c f e e t V a r i a t i o n accounted f o r , p e r c e n t  -0.0k3 819 76.0  -  +  0.725 20 76.0 0.139 514 94.4  -65-  BIBLIQGRAPHY  (1)  Black, R.L., I n t e r i m Report on the Decay o f Trembling Aspen (Populus tremuloides Michx.) i n the Upper P i c Region of Northern O n t a r i o . Unpublished r e p o r t , Canada Dept. A g r i c , Dominion F o r e s t Pathology, Toronto, Ontario, 1951.  (2)  Dwlght, T.W., Refinements of P l o t t i n g and Harmonizing Freehand Curves, F o r e s t r y Chronicle-, J u n e , 1937.  (3)  F i s h e r , R.A., and Frank Y a t e s , S t a t i s t i c a l Tables f o r B i o l o g i c a l , A g r i c u l t u r a l and Medical Research. Hafner P u b l i s h i n g Company, New York, 1949.  (4)  Garland, Hereford, Aspen f o r Veneer, U.S. Dept. A g r i c , Lake S t a t e s F o r , Expt. S t a . , Aspen Report 13, 1948*  (5)  H a l l i d a y , W.E.D., A F o r e s t C l a s s i f i c a t i o n f o r Canada, Dept. Mines and Resources, Dom.For.Serv. Bui,89,1937-  (6)  MacLeod, W.K., Y i e l d s o f Spruce-poplar Stands i n Northern A l b e r t a . Unpublished r e p o r t , Canada Dept, Resources and Development, F o r . Br,, Ottawa,  1951.  (7)  McArdle, R.E., Walter H. Meyer, and Donald Bruce, The Y i e l d of Douglas F i r i n the P a c i f i c Northwest. U.S, Dept. A g r i c , Tech. Bui 2 0 1 . Revised Oct. 1949.  (8)  Meineke, E.P., Quaking Aspen. U.S. Dept. A g r i c , Tech. B u i . 155,1929.  (9)  Meyer, H.A., A C o r r e c t i o n f o r Systematic E r r o r O c c u r r i n g i n the A p p l i c a t i o n of the L o g a r i t h m i c Volume Equation. Perm. State F o r e s t School Res. Paper 7, 1941.  (10)  Meyer, W.H., A study of the R e l a t i o n Between A c t u a l and Normal Y i e l d s o f Immature Douglas F i r F o r e s t s , J o u r . A g r i c Res., V o l . k l , No. 9, 635-665,1.930.  (11)  Meyer, W.H., A Method of Volume-diameter R a t i o s f o r Board-foot Volume Tables. J o u r . Forestry,, l\2 t  185-189,1944. (12)  Mulloy, G.A., E m p i r i c a l Stand D e n s i t y Y i e l d T a b l e s . Canada Dept. Mines and Resources, Dom.For,Serv., S i l v . Res. Note 7 3 , 1944.  (13)  Mulloy, G.A., E m p i r i c a l Stand D e n s i t y Y i e l d T a b l e s , Canada Dept. Mines and Resources, Dom. For.Serv., S i l v . Res. Note 8 2 , 1 9 4 7 ,  -66BIBLIOG-RAPHY  (lk)  O l m s t e a d , P.S., Association.  18: k95,19k7.  (15)  a n d J.W. Tukey, A C o r n e r T e s t f o r A n n a l s of M a t h e m a t i c a l S t a t i s t i c s , v  Osborne, J . C , and F . X. S c h u m a c h e r , T h e C o n s t r u c t i o n o f N o r m a l - y i e l d and S t a n d T a b l e s f o r E v e n aged T i m b e r S t a n d s . J o u r . A g r i c , R e s . , V o l . 5l>  No. 6, 547-56k, 1935.-  (16)  R e i n e k e , L.H., P e r f e c t i n g f o r Even-aged F o r e s t s .  No, 7,627-638, 1933.  (17)  a Stand-density Index J o u r . A g r i c . Res., Vol.4.6,  S c h a f e r , E.R., A s p e n f o r P u l p and A g r i c , Lake S t a t e s F o r . Expt.  13,1947.  Paper. U.S. Dept. S t a . , Aspen Report  (18)  S c h n u r , G.L., Y i e l d , S t a n d , a n d V o l u m e E v e n - a g e d U p l a n d Oak F o r e s t s . U . S . Tech. B u i . N c 560, 1937.  (19)  Spurr,  S.H.,  Company, (20)  Forest New  Inventory.  York,  The  Tables f o r Dept. A g r i c ,  Ronald  Press  1952.  Z e h n g r a f f , P a u l , P o s s i b i l i t i e s of Managing Aspen. U.S. D e p t . A g r i c , L a k e S t a t e s F o r . E x p t . S t a . , A s p e n R e p o r t 21, 1947.  

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