UBC Theses and Dissertations

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UBC Theses and Dissertations

The use of aerial photographs to distinguish between stocking and density of western hemlock stands on… Chiam, Yeow Chin 1967

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THE  USE OF AERIAL PHOTOGRAPHS TO DISTINGUISH  BETWEEN STOCKING AND DENSITY OF WESTERN HEMLOCK STANDS ON THE UNIVERSITY OF BRITISH COLUMBIA RESEARCH FOREST, ,  HANEY, BRITISH COLUMBIA,  by YEOW CHIN CHIAM B.Sc.  P r o v i n c i a l Chung-Hsing U n i v e r s i t y , Taiwan, China, 1965  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE  REQUIREMENTS FOR THE DEGREE OF MASTER OF FORESTRY  i n the F a c u l t y o f FORESTRY  We a c c e p t t h i s t h e s i s as conforming required  THE  t o the  standard  UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1967  In p r e s e n t i n g  t h i s t h e s i s in p a r t i a l  f u l f i l m e n t o f the requirements  f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y study.  a v a i l a b l e f o r r e f e r e n c e and  I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e  copying of t h i s  t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . . or p u b l i c a t i o n of t h i s w i t h o u t my w r i t t e n  thesis for financial  permission.  Department o f The U n i v e r s i t y o f B r i t i s h Vancouver 8, Canada Date  <T  I t i s u n d e r s t o o d that  V  Columbia  gain  shall  copying  not be a l l o w e d  ii ABSTRACT  Q u a n t i t a t i v e measures o f stand d e n s i t y and s t o c k i n g a r e v e r y i m p o r t a n t because o n l y w i t h f u l l f o r e s t be managed e f f i c i e n t l y . occupied  with trees.  the a r e a o c c u p i e d .  Density  knowledge o f t h e growing s t o c k can a Stocking  i s concerned w i t h f r a c t i o n o f a r e a  i s r e l a t e d t o t h e degree o f crowding w i t h i n  These q u a n t i t a t i v e v a l u e s  a r e determined by parameters  t h a t c o u l d be measured on t h e ground and on a e r i a l photographs. used t o e s t i m a t e are t h o r o u g h l y  height,  described.  The methods  crown w i d t h , and crown c l o s u r e from a e r i a l photographs The w r i t e r a l s o d e s c r i b e s t h e s t o c k i n g and d e n s i t y  c o n d i t i o n s under which t r e e s grow, w i t h i l l u s t r a t i o n s by b o t h t h e o r e t i c a l models and a c t u a l sample p l o t crown models. Forty-seven and  analysed  by simple  s e t s o f ground and photo-measurements were t a k e n and m u l t i p l e r e g r e s s i o n methods.  A comparison o f  photo and ground v a l u e s was t h e n made t o e v a l u a t e t h e u s e f u l n e s s photographs f o r d e n s i t y and s t o c k i n g measurements. r a t i o o f height age,  s i t e index,  The c o r r e l a t i o n o f t h e  (Ht) t o crown w i d t h (CW) from t h e ground and photo d a t a t o crown c l o s u r e , b a s a l a r e a , a d j u s t e d  f a c t o r and a d j u s t e d regarding  of a e r i a l  b a s a l area,  crowding f a c t o r were a l s o s t u d i e d .  n o r m a l i t y o f d e n s i t y and f u l l  Eight  crowding  assumptions  s t o c k i n g were made so t h a t the  i n t e r r e l a t i o n s h i p between t h e i n d i v i d u a l d e n s i t y and s t o c k i n g measurements c o u l d be s t u d i e d more e f f e c t i v e l y .  I t i s concluded t h a t Ht/CW r a t i o s a r e  measurable from a e r i a l photographs and shown t h a t t h e y a r e u s e f u l as a measure o f stand d e n s i t y and s t o c k i n g .  iii. TABLE OF CONTENTS PAGE TITLE  i  ABSTRACT  ii  TABLE OF CONTENTS  iii  LIST OF TABLES  vi  LIST OF FIGURES  ix  ACKNOWLEDGEMENTS  xi  1.  INTRODUCTION  1  2.  WESTERN HEMLOCK AS A SPECIES AND ITS CHARACTERISTICS  8  (a)  Its  distribution  8  (b)  Its  growth  8  (c)  F a c t o r s i n f l u e n c i n g the crown c h a r a c t e r i s t i c s o f western hemlock and f a c i l i t a t e i t s i d e n t i f i c a t i o n on a e r i a l photographs  3.  11  REVIEW OF LITERATURE A.  The a c c u r a c y and p r e c i s i o n o f c o n v e n t i o n a l photomeasurements : (a)  B.  18  Crown w i d t h  18  (b) Crown c l o s u r e  22  (c)  26  Height  The c o n v e n t i o n a l measurement o f : (a)  Stocking  35  (b) Stand d e n s i t y (c)  Crown v a r i a b l e s  42 and t r e e v a r i a b l e s used t o determine  stand d e n s i t y and s t o c k i n g  49  (i)  Height/Crown w i d t h r a t i o  54  Crown w i d t h / d i a m e t e r b r e a s t h e i g h t  55  Crown c l o s u r e  56  (ii) (iii) (iv)  L i v e crown l e n g t h and l i v e crown r a t i o  .  58  iv.  4.  IMPROVEMENTS IN METHODS OF MEASUREMENTS OF TREES AND STANDS . . . .  60  I l l u s t r a t i o n s o f how t r e e s and stands a r e measured: A.  V a r i a b l e s used f o r s t o c k i n g and d e n s i t y  measurement:  (i)  Height  60  (ii)  Crown w i d t h  68 72  ( i i i ) Crown c l o s u r e B.  Stocking grow:  and d e n s i t y c o n d i t i o n s under which t r e e s and stands  (a) S t o c k i n g  75  (i)  Open t r e e s and u n d e r - s t o c k e d stands  76  (ii)  Normal t r e e s and f u l l y - s t o c k e d stands  78  ( i i i ) F o r e s t t r e e s and o v e r - s t o c k e d  79  stands  80  (b) Stand d e n s i t y (i)  Open stand d e n s i t y  (ii)  Open-normal stand d e n s i t y  81 . . . .  82 83  ( i i i ) Normal stand d e n s i t y  85  (iv)  Normal-dense stand d e n s i t y  . . .  (v)  Dense stand d e n s i t y  86  (vi)  I n f l u e n c e o f crown c l o s u r e t o stand d e n s i t y  87  ( v i i ) I n f l u e n c e o f stand d e n s i t y on growth and o t h e r 88  t r e e and stand v a r i a b l e s 5.  DESCRIPTION AND LOCATION OF STANDS STUDIED  91  6.  METHOD OF DATA COLLECTION  93  (i)  C o l l e c t i o n o f f i e l d d a t a and making o f ground stereograms  . .  93  ( i i ) Measurements o f photo-data and c o n s t r u c t i o n o f crown c l o s u r e models 7.  95  INTERPRETATION OF PHOTO-MENSURATION DATA  97  A. D e s c r i p t i o n o f crown c l o s u r e models  97  V. B. D i s c u s s i o n : (i)  (ii) 8.  How w e l l do photo-models agree w i t h those t h e o r e t i c a l models? Ground stereograms  100  TEST OF PHOTO-INTERPRETATION AND FIELD DATA A n a l y s i s o f photo-mensuration multiple regression (i)  (ii)  (iii)  98  PHOTO-MENSURATION RESULTS AGAINST 102  d a t a and f i e l d d a t a by simple  and' 102  Crown width/diameter a t b r e a s t h e i g h t and t o t a l h e i g h t / crown w i d t h r a t i o from ground d a t a  104.  T o t a l height/crown w i d t h r a t i o from p h o t o - d a t a and h e i g h t / a v e r a g e crown w i d t h r a t i o from photo-data  105  B a s a l a r e a , a d j u s t e d b a s a l a r e a , crown c l o s u r e ,  average  crowding  f a c t o r and A d j u s t e d crowding f a c t o r 9.  106  DISCUSSION  14-8  Results of a n a l y s i s : (i)  Crown width/diameter a t b r e a s t h e i g h t r a t i o  (ii)  Height/crown w i d t h r a t i o , , from ground-data  148 14-8 150  ( i i i ) Height/crown w i d t h and average h e i g h t / a v e r a g e crown w i d t h r a t i o s from p h o t o - d a t a ..." (iv)  (v)  (vi)  10.  151  How w e l l were h e i g h t , crown w i d t h and crown c l o s u r e a c t u a l l y measured on the a e r i a l photographs? .  153  To what e x t e n t i s height/crown w i d t h r a t i o a f f e c t e d by crown c l o s u r e , age, s i t e i n d e x b a s a l a r e a and crowding factor?  154-  How w e l l can height/crown w i d t h r a t i o s measure s t o c k i n g and d e n s i t y o f stands?  155  CONCLUSION  163  BIBLIOGRAPHY  165  APPENDIX 1.  APPENDIX 2.  T h e o r e t i c a l models o f v a r i o u s s t a n d d e n s i t i e s d i f f e r e n t degree o f s t o c k i n g , w i t h t a b u l a t e d d e s c r i p t i v e d a t a on each model .  and  Models o f crown c l o s u r e o f each l o c a t i o n sampled, t a b u l a t e d d e s c r i p t i v e d a t a on each model  176 with 179  APPENDIX 3.  Ground Stereograms  233  APPENDIX 4-.  Mosaic  235  vi. LIST OF TABLES PAGE 1.  Volume ( c u . f t . )  l o g g e d i n B.C.  i n 1964  2.  Volume ( c u . f t . )  l o g g e d i n B.C.  i n 1965  3.  2 . . .  2  D e s i r e d s p e c i e s i n o r d e r o f p r e f e r e n c e c l a s s i f i e d by p r i n c i p a l f o r e s t products  3  4.  The crown a n g l e s and i t s  5.  Crown w i d t h r e s u l t s by t h r e e i n t e r p r e t e r s on 200 and 300 f e e t f l y i n g h e i g h t , and 1:20,000 RF photographs  20  6.  Grown w i d t h r e s u l t s of f o u r b e s t o p e r a t o r s  21  7.  Crown c l o s u r e r e s u l t s by t h r e e o p e r a t o r s on 200 and 300 f e e t f l y i n g h e i g h t , and 1:20,000 RF photographs  24  8.  Crown c l o s u r e r e s u l t s o f f o u r b e s t o p e r a t o r s  25  9.  Height r e s u l t s by t h o s e o p e r a t o r s on 200 and 300 f e e t h e i g h t , and 1:20,000 RF photographs  10.  Height r e s u l t s o f f o u r b e s t o p e r a t o r s  11.  D e n s i t y by v a r i o u s measures o f t h r e e c o n t r a s t i n g Douglas stands a f t e r t h i n n i n g  12.  Simple c o r r e l a t i o n c o e f f i c i e n t (r) and c o e f f i c i e n t o f d e t e r m i n a t i o n (r^) f o r crovm w i d t h on DBH and h e i g h t of f o r e s t and open-grown stands  13.  changes w i t h r e g a r d t o age  12  flying  Simple c o r r e l a t i o n c o e f f i c i e n t s and c o e f f i c i e n t s o f d e t e r m i n a t i o n percentage between X14 (Ht/CW,G), X15(CW/D), X45(Ht/CW,P) and X46(Av.Ht/Av.CW,P) on a l l t h e o t h e r independent v a r i a b l e s .  15.  Simple c o r r e l a t i o n c o e f f i c i e n t s and c o e f f i c i e n t s of d e t e r m i n a t i o n percentages between X l 6 , X19, X21, X73 and X74 on a l l the o t h e r independent v a r i a b l e s . . . . .  16.  34 fir  Mean, s t a n d a r d d e v i a t i o n , c o e f f i c i e n t o f v a r i a t i o n p e r c e n t (CV %), minimum and maximum f o r a l l v a r i a b l e s o f western hemlock  14.  33  51  52  107 108  109  Simple l i n e a r r e g r e s s i o n e q u a t i o n s , w i t h c o r r e l a t i o n c o e f f i c i e n t , s t a n d a r d e r r o r and degree of freedom on v a r i o u s independent v a r i a b l e s by t h e dependent v a r i a b l e s X 1 5 , X 1 4 , X 4 5 , X 4 6 , X16, X21 and X19 110  vii. 17.  18.  19.  20.  21.  22.  23.  24.  25.  26.  V a r i a n c e r a t i o v a l u e s o f independent v a r i a b l e s a t each stage i n t h e stepwise r e g r e s s i o n a n a l y s i s f o r f o u r t e e n v a r i a b l e e q u a t i o n and f o r t h r e e s e l e c t e d v a r i a b l e s f o r a l l combinations are a l s o g i v e n f o r dependent v a r i a b l e X15(CW/D)  Ill  V a r i a n c e r a t i o v a l u e s o f independent v a r i a b l e s a t each stage i n the stepwise r e g r e s s i o n a n a l y s i s f o r fourteen v a r i a b l e e q u a t i o n and f o r t h r e e s e l e c t e d v a r i a b l e s f o r a l l combinations are a l s o g i v e n f o r dependent v a r i a b l e XL4(Ht/CW,G)  112  V a r i a n c e r a t i o v a l u e s o f independent v a r i a b l e s a t each stage i n t h e stepwise r e g r e s s i o n a n a l y s i s f o r f o u r t e e n v a r i a b l e e q u a t i o n and f o r t h r e e s e l e c t e d v a r i a b l e s for:.: a l l combinations a r e a l s o g i v e n f o r dependent v a r i a b l e X45(Ht/CW,P)  113  V a r i a n c e r a t i o v a l u e s o f independent v a r i a b l e s a t each s t a g e o f t h e stepwise r e g r e s s i o n a n a l y s i s f o r f o u r t e e n v a r i a b l e e q u a t i o n and f o r t h r e e s e l e c t e d v a r i a b l e s f o r a l l combinations are a l s o g i v e n f o r dependent v a r i a b l e X46(Av.Ht/Av,CW,P)  114  V a r i a n c e r a t i o v a l u e s o f independent v a r i a b l e s a t each s t a g e o f t h e s t e p w i s e r e g r e s s i o n a n a l y s i s f o r seventeen v a r i a b l e e q u a t i o n and f o r t h r e e s e l e c t e d v a r i a b l e s f o r a l l combinations are a l s o g i v e n f o r dependent v a r i a b l e Xl6(BA,10) p h o t o - d a t a . . .  115  V a r i a n c e r a t i o v a l u e s o f independent v a r i a b l e s a t each s t a g e o f the s t e p w i s e r e g r e s s i o n a n a l y s i s f o r s i x t e e n v a r i a b l e e q u a t i o n and f o r t h r e e s e l e c t e d v a r i a b l e s f o r a l l combinations are a l s o g i v e n f o r dependent v a r i a b l e X l 6 ( B A , l 0 ) ground-data. . .  116  V a r i a n c e r a t i o v a l u e s o f independent v a r i a b l e s a t o f t h e stepwise r e g r e s s i o n a n a l y s i s f o r seventeen e q u a t i o n and f o r t h r e e s e l e c t e d v a r i a b l e s f o r a l l are a l s o g i v e n f o r dependent v a r i a b l e X 2 l ( A d j . B A )  117  each s t a g e variable combinations photo-data. . .  V a r i a n c e r a t i o v a l u e s o f independent v a r i a b l e s a t each s t a g e of the stepwise r e g r e s s i o n a n a l y s i s f o r f i f t e e n v a r i a b l e e q u a t i o n and f o r t h e t h r e e s e l e c t e d v a r i a b l e s f o r a l l combinations are a l s o g i v e n f o r dependent v a r i a b l e X 2 l ( A d j . B A ) ground-data . .  118  V a r i a n c e r a t i o v a l u e s o f independent v a r i a b l e s a t each stage of the stepwise r e g r e s s i o n a n a l y s i s f o r seventeen v a r i a b l e e q u a t i o n and f o r t h r e e s e l e c t e d v a r i a b l e s f o r a l l combinations a r e a l s o g i v e n f o r dependent v a r i a b l e X73(CF) p h o t o - d a t a . . . .  119  V a r i a n c e r a t i o v a l u e s o f independent v a r i a b l e s a t each stage o f t h e stepwise r e g r e s s i o n a n a l y s i s f o r s i x t e e n v a r i a b l e e q u a t i o n and f o r t h r e e s e l e c t e d v a r i a b l e s f o r a l l combinations are a l s o g i v e n f o r dependent v a r i a b l e X73(CF) ground-data . . . .  120  viii.  27.  28.  29.  30.  31.  32.  33.  V a r i a n c e r a t i o v a l u e s of independent v a r i a b l e s a t each stage o f the stepwise r e g r e s s i o n a n a l y s i s f o r seventeen v a r i a b l e e q u a t i o n and f o r t h r e e s e l e c t e d v a r i a b l e s f o r a l l combinations a r e a l s o g i v e n f o r dependent v a r i a b l e X74(Adj.CF) photo-data  121  V a r i a n c e r a t i o v a l u e s o f independent v a r i a b l e s a t each stage o f the s t e p w i s e r e g r e s s i o n a n a l y s i s f o r s i x t e e n v a r i a b l e s e q u a t i o n and f o r t h r e e s e l e c t e d v a r i a b l e s f o r a l l combinations are a l s o g i v e n f o r dependent v a r i a b l e X74(Adj.CF) ground-data  122  V a r i a n c e r a t i o v a l u e s o f independent v a r i a b l e s a t each stage o f t h e stepwise r e g r e s s i o n a n a l y s i s f o r e i g h t e e n v a r i a b l e e q u a t i o n and f o r the t h r e e s e l e c t e d v a r i a b l e s f o r a l l combinations a r e a l s o g i v e n f o r dependent v a r i a b l e X19(CC,P) photo-data  123  V a r i a n c e r a t i o v a l u e s o f independent v a r i a b l e s a t each stage o f the s t e p w i s e r e g r e s s i o n a n a l y s i s f o r seventeen v a r i a b l e e q u a t i o n and f o r t h r e e s e l e c t e d v a r i a b l e s f o r a l l combinations a r e a l s o g i v e n f o r the dependent v a r i a b l e X19(CC,P) ground-data  124  Regression equations of the three v a r i a b l e s s e l e c t e d f o r a l l combinations f o r v a r i o u s dependent v a r i a b l e s  125  C o r r e l a t i o n c o e f f i c i e n t s (R), c o e f f i c i e n t s o f d e t e r m i n a t i o n (R ) p e r c e n t a g e s and s t a n d a r d e r r o r o f e s t i m a t e f o r a l l e q u a t i o n s i n the stepwise r e g r e s s i o n a n a l y s i s o f X14> X15> X45 and X46 . . . .  126  C o r r e l a t i o n c o e f f i c i e n t s (R), c o e f f i c i e n t s o f d e t e r m i n a t i o n (R ) percentages and standard e r r o r o f e s t i m a t e f o r a l l equations i n the stepwise r e g r e s s i o n a n a l y s i s of X l 6 p , X l 6 g , X74p» X74g . . . .  127  2  34.  C o r r e l a t i o n c o e f f i c i e n t s (R) c o e f f i c i e n t s of d e t e r m i n a t i o n (R ) p e r c e n t a g e s and s t a n d a r d e r r o r o f e s t i m a t e f o r a l l e q u a t i o n s i n t h e stepwise r e g r e s s i o n a n a l y s i s o f X73p» X73g, X21p, X21g . . . .  128  2  35.  36.  37.  38.  C o r r e l a t i o n c o e f f i c i e n t s (R), c o e f f i c i e n t s o f d e t e r m i n a t i o n (R ) p e r c e n t a g e s and s t a n d a r d e r r o r o f e s t i m a t e f o r a l l equations i n t h e stepwise r e g r e s s i o n a n a l y s i s o f X19p, X19g  129  M u l t i p l e r e g r e s s i o n of dependent v a r i a b l e s X14(Ht/CW,G), X15(CW/D), X45(Ht/CW,P), and X46(Av.Ht/Av.CW,P) on t h e independent v a r i a b l e s t h a t made up t h e i r r a t i o s . And t h e i r mean, s t a n d a r d d e v i a t i o n and s t a n d a r d e r r o r o f estimate of h e i g h t , crown w i d t h and crown c l o s u r e from ground and photo d a t a  130  Mean, s t a n d a r d d e v i a t i o n and s t a n d a r d e r r o r of mean of h e i g h t , crown w i d t h and crown c l o s u r e from ground and photo d a t a  154  The q u a n t i t a t i v e v a l u e s s e c u r e d from F i g u r e s 1 6 t o 27 by the e i g h t assumptions and t h e i r means  160  ix. LIST OF FIGURES PAGE 1.  P r o s p e c t o f t h e Canadian f o r e s t i n d u s t r y t o 1980 v a l u e o f p r o d u c t i o n i n m i l l i o n s o f c o n s t a n t 1955 d o l l a r s  2.  The growth o f B r i t i s h C o l u m b i a ' s p u l p and paper industry  33.  6  (1950-1976)  7  Angle o f t h e sun and shadow l e n g t h  4.  Measurement o f shadow l e n g t h  5.  Illustrations  of effectiveness  61 62  o f shadow l e n g t h  measurement 6. 7.  8.  f l o a t i n g dot  64  Diagrams showing n e g a t i v e b i a s based on RF 1:16,000 photographs due t o l i m i t a t i o n i n r e s o l v i n g power o f photographs  65  'Loss o f h e i g h t ' on v e r t i c a l  9.  63  Measurement by p a r a l l a x b a r and e x p l a n a t i o n o f t h e  due t o i m p e r f e c t r e g i s t e r o f t r e e image  photographs  65  Diagrams o f p a r a l l a x wedge measurement and t h e i n f l u e n c e o f r e s o l v i n g power o f photographs  10.  67  Diagrams o f micrometer and d o t wedge measurement o f crown width  70  11.  H e l i c o p t e r stereogram (350 f e e t f l y i n g h e i g h t , Douglas f i r ) .  12.  H e l i c o p t e r stereogram (350 f e e t f l y i n g h e i g h t ,  .  lodgepole  pine)  71  13.  The d i f f e r e n c e s o f photo base on ground stereograms  14.  The r e l a t i o n s h i p o f h e i g h t t o crown w i d t h o f western  101  hemlock 15.  71  134  The r e l a t i o n s h i p o f crown w i d t h t o diameter a t b r e a s t height  135  16.  The r e l a t i o n s h i p o f crown w i d t h / d i a m e t e r o f b r e a s t  height  17.  r a t i o t o crowding f a c t o r and a d j u s t e d crowding f a c t o r . . . . The r e l a t i o n s h i p o f height/crown w i d t h r a t i o t o crowding  136  f a c t o r and a d j u s t e d crowding f a c t o r  137  X.  18.  19.  20.  The r e l a t i o n s h i p o f height/crown w i d t h r a t i o t o crown w i d t h / diameter a t breast height r a t i o  138  The r e l a t i o n s h i p o f height/crown w i d t h r a t i o t o b a s a l and a d j u s t e d b a s a l a r e a  139  area  The r e l a t i o n s h i p o f height/crown w i d t h r a t i o t o crown closure  14-0  21.  The r e l a t i o n s h i p  22.  The r e l a t i o n s h i p o f b a s a l a r e a and a d j u s t e d b a s a l a r e a t o crowding f a c t o r and a d j u s t e d crowding f a c t o r  142  23.  The r e l a t i o n s h i p o f crown w i d t h / d i a m e t e r a t b r e a s t r a t i o t o b a s a l a r e a and a d j u s t e d b a s a l a r e a  height 143  The r e l a t i o n s h i p  height  24.  o f height/crown w i d t h r a t i o t o age  o f crown width/diameter a t b r e a s t  141  r a t i o t o age 25.  The r e l a t i o n s h i p  144 o f b a s a l a r e a and a d j u s t e d b a s a l a r e a t o  crown c l o s u r e 26.  27.  28.  The r e l a t i o n s h i p stems p e r a c r e  145 o f crown c l o s u r e from a e r i a l photographs t o 146  The r e l a t i o n s h i p o f crovm c l o s u r e from a e r i a l photographs t o crowding f a c t o r and a d j u s t e d crowding f a c t o r  147  The b a s i c crown w i d t h / d i a m e t e r a t b r e a s t h e i g h t and h e i g h t / crown w i d t h r a t i o s b e i n g a c h i e v e d by v a r y i n g the d.b.h. crovm w i d t h and h e i g h t o f t r e e s  161  xi.  ACKNOWLEDGEMENTS The w r i t e r wishes t o express h i s s i n c e r e a p p r e c i a t i o n t o the U n i v e r s i t y assistantships,  o f B r i t i s h Columbia f o r t h e g r a n t i n g o f t h e t e a c h i n g t o Mr. J . R .  Osborn f o r h i s a s s i s t a n c e i n c o l l e c t i n g  the f i e l d d a t a and r e v i e w i n g the m a n u s c r i p t s , and t o M r . J .  Walters,  D i r e c t o r o f t h e U n i v e r s i t y Research F o r e s t f o r h e l p i n g i n t h e c o l l e c t i o n of f i e l d data. Forestry,  University  Thanks a r e a l s o due t o the F a c u l t y o f  of B r i t i s h Columbia, e s p e c i a l l y t o D r . J . H . G .  Smith f o r h i s g u i d a n c e , a d v i c e and encouragement, t o D r . A. Kozak and Mr. D.D. Munro f o r t h e i r a s s i s t a n c e i n a n a l y s i s and i n t e r p r e t a t i o n o f t h e d a t a and t o M r s . F r o e s e f o r d a t a p r o c e s s i n g .  And f i n a l l y t h e  r e s e a r c h a s s i s t a n t s h i p o f f e r e d by Cominco and N a t i o n a l Research C o u n c i l d u r i n g t h e summer o f 1966 a r e g r a t e f u l l y  acknowledged.  INTRODUCTION Western hemlock (Tsuga h e t e r o p h y l l a  (Ref.) Sarg.)  is  c o n s i d e r e d as one o f the most i m p o r t a n t s p e c i e s b e s i d e s Douglas (Psendotsuea m e n z i e s i i (Mirb*) F r a n c o ) , p l i c a t a Donn) i n B r i t i s h C o l u m b i a .  and w e s t e r n r e d cedar  The merchantable volume  w i t h dbh o f 10 i n c h e s and over) f o r each o f the above t h r e e i s 12,14.0.9 m i l l i o n c u b i c f e e t f o r Douglas f i r ,  fir  (Thuja.  (trees species  18,061.6 m i l l i o n cubic  f e e t f o r western hemlock, 3 7 , 3 6 9 . 8 m i l l i o n c u b i c f e e t f o r western  red  cedar and 1 0 2 , 1 7 1 . 0 m i l l i o n c u b i c f e e t f o r a l l o t h e r s p e c i e s  thus  g i v i n g a t o t a l o f 169,743.3 m i l l i o n c u b i c f e e t .  forests  c o n t a i n about 54.6 b i l l i o n c u b i c f e e t f o r e s t s about 115 b i l l i o n c u b i c f e e t volume ( B . C .  The c o a s t a l  (32.2 p e r cent) and t h e (67.8 p e r c e n t ) o f the  interior  total  Government News J u l y 1 9 6 6 ) .  In t h e U n i v e r s i t y o f B r i t i s h  Columbia Research F o r e s t  growth western hemlock c o n s t i t u t e s t h e second l a r g e s t volume, l e s s than cedar.  In second growth, western hemlock has the  volume ( U . B . C . Research F o r e s t 1948-1958). s i d e from 400-1,500 f e e t e l e v a t i o n ,  old  one-third  largest  However on t h e south west  2,000 a c r e s o f pure and mixed second  growth o f w e s t e r n r e d c e d a r , western hemlock and Douglas f i r were f o u n d . Douglas f i r was found t o account f o r n e a r l y t w o - t h i r d o f the volume (Walters e t a l . 1 9 6 1 ) .  total  W a l t e r s a g a i n r e p o r t e d i n 1964 t h a t  w e s t e r n hemlock was the most important timber p r o d u c e r among the f o u r s p e c i e s o f hemlocks and ranks o n l y second t o Douglas f i r a t Research  U.B.C.  forest. Smith e_. a l .  America's Future  (1961)  c i t e d from the .Timber Resources  for  ( U n i t e d S t a t e s F o r e s t S e r v i c e 1958) p r e d i c t i o n t h a t  t h e demand f o r softwood:! imports would be 1.5 b i l l i o n c u b i c f e e t  in  2. 1975 and i n t h e y e a r 2000 w i l l be 1.6 b i l l i o n c u b i c f e e t .  The p r o s p e c t s  f o r Canadian f o r e s t i n d u s t r y as a whole are shown by D a v i s e t r e p r o d u c e d i n f i g u r e 1. in total  al.(1957)  The u t i l i z a t i o n f a c t o r s were s l i g h t l y  c u b i c f e e t volume f o r Douglas f i r  w e s t e r n r e d c e d a r o f t h e same d i a m e t e r .  higher  t h a n western hemlock o r  T h i s may be due t o t h e  difference  i n t o t a l h e i g h t a t the same age (Smith et. a l . 1 9 6 1 ) . The volume l o g g e d f o r t h e t h r e e  s p e c i e s i n B r i t i s h Columbia  are shown i n t a b l e s 1 and 2 . T a b l e 1 - Volume ( c u . f t . ) l o g g e d i n B.C. Location Species  Vancouver Forest D i s t r i c t Volume  A l l other  %  i n 1964*  areas  %  Volume  %  Total  B.C.  Volume  %  %  F  201,097,137  27.5  49.9  201,398,902  28.7  50.1  402,496,039  26.6  H  234,306,181  33.2  72.9  90,234,499  11.5  27.1  333,540,680  22.0  C  154,338,241  21.1  78.0  51,555,472  6.6  25.0  205,893,713  13.6  Others  133,421,509  18.2  23.3  439,243,235  56,2  76.7  572,664,744  37.8  Total  732,163,068  100  48.3  782,432,108  100  51.7  » B . G . F . S ..  Species  100  (1965) T a b l e 2 - Volume ( c u . f t . ) l o g g e d i n  Location  1,514,595,176  Vancouver Forest D i s t r i c t Volume  %  A l l other  %  Volume  B.C. i n 1965* areas  %  Total  %  B.C.  Volume  %  F  204,380,501.. 27.3  53.8  175,347,465  22.3  46.2  379,728,488  24.8  H  300,364,680  40.1  87.6  43,350,653  5.5  12.4  342,715,333  22.4  C  169,735,188  22.7  82.9  35,013,920  4.5  17.1  204,749,108  13.4  12.2  531,073,211  67.7  87.8  605,929,865  33.4  48.8  784,785,249  100  51.2 1,533,112,794  Others Total *B.C.F.S.  73,847,176 748,327,545 (1966)  9.9 100,  100  3. From t h e above two t a b l e s i t  can be seen t h a t the t o t a l volume l o g g e d  f o r B r i t i s h Columbia has i n c r e a s e d , but the Douglas f i r  total  has  d e c r e a s e d w h i l e the western hemlock volume i n c r e a s e d by 9,174,653 c u b i c feet. fir  T h i s t r e n d w i l l most p r o b a b l y c o n t i n u e as t h e volume o f Douglas  decreases.  Thus western hemlock w i l l i n f u t u r e be a v e r y  important  species. The importance o f western hemlock can a g a i n be seen from t h e t a b l e below showing t h e i m p o r t a n t use o f t i m b e r i n Canada by d e s i r a b l e species. Table 3 - Desired Species i n order of preference by p r i n c i p a l f o r e s t p r o d u c t s * Product  classified  Species  Lumber  Douglas f i r , western hemlock, r e d c e d a r , balsam  Plywood  Douglas f i r , w e s t e r n hemlock, balsam, b l a c k cottonwood.  Laminated  timbers  Douglas f i r ,  western  western  hemlock.  Pulp-Sulphite  Western hemlock, b a l s a m .  Pulp-Sulphate  Western hemlock, balsam, Douglas western red cedar.  Pulp-Sulphite-dissolving  Western hemlock, b a l s a m .  Newsprint  Western hemlock, balsam.  *Ker et  fir,  al.(i960)  The expansion o f t h e p u l p and paper i n d u s t r y w i l l d e f i n i t e l y g i v e importance t o western hemlock as a s p e c i e s . paper i n d u s t r y w i l l c e r t a i n l y Paper I n d u s t r y i n B r i t i s h  The growth o f t h e p u l p and  take p l a c e as r e p o r t e d i n t h e " P u l p  Columbia" (1966).  further  and  F i g u r e 2 w i l l show the  past,  4-. p r e s e n t and f u t u r e t r e n d s o f p u l p and paper i n d u s t r y i n  British  Columbia. S i n c e t h e f u t u r e demand o f western hemlock l o o k s v e r y p r o m i s i n g , t h e s t u d y o f stand d e n s i t y and s t o c k i n g w i l l f a c i l i t a t e o f hemlock s t a n d s .  b e t t e r management  The u s e o f a e r i a l photographs t o a c h i e v e t h i s purpose  i s being studied i n t h i s t h e s i s .  A e r i a l photographs have been used f o r  many y e a r s t o supplement f i e l d survey c h i e f l y i n c l a s s i f i c a t i o n and mapping.  In r e c e n t y e a r s l a r g e s c a l e  ( 1 : 1 , 2 0 0 RF)  photographs and  h e l i c o p t e r stereograms are a l s o b e i n g used f o r f o r e s t r y purposes i n Canada and t h e U n i t e d S t a t e s .  The usage o f l a r g e s c a l e photographs w i l l  be c o n f i n e d t o c o u n t r i e s w i t h l a r g e f o r e s t e d a r e a s ,  especially in a  c o u n t r y where f o r e s t management and wood u t i l i z a t i o n a r e w e l l advanced, and where the f o r e s t r e s o u r c e c o n t r i b u t e s i n l a r g e measures t o the industry.  country's  A e r i a l photographs can be used as a t o o l t o p r o v i d e more r e f i n e d  degree o f knowledge about the r e s o u r c e s . The p r e s e n t t r e n d s o f stand d e n s i t y and s t o c k i n g e v a l u a t i o n based on v a r i a b l e s measurable from a e r i a l photographs e . g .  are  direct  e s t i m a t i o n o f crown w i d t h , h e i g h t and crown c l o s u r e and i n d i r e c t l y d b h , b a s a l a r e a and number o f t r e e s can a l s o be c a l c u l a t e d .  This w i l l  provide  f a s t e r and cheaper ways t o a s s e s s t h e degree o f growing s t o c k w i t h i n stand or forested areas. can be used e f f e c t i v e l y ,  However,  b e f o r e t h e s e r a t i o s o f CW/D and H/GW  a b a s i c understanding of the b i o l o g i c a l aspect of  f o r e s t stands must be d e v e l o p e d . this  any  This aspect i s also discussed b r i e f l y  in  thesis. The use o f a e r i a l photographs t o a s s e s s the v a s t t i m b e r r e s o u r c e s  i n B r i t i s h Columbia i s v e r y i m p o r t a n t because o f l a r g e i n a c c e s s i b l e  forested  5. areas.  Photo e s t i m a t i o n i s n o t o n l y cheaper and f a s t e r but i t may a l s o  be as a c c u r a t e as c o n v e n t i o n a l ground measurements.  However,  ground  check w i l l always be needed t o ensure a c c u r a t e p h o t o - i n t e r p r e t a t i o n and measurements.  The aim o f t h i s t h e s i s i s t o l a y out an approach w h i c h  can be used e f f e c t i v e l y  t o measure stand d e n s i t y and s t o c k i n g and a l s o  t o f i n d out how a c c u r a t e l y  a e r i a l photo-measurements can be o b t a i n e d w i t h  t h e c o n t r o l o f ground measurements.  6 Figure  1 . Prospects o f the Canadian f o r e s t i n d u s t r y to 1980. Value of production i n m i l l i o n s o f constant 1 9 5 5 d o l l a r s . (Davis e t , a l . 1 9 5 7 )  2800H  4001 1950  YEAR  I960  7  MILLIONS OF SHORT TONS 10  /  /  /  / (1)  /  /  / / /f  /  /  / / (2)  _  1950  -  58  54 TOTAL  (I)  PULP  ESTIMATED ( )  NEWSPRINT-  2  ESTIMATED CAPACITY  Figure  2.  62  74  70  66  YEAR PRODUCTION RATED  PULP  AND  PAPER  RATED  CAPACITY PRODUCTION  NEWSPRINT  AND  PAPER  The growth o f B r i t i s h Columbia's pulp and paper i n d u s t r y . ( 1950-1976 ) (The pulp and paper i n d u s t r y o f B r i t i s h Columbia, Oct. 1966.)  8. 2.  WESTERN HEMLOCK AS A SPECIES AND ITS (a)  Its  CHARACTERISTICS  Distribution The t h r e e most i m p o r t a n t c o n i f e r s p e c i e s i n  Columbia a r e Douglas f i r , cedar.  British  western hemlock and western r e d  As a whole, t h e s e t h r e e s p e c i e s a r e w e l l d i s t r i b u t e d  n a t u r a l l y throughout most o f t h e p r o d u c t i v e f o r e s t areas Vancouver F o r e s t  of  District.  Western hemlock o c c u r s throughout t h e wet b e l t of c o a s t a l and i n t e r i o r o f B r i t i s h C o l u m b i a .  On t h e c o a s t  it  grows up t o 2,600 f e e t above s e a l e v e l b u t as h i g h as 5,000 f e e t i n the i n t e r i o r .  The b e s t growth i s found where t h e  soil  i s deep and porous b u t hemlock a l s o grows on m o i s t s h a l l o w w i t h a l o t o f humus.  soil  U s u a l l y hemlock i s found i n m o i s t c o o l  s i t e s and a l s o on r o t t e n wood (Smith e t , a l . I 9 6 l ) .  It  a l s o grows  w e l l i n pure as w e l l as mixed stands o f Douglas f i r and w e s t e r n red cedar. Eis  (1962), who s t a t i s t i c a l l y  analysed f o r e s t  habitats  and t r e e growth, c o n c l u d e d t h a t western hemlock and cedar  stands  were f o u n d on w e t t e r s i t e s up t o 2,600 f e e t above sea l e v e l  and  mixed w e s t e r n hemlock and balsam stands were l i m i t e d t o h i g h e r altitudes.  Western hemlock, w e s t e r n r e d cedar and Douglas  s t a n d s H e r e found on d r i e r s i t e s up t o 2,600 f e e t .  The r e p l a c i n g  o f o t h e r stands by second growth hemlock i s f r e q u e n t l y Hemlock a l s o i n c r e a s e s w i t h d e n s i t y as i t  fir  seen.  i s a tolerant  species  and w i l l n o t e a s i l y d i e out i n c o m p e t i t i o n and under s u p p r e s s i o n . (b)  Its  Growth The r a t e o f growth w i t h i n and among i n d i v i d u a l  trees  o r i n stands i s h i g h l y v a r i a b l e .  The growth o f f o r e s t t r e e s  is  m a i n l y dependent upon age, s i t e i n d e x , s p e c i e s , number and d i s t r i b u t i o n o f t r e e s w i t h i n any g i v e n u n i t Growth i s a r e l a t i v e measurej i t tree i n r e l a t i o n to i t s neighbours.  area. i s t h e growth o f one  Thus t h e s i z e o f t r e e t o be  grown depends upon t h e judgement o f t h e management o f t h e Individual  forest.  t r e e s a r e permanent w i t h r e s p e c t t o t h e i r p o i n t o f  germination or planting therefore consideration of s i t e i s i m p o r t a n t t o f u t u r e growth.  D i f f e r e n t s p e c i e s have  very  different  r a t e s o f growth e . g . Douglas f i r grows f a s t e r than western hemlock o f t h e same age and s i t e q u a l i t y , height.  it  i s b i g g e r i n diameter and i n  The number and d i s t r i b u t i o n o f t r e e s i n a stand are  c l o s e l y a s s o c i a t e d w i t h r a t e o f growth.  T h i s i s because  also  trees  growing i n t h e open w i l l r e c e i v e more s u n l i g h t and t h e y have a b i g g e r crown s u r f a c e  (crowns almost r e a c h t h e g r o u n d ) .  This  is  n o t o n l y t r u e f o r d i a m e t e r a t b r e a s t h e i g h t growth but a l s o h e i g h t growth as the h e i g h t i s u s u a l l y t a l l e r i n comparison w i t h f o r e s t - g r o w n t r e e s . density,  for  f o r the same dbh  Trees growing i n  different  e . g . open, open-normal, n o r m a l , and dense stand d e n s i t y ,  a l s o have d i f f e r e n t r a t e s o f growth.  T h e i r r a t e o f growth d e c r e a s e s  from open t o normal and i s l e a s t i n a dense stand because t h e are so c l o s e t h a t o n l y t h e t o p p a r t o f t h e crowns are sunlight.  trees  receiving  In t h e dense stands m o r t a l i t y i s a l s o h i g h e r t h u s  r e d u c i n g t h e stand back t o n o r m a l i t y as t h e age i n c r e a s e s .  On t h e  o t h e r hand, open t r e e s c o n t i n u e t o grow and t h e y tend t o p r o c e e d towards normal d e n s i t y i f  the stand i s s u f f i c i e n t l y s t o c k e d .  10. The growth o f western hemlock and spruce was found t o be 2^ c o r d s p e r a c r e i n t h e P a c i f i c  Northwest  ( B r i e g l e b 194-0).  Square s p a c i n g d i s t a n c e o r GW//D r a t i o may be used t o c o n t r o l r a t e o f Douglas f i r  growth  and western hemlock from open t o normal stand  c o n d i t i o n s (Smith et. a l . 1 9 6 0 ) . r a p i d growth and i n f u l l y  The b e s t s i t e s w i l l p r o v i d e  stocked stands the most v i g o r o u s  very trees  w i l l be t w i c e as b i g as the average w h i l e the l e a s t v i g o r o u s o n e - h a l f o f average f o r b o t h s p e c i e s .  Maximum r a t e o f growth  o b t a i n e d when the r a t i o o f 6W/D i s 2.0 o r more.  Smith  of  and concluded t h a t s u p e r i o r s e e d l i n g s p l a n t e d on t h e  most a c c e s s i b l e s i t e s w i t h w i d e r  s p a c i n g would p r o v i d e  faster  growth and t h i s would y i e l d optimum economic b e n e f i t s . (1964)  Walters  r e p o r t e d t h a t f a s t growth r a t e o f western hemlock was  a c h i e v e d on s i t e s c o n s i d e r e d good f o r Douglas f i r .  The h i g h e s t  annual h e i g h t growth was found when s e e d l i n g s are grown on r o t t e n - w o o d .  entirely  Growth o f w e s t e r n hemlock i s a l s o s t i m u l a t e d by  a p p l i c a t i o n of organic Griffith  fertilizers.  (1959)  s t a t e d t h a t the h e i g h t growth o f  w e s t e r n hemlock s t a r t e d from f i r s t week o f May and t e r m i n a t e d t h e l a s t week o f September o r f i r s t week o f O c t o b e r . W a l t e r s and Soos  (1963)  among i n d i v i d u a l t r e e s .  at  However,  found t h a t t h e r a t e o f growth and d a t e s  o f b e g i n n i n g and ending o f growth a n n u a l l y to be h i g h l y  years.  is  (1963)  again discussed the use of wider spacing f o r b e t t e r y i e l d Douglas f i r  only  It  W a l t e r s et, a l . ( 1 9 6 1 )  i s also d i f f e r e n t with  variable  successive  s t u d i e d growth t o b r e a s t h e i g h t and  11.  found t h a t w e s t e r n hemlock was slower t h a n Douglas f i r .  It  t a k e s an average o f 6 . 4 y e a r s t o r e a c h b r e a s t h e i g h t on s i t e c l a s s 180, an average o f 8.6 y e a r s on s i t e c l a s s o f I4O, an average o f 1 0 . 6 y e a r s on s i t e c l a s s 9 0 .  Crown c l a s s  and also  influences years to reach breast height. F a c t o r s i n f l u e n c i n g the crown c h a r a c t e r i s t i c s o f w e s t e r n hemlock and f a c i l i t a t e  i t s i d e n t i f i c a t i o n on a e r i a l photographs  The most apparent d i f f e r e n c e o f t r e e  characteristics  from a e r i a l photographs i s the crown, and even on the ground t h i s also holds t r u e .  T h i s i s because t h e crown i s t h e l a r g e s t  component o f the t r e e , and i t d e n s i t y and s t o c k i n g , e t c .  changes w i t h age, s i t e i n d e x , s t a n d  Thus when i d e n t i f y i n g t r e e s p e c i e s  t h e i n f l u e n c e o f t h e s e f a c t o r s s h o u l d be c o n s i d e r e d w i t h  size,  shape, t o n e , t e x t u r e and shadow p a t t e r n . Age Age i s t h e most i m p o r t a n t f a c t o r t h a t i n f l u e n c e s t h e t r e e crown c h a r a c t e r i s t i c s .  V e r y young t r e e s have no  c h a r a c t e r i s t i c crown shape but as a t r e e grows o l d e r a t y p i c a l shape w i l l be formed.  Ronay (1961)  found t h a t t h i s takes  place  a t about 30-35 y e a r s f o r western hemlock growing i n dense s t a n d s . The upper and lower p o r t i o n s o f a crown changes q u i t e  differently.  The average a n g l e o f the upper p o r t i o n changes i s l i s t e d i n table  below:  the  12. T a b l e 4 - The crown a n g l e s and i t s changes w i t h r e g a r d t o age Years  Average Angle changes  Range o f A n g l e s  20  27  15-28  50  35  25-37  70  4-3  33-45  90  49  43-56  110  54  50-70  67  61-80  121 and above  Ronay a l s o r e p o r t e d t h a t t h e r e i s no s i g n i f i c a n t d i f f e r e n c e i n crown shape o f western hemlock t h a t c o u l d be attributed to differences i n  elevation.  Size Size i s a relative variable;  that i s , i t  can o n l y be used  t o r e f e r t o the s u r f a c e a r e a o c c u p i e d by one o b j e c t i n r e l a t i o n t o another.  The s i z e o f crown can s e r v e as a u s e f u l i n d i c a t i o n t o  s p e c i e s i d e n t i f i c a t i o n , e s p e c i a l l y on a e r i a l p h o t o g r a p h s . a v e r y weak c l u e as crown s i z e v a r i e s  so g r e a t l y ,  a r e d i s t i n c t d i f f e r e n t i a t i o n s between s p e c i e s , i t an a p p r o x i m a t i o n o f t h e s p e c i e s . factors i t  But i t  thus u n l e s s  is  there  can o n l y g i v e us  However, when combined w i t h o t h e r  i s very u s e f u l .  Shape The shape o f an o b j e c t i s i t s g e n e r a l o u t l i n e o r form on a p l a n e s u r f a c e o r on a s i n g l e a e r i a l p h o t o g r a p h .  A three dimension  view o f shape can be o b t a i n e d from a p a i r o f v e r t i c a l  aerial  13.  photographs by v i e w i n g under a s t e r e o s c o p e . i d e n t i f i c a t i o n as we can see i t s t h a t i s whether i t  is flat,  This greatly  o u t l i n e as w e l l as i t s  conic, triangular,  depth,  round o r o v a l ,  Shape a l o n e does n o t g i v e a d i s t i n c t c h a r a c t e r i s t i c but i f  helps  t o any  etc.  object  shape i s used i n r e l a t i o n to s i z e i t w i l l be more m e a n i n g f u l .  The shape o f crowns o f immature western hemlock i s t y p i c a l l y w i t h a narrow t o p .  conical  The shape and s i z e a l s o changes w i t h a g e .  It  becomes p y r a m i d a l when mature but tends t o b r o a d e n , becomes s h o r t e r and dome-shape w i t h i n c r e a s e o f age, and some a l s o become Western hemlock has a denser crown and i s narrower i n than t h a t o f Douglas  "feathery".  appearance  fir.  Tone Tone i s caused by t h e d i f f e r e n c e i n b r i l l i a n c e o f r e f l e c t e d from o b j e c t s .  On b l a c k and w h i t e photographs i t  as a range o f g r e y from n e a r w h i t e t o n e a r b l a c k .  light appears  Tone t h a t can be  u s e d f o r i d e n t i f i c a t i o n and o b s e r v a t i o n has s l i g h t v a r i a t i o n g i v e s c e r t a i n i n d i v i d u a l s a d i s t i n c t i v e tone i n a homogeneous g r o u p . variation.  It  that  relatively  T o t a l w h i t e and/or b l a c k w i l l show no t o n a l  i s known t h a t l i g h t e r c o l o u r e d o b j e c t s  r e f l e c t l i g h t b e t t e r than dark c o l o u r o b j e c t s .  generally  Since leaves  i n shades o f green and a l s o r e f l e c t d i f f e r e n t amounts o f  vary  light  depending on t h e a n g l e a t which the l e a v e s a r e a r r a n g e d on t h e  branches  and twigs t h e y c a n d i f f e r g r e a t l y i n t o n e .  within  V a r i a t i o n s i n tone  photographs a l s o a r e due t o t h e a n g l e o f view and amount o f shaded and s u n - l i t p o s i t i o n s o f t h e t r e e examined.  14 Tone i s f r e q u e n t l y u s e d t o i d e n t i f y f o r e s t  types;  d i s t i n c t l y d i f f e r e n t tones are a s s o c i a t e d w i t h c o n i f e r s and hardwoods. C o n i f e r s a r e d a r k e r due t o the presence o f " c o n t a i n e d shadow"  (this  i s the e f f e c t o f innumerable s m a l l shadows o f dents caused by numerous s m a l l l e a v e s o f a s u r f a c e , which a r e too s m a l l t o  register  i n d i v i d u a l l y because t h e y exceed the l i m i t o f r e s o l u t i o n ) .  Hardwoods  a r e l i g h t e r because the l e a v e s are much b i g g e r and u s u a l l y o v e r l a p p i n g , l e a v i n g few shadows and f o r m i n g a r e l a t i v e l y r e f l e c t s more l i g h t .  smooth s u r f a c e which  However, f o r i d e n t i f i c a t i o n o f s p e c i e s , t h e  i s never used a l o n e u n l e s s i t  is  c o n f u s e d w i t h any o t h e r s p e c i e s .  so d i s t i n c t t h a t i t  tone  cannot be  Otherwise t h e shape, s i z e ,  texture  and shadow a r e always c o n s i d e r e d t o g e t h e r . The d e c r e a s e o f s c a l e o f t h e photographs w i l l change t h e tone from d a r k e r t o l i g h t e r ,  from medium t o medium l i g h t i n young  western hemlock stands and from medium dark t o medium l i g h t on o l d growth.  Western hemlock and Douglas f i r have i n t e r m e d i a t e tone on  b l a c k and w h i t e photographs but u n f o r t u n a t e l y the ranges o f tones many c a s e s o v e r l a p .  T h i s may be e x p l a i n e d by t h e s p e c t r a l  in  analysis  which r e p o r t e d t h a t t h e d i f f e r e n c e s i n r e f l e c t i o n between the two s p e c i e s were o f t e n s m a l l e r than t h e d i f f e r e n c e s between two o f the same s p e c i e s ( H i n d l e y and Smith 1 9 5 7 ) .  Western hemlock i s  d a r k e r than western r e d cedar and l i g h t e r than amabiles f i r . u s u a l l y i s measured by comparison w i t h a tone  plants  Tone  scale.  Tone i s an i m p o r t a n t element i n p h o t o - i n t e r p r e t a t i o n but i t s r e l a t i o n and i n f l u e n c e by o t h e r f a c t o r s must n o t be d i s r e g a r d e d .  15. when tone i s used as a d i s t i n c t v a r i a b l e f o r  interpretation.  Texture T e x t u r e i s t h e f r e q u e n c y o f tone changes w i t h i n t h e image and i t  i s determined by s i z e ,  f e a t u r e s a c r o s s t h e image. appearance o f t h e s t a n d s . t e x t u r e appears f i n e .  shape, tone and d i s t r i b u t i o n o f  Shadow a l s o g r e a t l y a f f e c t s t h e If  textural  t h e components are r e l a t i v e l y  When t h e d e t a i l s o f f i n e n e s s  i n d i s t i n g u i s h a b l e t h e t e x t u r e i s termed smooth.  small,  are  G e n e r a l l y where  l a r g e d i f f e r e n c e s o f l i g h t and dark t o n e s a r e f r e q u e n t t h e on t h e a e r i a l photographs i s c o a r s e and r o u g h .  unit  texture  Fine texture  is  t y p i c a l o f f u l l y s t o c k e d young even-aged s t a n d s , but smooth t e x t u r e is  seldom found i n f o r e s t except on g r a s s l a n d s o r v e r y young  regeneration areas.  Coarse and rough t e x t u r e i s found i n mature and  old-growth s t a n d s .  The t e x t u r e o f a s i n g l e t r e e i s caused by c o l o u r ,  shape, age, s p a c i n g between the branches and w h o r l s , q u a n t i t y o f f o l i a g e and crown d e n s i t y .  The o l d e r a t r e e i s the l e s s e r w i l l be  i t s f o l i a g e , crown d e n s i t y and t h e w i d e r w i l l be t h e s p a c i n g o f branches and t h e more i r r e g u l a r t h e shape. The change o f s c a l e s w i l l a f f e c t t h e t e x t u r e o f young hemlock t o t h e same e x t e n t as t h a t o f young Douglas f i r .  So immature  hemlock i s n o t s i g n i f i c a n t l y d i f f e r e n t from any o t h e r immature s p e c i e s but mature hemlock has r e l a t i v e l y  r e g u l a r dense crown and appears  s l i g h t l y " h a z y " w h i l e old-growth i s r e l a t i v e l y f i n e r t h a n Douglas f i r .  coarse but  nevertheless  T h i s c o a r s e n e s s i s produced by the broadening  16. o f crown as i t  grows o l d e r .  "Feathery"  appearance i s a l s o shown by  over-mature hemlock d i f f e r i n g from t h e " c h u n k y " and " s p o k e d " o f o l d Douglas  feature  fir.  T e x t u r e w i l l denote t h e m a t u r i t y o r age and a t t h e same time a s s i s t i n t e r p r e t a t i o n . function of size,  It  must be r e a l i z e d t h a t t e x t u r e i s  shape and tone b e f o r e i t  can be used  a  effectively.  Shadow Image q u a l i t y o f a e r i a l photographs i s m o s t l y determined by t h e a n g u l a r r a y s from t h e s u n .  From t h e p a t t e r n o f shadows  c r e a t e d , t h e o b s e r v e r knows whether t h e o b j e c t s a r e l a r g e o r s m a l l , i n f o r m a t i o n which i s v e r y i m p o r t a n t i n q u a l i t a t i v e Tone, t e x t u r e ,  photo-interpretation.  and shape a r e c l o s e l y a s s o c i a t e d w i t h shadows.  Many o b j e c t s can be r e c o g n i z e d by t h e shadows t h e y (the o u t l i n e o r p r o f i l e o f i t s e l f ) . s i d e o f an i l l u m i n a t e d o b j e c t . crown f r e q u e n t l y f a c i l i t a t e s identify species.  east  Shadow a l s o appears on t h e o p p o s i t e  T h i s shadow on t h e shaded s i d e o f  identification.  the  Shadow can be u s e d t o  S i n c e c o n i f e r s and hardwoods have d i f f e r e n t l y  shaped crowns t h e y produce d i f f e r e n t t y p e s o f shadows on the shady s i d e and t h e y a l s o c a s t d i f f e r e n t shadows on t h e g r o u n d .  Even w i t h i n  c o n i f e r o r hardwood s p e c i e s groups some i n d i v i d u a l s p e c i e s can be r e c o g n i z e d from t h e i r  shadows.  Shadow w i l l o b s c u r e a l l t h e f e a t u r e s w i t h i n i t it.  So shadow can f a c i l i t a t e  interpretation. cast  as w e l l as i n h i b i t i d e n t i f i c a t i o n and  Immature hemlocks w i t h c o n i c a l shaped crowns w i l l  s i m i l a r shadows.  characteristic  o r shaded by  Mature and over-mature hemlocks show t h e  "rounding" of the p r o f i l e .  The shadow on t h e  all  17 u n i l l u m i n a t e d s i d e i s n o t so s h a r p l y d e f i n e d due t o l o n g and slender branches. Shadow has i t s d i s a d v a n t a g e s but i t s p e c i e s i d e n t i f i c a t i o n and g e n e r a l u t i l i t y  also contributes  to  of the photographs.  Many o f the f a c t o r s d i s c u s s e d above f o r western hemlock are o v e r l a p p i n g w i t h t h e o t h e r s p e c i e s , e s p e c i a l l y Douglas T h i s makes i t  h a r d t o i d e n t i f y w e s t e r n hemlock on the  photographs.  However,  fir.  aerial  i d e n t i f i c a t i o n i s p o s s i b l e with experience  i n t h e f o r e s t c o n d i t i o n s and i n s p e c i e s t o be i d e n t i f i e d .  18. REVIEW OF LITERATURE A. (a)  The a c c u r a c y and p r e c i s i o n o f c o n v e n t i o n a l photo-measurements; Crown w i d t h Crown w i d t h i s a v e r y i m p o r t a n t t r e e v a r i a b l e  which  i n d i c a t e s the v i g o r , growth r a t e and a l s o can be used t o t h e volume o f a t r e e .  An a c c u r a t e measurement i s n o t e a s i l y made,  thus many methods are b e i n g used t o measure i t However,  estimate  from t h e g r o u n d .  o c u l a r e s t i m a t i o n w i t h a tape i s f r e q u e n t l y u s e d as  the  o t h e r methods a r e too t r o u b l e s o m e , e s p e c i a l l y i n t h i c k l y wooded areas.  The ground measurement always g i v e s a crown w i d t h t h a t  is  b i g g e r than crown d i a m e t e r v i s i b l e i n a e r i a l photographs because the outer-most branches p r o t r u d i n g from the g e n e r a l crown shape can be s e e n .  On a e r i a l photographs t h e p r o t r u d i n g branch t i p s  n e v e r seen and t h e e s t i m a t i o n from above i s t h e r e f o r e smaller.  usually  The two measurements are thus i n c o m p a r a b l e ; however  b i g g e r the s c a l e o f photographs t h e n e a r e r p h o t o - e s t i m a t e s approach the ground measurements.  are  T h i s i s because l a r g e r  the  will scale  w i l l g i v e a c l e a r e r view o f the crown width t h a n h i g h e r u p . It  i s p o s s i b l e t o d i v i d e t h e crowns i n t o d i f f e r e n t  w i t h d i f f e r e n c e of p h o t o - s c a l e . Spurr  (194-8)  U s i n g Harvard F o r e s t photographs  showed t h a t crown w i d t h can be c o n s i s t e n t l y  t o w i t h i n 2 f e e t c l a s s e s at 1:12,000, 3 f e e t c l a s s e s at and 5 f e e t c l a s s e s a t 1:20,000 RF p h o t o g r a p h s . Moessner (1949)  after  classes  classified 1:15,000  Garner and  s t u d y i n g t h e use o f dot-wedge on 1:20,000  19. s c a l e photographs a l s o came t o the same c o n c l u s i o n as S p u r r (1948).  The s t u d y o f Miner (1951) on Southern p i n e a g a i n  c o n f i r m e d S p u r r ' s and M o e s s n e r ' s r e p o r t s  earlier.  The a c c u r a c y and p r e c i s i o n o f crown w i d t h measurements have been r e p o r t e d by many a u t h o r s .  Nash (1949) u s i n g a shadow  wedge t o measure crown w i d t h found a s t a n d a r d e r r o r o f + 1.8 f e e t .  An average s t a n d a r d e r r o r o f 3«7 f e e t was f o u n d  among t h e o b s e r v e r s ( W o r l e v e t o a l . 1 9 5 5 ) . and t h e shadow wedge gave more a c c u r a t e r e s u l t s than t h e d o t s c a l e due t o  systematic  e r r o r of the dot s c a l e . Losee (1953) u s i n g 1:1,200 and 1:7,200 RF photographs o b t a i n e d average e r r o r s o f - 0 . 0 9 and +-0.33 f e e t a t 95 p e r c e n t p r o b a b i l i t y f o r the f i r s t  s e t o f measurements and the second s e t  was n o t as a c c u r a t e as t h e f i r s t . Douglas f i r ,  Ronay (1961)  s t u d i e d 184  166 western hemlock and 77 w e s t e r n r e d cedar o f age  from 21 t o 121 and above y e a r s .  He secured average crown w i d t h s  o f 2 1 . 5 , 1 8 . 9 and 1 7 . 9 f e e t w i t h a s t a n d a r d d e v i a t i o n o f 7 . 3 , and 6.5 f e e t r e s p e c t i v e l y .  6.7  Moessner (1962) r e p o r t e d on t h e use o f  average crown d i a m e t e r o f dominant t r e e s which gave a s t a n d a r d d e v i a t i o n o f + 3.2 f e e t w i t h a c o r r e l a t i o n c o e f f i c i e n t o f 0 . 6 3 2 . Wang (1965) d e v i s e d a f i n e crown wedge t h a t can measure 6 f e e t crown w i d t h and w i t h o n l y two r e a d i n g s taken from each t r e e he o b t a i n e d s t a n d a r d e r r o r s o f t h e mean d i f f e r e n c e which ranged from + 0.21 f o o t f o r 53 Douglas f i r  and + 0 . 5 8 f o o t f o r 12 a l d e r s .  20. The i n f l u e n c e o f v a r i o u s s c a l e s was a l s o s t u d i e d byvarious authors.  A n a l y s i s o f v a r i a n c e f o r d i f f e r e n t s c a l e s was  used by Bateson (1952) t o show t h a t two groups o f e x p e r i e n c e d i n t e r p r e t e r s were almost t h e same.  The average d i f f e r e n c e o f  crown w i d t h was 1.6 f e e t f o r 1 : 2 0 , 0 0 0 , 2.2 f e e t f o r 1 : 1 5 , 0 0 0 , 2.0 f e e t f o r 1:10,000 and 1.9 f e e t f o r 1:5,000 RF p h o t o g r a p h s , and t h e r e s u l t s a r e n o t s i g n i f i c a n t l y d i f f e r e n t .  He a l s o t e s t e d  t h e crown w i d t h measured w i t h s t a n d s i z e , f o r e s t t y p e s and i n t e r p r e t e r s w i t h d i f f e r e n t s c a l e s and found t h a t crown w i d t h shows no s i g n i f i c a n t d i f f e r e n c e w i t h s c a l e s but h i g h l y s i g n i f i c a n t d i f f e r e n c e s between i n t e r p r e t e r s , between s t a n d s i z e and between forest types.  Two and three-way i n t e r a c t i o n s were a l s o  significant. Avery (1958) measured crown w i d t h on H e l i c o p t e r stereograms a t 200 and 300 f e e t f l y i n g h e i g h t found o n l y s l i g h t from 1:20,000 RF p h o t o g r a p h s . a r e shown i n t h e  difference  The r e s u l t s o f t h e t h r e e  interpreters  table.  T a b l e 5 - Crown w i d t h r e s u l t s by t h r e e i n t e r p r e t e r s on 200 and 300 f e e t f l y i n g h e i g h t and 1:20,000 RF photographs Operators  Flying h e i e h t Tft.)  R  F  Mean difference  (ft.)  SD  (ft.)  1 2 3  200  + 0.3 + 0.7 - 0.3  + 0.8  1 2 3  300  - 1.0 - 0.8 - 1.0  + 0.8 + 1.1 + 0.8  0.0 - 2.2 - 4.0  + 1.0 + 1.7 + 1.7  1 2 3  1:20,000  + 1.3 + 0.7  21.  Rogers (1958) u s i n g medium and l a r g e s c a l e photographs t o measure crown w i d t h o b t a i n e d a s t a n d a r d d e v i a t i o n o f 3.5 and 4 . 0 f e e t on 1:10,000 and 1:15,000 RF p h o t o g r a p h s , 1.8 and 1.9 f e e t on 1:5,000 and 1 : 7 , 0 0 0 RF p h o t o g r a p h s , and 0.54- f e e t on 1:1,200 RF p h o t o g r a p h s . I n 1959 he a g a i n r e p o r t e d on t h e r e s u l t s o f t h r e e d i f f e r e n t  scales  ( 1 : 1 , 0 0 0 , 1:5,000 and 1:15,800 RF photographs) u s i n g o n l y t h e t h r e e tallest  trees,  t h a t crown w i d t h measurement was s i g n i f i c a n t l y  different  between s c a l e s and a l s o t h e r e was s i g n i f i c a n t d i f f e r e n c e o f i n t e r a c t i o n between s c a l e s and i n t e r p r e t e r s .  The mean ground measurement was  1 6 . 0 8 f e e t and the mean photo-measurement was 1 2 . 7 2 , 1 3 . 0 8 and 1 5 . 5 6 i n respective to scales. Smith e t ; a l .  (i960) s t u d i e d f i v e d i f f e r e n t s c a l e s ( 1 : 1 4 , 0 0 0 ,  1 : 1 4 , 4 0 0 , 1 : 1 5 , 6 0 0 , 1:15,900 and 1:28,800 RF photographs) and two f o c a l l e n g t h s (6 and 12 i n c h e s ) w i t h 10 o p e r a t o r s . i n t e r p r e t a t i o n of operators varies g r e a t l y . f o u r o p e r a t o r s a r e as t h e t a b l e  They found t h a t  The r e s u l t s o f the b e s t  below.  T a b l e 6 - Grown w i d t h r e s u l t s o f f o u r b e s t o p e r a t o r s Operators Operators  A v e r c  w  (  agf f  t  >  )  S  ( \ SD I f t . j D  f t  A  19.87  1.55  B  25.73  2.25  E  21.20  3.10  F  17.53  3.09  A v  A l l trees . W(ft.) SD ( f t . ) C  22.87  3.89  Five  tallest trees SD (ft.)  Av.CW(ft.T 24.80  3.47  W i t t g e n s t e i n and A l d r e d (1967) measured crown w i d t h on l a r g e - s c a l e photographs ( 1 : 1 , 2 0 0 RF) and t h e y f o u n d a s t a n d a r d e r r o r o f + 2 f e e t .  22. From t h e above i t  can be seen t h a t q u i t e c o n s i s t e n t  w i d t h c l a s s e s can be d e f i n e d on a e r i a l p h o t o g r a p h s .  crown  The d i f f e r e n c e  o f s c a l e s a l s o i s n o t s i g n i f i c a n t by most r e p o r t s , however i t be s a i d t h a t the l a r g e r the s c a l e the more a c c u r a t e and t h e t h e s c a l e t h e l e s s a c c u r a t e w i l l measurements b e .  The o n l y v a r i a b l e  w i d t h measurements g r e a t l y i s t h e i n t e r p r e t e r  smaller  Measurements on  s m a l l s c a l e photographs w i l l be more p r e c i s e because t h e appears t o be more compact.  can  crown  that affects  crown  himself.  Crown c l o s u r e Crown c l o s u r e i s t h e p r o p o r t i o n o f t h e stand o c c u p i e d o r covered by t h e crowns o f t r e e s w i t h i n a u n i t a r e a . crown c l o s u r e o f a l l l e v e l s  Either  total  (second growth, co-dominant and dominant)  o r o n l y t h e upper l e v e l o f dorninant and co-dominant t r e e s may be u s e d . The crown c l o s u r e i s e x p r e s s e d as a p e r c e n t a g e .  It  i s an i m p o r t a n t  v a r i a b l e f o r s t u d y i n g o f stands and f o r d e t e r m i n a t i o n o f t h e i r volume, d e n s i t y and s t o c k i n g .  The measurement o f crown c l o s u r e on t h e ground  i s u s u a l l y under o r over e s t i m a t e d because o f t h e d i f f e r e n c e on emphasis o f s m a l l openings and p r o t r u d i n g branches o f i n d i v i d u a l depending upon i n d i v i d u a l judgement. area of v i s i o n .  T h i s i s a l s o due t o the  trees  limited  On a e r i a l photographs t h e s m a l l openings cannot be  seen and t h e i r r e g u l a r i t i e s  o f s i n g l e crowns are a l s o n o t so o b v i o u s ,  t h u s t h e crown c l o s u r e may be a l i t t l e u n d e r - e s t i m a t e d .  Since the  a e r i a l photographs g i v e a b i r d ' s eye view o f any f o r e s t a r e a , e s t i m a t e i s more r e a l i s t i c  the  i n comparison w i t h t h o s e on t h e g r o u n d .  23. The a c c u r a c y and p r e c i s i o n o f crown c l o s u r e e s t i m a t i o n on a e r i a l photographs have been r e p o r t e d by many a u t h o r s .  Moessner  (194-9) r e p o r t e d t h a t by u s i n g the crown d e n s i t y s c a l e , t h e measurement o f crown c l o s u r e can be made by 10 p e r c e n t c l a s s e s w i t h l i t t l e training.  Spurr  RF p h o t o g r a p h s .  (194-8) a l s o r e p o r t e d s i m i l a r r e s u l t s w i t h 1:20,000 He p l a c e d emphasis on t h e p h o t o g r a p h i c images by  s t a t i n g t h a t t h e b e t t e r the p h o t o g r a p h i c images, the more  clearly  seen w i l l be t h e s m a l l openings i n t h e canopy and t h e lower w i l l be t h e e s t i m a t e and v i c e v e r s a .  Garner and Moessner (1949)  t h a t the v a r i a t i o n of i n t e r p r e t e r s  a g a i n found  seldom exceeds 10 p e r c e n t  although  c a r e f u l o b s e r v a t i o n s must be made n o t t o i n c l u d e t h e shadows. The v a r i a n c e o f d i f f e r e n t s c a l e s was a n a l y s e d by (1952).  He used f o u r d i f f e r e n t  scales  Bateson  ( 1 : 5 , 0 0 0 , 1 : 1 0 , 0 0 0 , 1:15,000  and 1:20,000 RF photographs) t o t e s t crown c l o s u r e r e l a t i o n w i t h stand s i z e f o r e s t t y p e s and two groups o f i n t e r p r e t e r s .  The f i r s t  group gave  i n s i g n i f i c a n t v a r i a t i o n between i n t e r p r e t e r and s c a l e b u t h i g h l y s i g n i f i c a n t v a r i a t i o n between stand s i z e and between t y p e s . second group gave h i g h l y s i g n i f i c a n t v a r i a t i o n between  The  interpreters  and between stand s i z e but no s i g n i f i c a n t v a r i a t i o n between s c a l e and forest  types. Losee (1952)  s t u d i e d 1:15,840 RF photographs and found t h a t  t h e s t a n d a r d e r r o r o f crown c l o s u r e e s t i m a t e was + 13 t o + 23 p e r c e n t . A g a i n i n 1953 he compared t h e crown c l o s u r e o f two d i f f e r e n t  scales  ( 1 : 1 , 2 0 0 and 1:7,200 RF photographs) w i t h a 6 i n c h f o c a l l e n g t h . average e r r o r s were - 0.3 t o + 9 . 9 p e r c e n t and - 0.3 t o + 5.5  The  percent  24. both a t 95 p e r c e n t p r o b a b i l i t y r e s p e c t i v e l y .  There was no  significant  d i f f e r e n c e between b o t h s c a l e s but he found l a r g e d i s p l a c e m e n t o f photoimage towards t h e edge o f t h e photographs because o f a 6 i n c h f o c a l l e n g t h was used which reduced t h e apparent s i z e o f t h e crown openings towards t h e edges. Worley and Meyer (1955) compared dot count and g r i d methods which gave an average s t a n d a r d e r r o r o f 0.10 on 1:1,200 RF photographs.  Comparisons  p e r c e n t f o r crown c l o s u r e  o f crown d e n s i t y s c a l e and  methods were made by G i n g r i c h and Meyer (1955). d o t g r i d method was  They c o n c l u d e d t h a t t h e  somewhat s u p e r i o r t o t h a t o f crown d e n s i t y s c a l e but  the a c c i d e n t a l e r r o r o f b o t h were about 10 p e r c e n t . e r r o r was  grid  However, t h e s y s t e m a t i c  s m a l l e r f o r t h e dot g r i d t h a n t h e crown d e n s i t y  scale.  Avery (1958) measured crown c l o s u r e on H e l i c o p t e r stereograms o f 200 and 300 f e e t f l y i n g h e i g h t and compared them w i t h 1:20,000 RF photographs.  The r e s u l t s o f t h e t h r e e e x p e r i e n c e d o p e r a t o r s a r e l i s t e d  below:  T a b l e 7 - Crown c l o s u r e r e s u l t s by t h r e e o p e r a t o r s on 200 300 f e e t f l y i n g h e i g h t and 1:20,000 RF Operators  Flying height ( f t . )  RF  and  photographs  Mean difference ( f t . )  SD ( f t . )  1 2 3  200  + 2.0 + 3.0 + 3.0  + + +  1 2 3  300  + + +  0.2 4.4 2.4  + 1.3 + 1.8 + 1.8  + -  2.0 6.0 2.0  + 5.8 + 4.0 + 2.0  1 2 3  1:20,000  1.5 1.6 1.6  25 He found t h a t o n l y s l i g h t d i f f e r e n c e s between t h e Rogers e _ . _ l .  (1959a)used t h r e e d i f f e r e n t  scales. scales  (1:1,000,  1:5,000 and 1:15,840 RF photographs) and c o n c l u d e d t h a t crown c l o s u r e percent d i f f e r s s i g n i f i c a n t l y with s c a l e .  It  was a l s o found t h a t  in  comparison t o average ground crown c l o s u r e o f 55 p e r c e n t t o be 4 percent lower, to s c a l e s .  4 p e r c e n t h i g h e r and 10 p e r c e n t h i g h e r  Only t h e 10 p e r c e n t d i f f e r e n c e was found t o be s i g n i f i c a n t .  A g a i n i n 1959b t h e y c o n f i r m e d the r e p o r t s o f S p u r r (1949)  respectively  and Garner and Moessner (1949)  (1948), Moessner  t h a t 10 p e r c e n t c l a s s e s can be  c o n s i s t e n t l y measured. Smith e t . a l .  (i960) u s e d 10 o p e r a t o r s t o compare t h e  o f crown c l o s u r e w i t h f i v e s c a l e s  differences  (1:14,000, 1:14,400, 1:15,600,  1:15,900 and 1:28,800 RF photographs) and t h e b e s t f o u r r e s u l t s  are  l i s t e d below: T a b l e 8 - Crown c l o s u r e r e s u l t s o f f o u r b e s t o p e r a t o r s Operators  Average A . C . ( f t . )  SD  (ft.)  A  72.20  6.66  B  77.00  7.27  E  58.33  14.47  F  53.00  18.50  They found t h a t t h e i n t e r p r e t e r s were t h e most i m p o r t a n t s o u r c e o f variation.  V a r i a t i o n f o r d i f f e r e n c e s i n crown c l o s u r e among t h e  s c a l e s was n o t s i g n i f i c a n t .  five  A l l i s o n and Breadon (I960) u s i n g double  s a m p l i n g t o c a l c u l a t e t h e s t a n d a r d e r r o r o f crown c l o s u r e ,  obtained  26 a s t a n d a r d e r r o r o f + 1.55  f e e t f o r 165  sample p l o t s .  Crown c l o s u r e can be measured by many methods. (194-7) d e v i s e d a crown d e n s i t y s c a l e t o be used w i t h little  training.  relatively  Dot count and g r i d methods were used by Worley  and Meyer (1955).  They a l s o c o n c l u d e d t h a t t h e crown c l o s u r e  measured on the ground and a e r i a l photographs were n o t related.  Moessner  directly  A t h r e e dimension view o f t h e crown d e n s i t y s c a l e was  advocated by Lee  (1959). Avery and Myhre (1959) found t h a t  i n e x p e r i e n c e d i n t e r p r e t e r s tend t o o v e r e s t i m a t e crown c l o s u r e due t o t h e f a c t t h a t no allowance was made f o r t h e crown shadows and small openings.  Pope  (i960) suggested t h e use o f t h e crown cramming  method t o measure crown c l o s u r e , t h a t i s  s c a t t e r e d t r e e s a r e crammed  t o g e t h e r and c l o s u r e e s t i m a t e d . From t h e above r e v i e w s i t  i s p o s s i b l e t o say t h a t  c l o s u r e can be e s t i m a t e d t o w i t h i n 10 p e r c e n t c l a s s e s . v a r i e s g r e a t l y from i n t e r p r e t e r  to i n t e r p r e t e r .  crown  The p r e c i s i o n  The most i m p o r t a n t  f a c t o r t h a t determines t h e a c c u r a c y and p r e c i s i o n i s t h e  interpreter  himself. Height H e i g h t i s one o f t h e most i m p o r t a n t v a r i a b l e s i n measuration.  It  forest  can be used as an i n d i c a t o r of s i t e i n d e x , age, volume  and o t h e r v a r i a b l e s .  Thus many methods have been d e v i s e d t o measure  on t h e ground as w e l l as on a e r i a l p h o t o g r a p h s .  Measurements on t h e  ground w i t h an e r r o r o f 1 t o 2 f e e t are n o t uncommon under f a v o u r a b l e c o n d i t i o n s and even 3 t o 5 f e e t o r more can be encountered i n  it  27. u n f a v o u r a b l e c o n d i t i o n s (Bruce and Schumacher 1 9 5 0 ) . photo-measurements w i l l be c o n s i d e r e d f u r t h e r  Only  aerial  here.  The a c c u r a c y and p r e c i s i o n o f v a r i o u s methods o f h e i g h t measurements on a e r i a l photographs were r e p o r t e d by many a u t h o r s . The p a r a l l a r b a r was i n t r o d u c e d by Andrews (1936) height.  t o measure t r e e  A c c u r a c y f o r 56 t r e e s w i t h an average h e i g h t o f 88 f e e t ,  was w i t h i n 6 f e e t on 1:9,000 RE p h o t o g r a p h s .  Sammi (1953)  studied  1:9,600 RF photographs and came t o t h e c o n c l u s i o n t h a t the h i g h e r t h e t r e e the g r e a t e r i s t h e s t a n d a r d e r r o r o f measurement.  He a l s o  observed t h a t 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 r e p e a t e d h e i g h t measurements i n c r e a s e d w i t h p a r a l l a r d i f f e r e n c e t o a maximum o f 12 p e r c e n t . Smith (1957)  t e s t e d the a b i l i t y o f i n t e r p r e t e r s  15 t r e e s r a n g i n g from 93 t o 206 f e e t ,  with  and an average o f 123 f e e t .  A f t e r 15 hours p r a c t i c e one o p e r a t o r s e c u r e d an average e s t i m a t e o f + 4 . 7 f e e t from t h e mean h e i g h t but t h e a c c u r a c y i n c r e a s e d t o + 0 . 9 f e e t a f t e r 25 hours p r a c t i c e .  Another o p e r a t o r improved h i s  e s t i m a t i o n from an average e r r o r o f -22.2 f e e t i n t h e f i r s t r u n t o - 6 . 5 f e e t i n the second s e r i e s o f measurements o f the same t r e e s . Collins  (1957), u s i n g 40 t r e e s on 1:1,700 f R E t photographs  w i t h 12 i n c h f o c a l l e n g t h f o u n d the s t a n d a r d e r r o r o f e s t i m a t e  for  a l l i n d i v i d u a l t r e e h e i g h t t o be + 6.1 f e e t and maximum e r r o r o f -15 f e e t .  However,  e r r o r o f ± 5.1 f e e t .  t h e measurement o f dominant h e i g h t o n l y g i v e an Lee (1959) u s i n g an Abrams h e i g h t - f i n d e r found  t h a t t h e e r r o r o f average dominant and codominant t r e e h e i g h t s can  28 be r e d u c e d from + 5 f e e t t o + 2 f e e t f o r 8 open grown t r e e s . a l s o advocated t h a t the d i s t a n c e o f i n t e r p r e t e r ' s  He  eyes from t h e  l e n s e s o f t h e s t e r e o s c o p e t o be h e l d c o n s t a n t and i f  local  c o n d i t i o n s p e r s i s t t h e d o t s must be p l a c e d a t the lower r i g h t hand corner of the  trees.  H i n d l e y (1959) found t h a t immature stands cannot be measured a c c u r a t e l y and c o n s i s t e n t l y and he suggested t h a t c o r r e c t i o n f a c t o r s be used w i t h s t a n d a r d e r r o r o f +6*1 f e e t on the b a s i s o f 35 sample p l o t s .  A l l i s o n and Breadon (i960) suggested t h a t  measurements o f t r e e h e i g h t s must be c o n t i n u e d u n t i l two parallar differences  identical  (dp) were o b t a i n e d and found t h a t t h i s  needed t o t a k e more than f o u r r e a d i n g s .  seldom  They a l s o gave a comparison  between 2 and 16 r e a d i n g s w i t h s t a n d a r d e r r o r o f ± 1 6 . 2 f e e t + 15.5 f e e t r e s p e c t i v e l y . statistically  and  The r e s u l t s o f A l l i s o n and Breadon were  a n a l y s e d by M i t c h e l l  (l96l).  He c o n c l u d e d t h a t  at  l e a s t 6 r e a d i n g s must be made and the s t a n d a r d e r r o r i s lower  for  mean h e i g h t t h a n 2 i d e n t i c a l r e a d i n g s as s u g g e s t e d . Low e l e v a t i o n H e l i c o p t e r s t e r e o - p h o t o g r a p h s were used by Lyons ( 1 9 6 1 ) .  The t r e e s measured ranged from 50 t o 70 f e e t  h e i g h t w i t h mean e r r o r s o f 1.7 and 3.4- f e e t r e s p e c t i v e l y .  in Again  i n 1964 he measured 682 t r e e s which ranged from 45 t o 125 f e e t h e i g h t and o b t a i n e d a s t a n d a r d e r r o r o f + 4 . 5  in  feet.  Wang (1965) who s t u d i e d 95 t r e e s on t h e U n i v e r s i t y  Research  F o r e s t found a s t a n d a r d e r r o r o f mean d i f f e r e n c e o f + 0.25 f e e t , t h e s t a n d a r d e r r o r o f mean d i f f e r e n c e f o r c o n i f e r s and hardwoods  but  29 were + 0.30 aad + 0.41 f e e t r e s p e c t i v e l y .  No c o n s i s t e n t r e s u l t  seemed t o f a v o u r any one s p e c i e s but c o n i f e r s g e n e r a l l y better r e s u l t s .  Large s c a l e photographs ( 1 : 1 , 2 0 0 RF)  W i t t g e n s t e i n and A l d r e d s e c u r e d a 3.5  feet  (1967)  give  were used by  t o e s t i m a t e t r e e volumes, and t h e y  standard e r r o r o f e s t i m a t e .  The p a r a l l a r wedge was i n t r o d u c e d by S p u r r (1945)  as a  s i m p l e and i n e x p e n s i v e h e i g h t measuring d e v i c e , and he a l s o o b t a i n e d an average e r r o r o f +  3rfeet  on 1:12,000 p h o t o g r a p h s .  He t e s t e d t h e  wedge i n Harvard F o r e s t i n 1948 and f o u n d 3 t o 20 f e e t were o b t a i n e d f o r 1:12,000 and 1:15,840 RF photographs r e s p e c t i v e l y .  I n t h e same  y e a r he made a n o t h e r t e s t , which showed t h a t s k i l l e d i n t e r p r e t e r s c o u l d o b t a i n 3,  5 and 9 f e e t d i f f e r e n c e f o r 1 : 6 , 0 0 0 , 1:12,000 and  1:18,000 RF photographs r e s p e c t i v e l y . Stereograms o f a e r i a l photographs were used t o  train  b e g i n n e r s t o be e f f i c i e n t i n p a r a l l a r t r e e h e i g h t measurements by Moessner 1950a.  He found t h a t the mean d e v i a t i o n f o r saw t i m b e r  was 6.7 f e e t and f o r a l l t h e t r e e s i n t h e stand 9.2 f e e t .  In  the  same y e a r he a g a i n s t u d i e d 1:20,000 RF photographs and o b t a i n e d an average o f l e s s t h a n 6 f e e t i n comparison w i t h f i e l d measured h e i g h t s by Abney l e v e l . B e r n s t e i n (1958) found t h a t t h e r e was no s i g n i f i c a n t i n c r e a s e s i n a c c u r a c y by m a g n i f i c a t i o n but t h i s v a r i e s interpreters.  with  S i t e i n d e x can be e s t i m a t e d from a e r i a l photographs  (Smith e t a l . 1 9 6 1 ) . ;  A c o r r e l a t i o n c o e f f i c i e n t o f 0.65 and standard  d e v i a t i o n o f + 16.4 f e e t were o b t a i n e d , which was b e t t e r t h a n t h e ground e s t i m a t e s .  30. Comparisons o f b o t h t h e p a r a l l a r wedge and p a r a l l a r b a r were made by a few a u t h o r s .  Ker  (1953)  after intensive estimation of tree  h e i g h t s from 1:15,840 RF photographs came t o t h e c o n c l u s i o n t h a t r e a s o n a b l y l a r g e e r r o r s seem t o e x i s t but a degree o f c o n s i s t e n c y c o u l d be o b t a i n e d .  Worley and L a n d i s  (1954)  r e p o r t e d the use o f 1:12,000  RF photographs by t h r e e e x p e r i e n c e d i n t e r p r e t e r s . gave average s y s t e m a t i c e r r o r s o f -4.4, -3.4  The p a r a l l a r wedge  and - 7 . 0 f e e t  respectively  b u t p a r a l l a r b a r gave l a r g e r average s y s t e m a t i c e r r o r s o f - 5 . 0 , and - 1 7 . 8 f e e t r e s p e c t i v e l y f o r c o n i f e r s . for  -9.6  The average s y s t e m a t i c  hardwoods were s m a l l e r f o r both i n s t r u m e n t s .  The average  errors  systematic  e r r o r s c o u l d be reduced by t a k i n g i n c r e a s i n g number o f measurements. A c c i d e n t a l e r r o r s o f measurements e x p r e s s e d i n s t a n d a r d e r r o r s were found t o be 8 t o 10 f e e t f o r b o t h i n s t r u m e n t s but were i n s i g n i f i c a n t . The r e p o r t f o r working group 4 ( F o r e s t e r s ) International  Commission V I I  S o c i e t y o f Photogrammetry (Rogers 1958) s t a t e d t h a t  average  h e i g h t f o r dominant t r e e s i n hardwoods stands c o u l d be measured t o 10 p e r c e n t , two times out o f t h r e e .  within  On 1:12,000 RF photographs t h e  i n d i v i d u a l t r e e c o u l d be e s t i m a t e d w i t h a s t a n d a r d e r r o r o f 9 f e e t . Moessner (1961) u s i n g 15 p l o t s on 1:20,000 RF photographs found t h a t p a r a l l a r wedge and b a r c o u l d be used w i t h e q u a l speed and a c c u r a c y and no s i g n i f i c a n t d i f f e r e n c e was found on l a r g e r s c a l e p h o t o g r a p h s . Johnson (1958a)  s t a t e d t h a t about 21 t o 26  hours o f t r a i n i n g  were r e q u i r e d b e f o r e t h r e e o p e r a t o r s became p r o f i c i e n t w i t h b o t h p a r a l l a r instruments. percent.  The c o r r e l a t i o n c o e f f i c i e n t u s u a l l y l a y between 60 and 70  Avery (1961) r e p o r t e d t h a t i f  an i n t e r p r e t e r c o u l d d e t e c t a  p a r a l l a x d i f f e r e n c e o f 0.002 i n c h (0.05mm) he would be a b l e t o measure t o w i t h i n 10 f e e t t r e e h e i g h t on 1:10,000 t o 1:15,000 RF p h o t o g r a p h s .  31 A shadow wedge was u s e d as e a r l y as 1935 by S e e l y t o measure tree heights.  Nash (1949) who s t u d i e d 1:7,200 RF photographs f o u n d a  s t a n d a r d e r r o r o f + 3 f e e t and a l s o a h i g h c o r r e l a t i o n between ground and a e r i a l photo-measurements.  Losee (1952) w i t h 1:15,840 RF photographs  and shadow wedge o b t a i n e d a s t a n d a r d d e v i a t i o n o f + 7 t o + 11 f e e t  for  s i n g l e t r e e measurements. The d o t wedge was u s e d by Garver et, a l . ( 1 9 4 9 )  who r e p o r t e d  t h a t a s k i l l e d i n t e r p r e t e r c o u l d o b t a i n e d an e r r o r o f l e s s than + 10 f e e t two times out o f t h r e e on 1:12,000 RF p h o t o g r a p h s . The i n f l u e n c e o f s c a l e on h e i g h t measurement has been determined by many a u t h o r s .  Bateson (1952) used the t e s t o f a n a l y s i s o f v a r i a n c e  for  d i f f e r e n t s c a l e s ( 1 : 5 , 0 0 0 , 1 : 1 0 , 0 0 0 , 1 : 1 5 , 0 0 0 , 1:20,000 RF photographs) f o r measuring t r e e h e i g h t s i n r e l a t i o n t o s t a n d s i z e , f o r e s t type and interpreters.  The f i r s t group f o u n d t h a t t h e v a r i a t i o n between i n t e r p r e t e r s  and between s t a n d s i z e was not s i g n i f i c a n t but t h e second group found them t o be h i g h l y s i g n i f i c a n t .  The f i r s t group a l s o found t h a t the  difference  o f s c a l e i s s i g n i f i c a n t w h i l e the second group gave an i n s i g n i f i c a n t r e s u l t . The i n t e r a c t i o n between s t a n d s i z e and type i s  s i g n i f i c a n t f o r the  first  g r o u p , and t h e second group found i n t e r a c t i o n between i n t e r p r e t e r s and stand s i z e ,  and i n t e r p r e t e r and t y p e s t o be s i g n i f i c a n t .  The i n t e r a c t i o n  o f v a r i a t i o n between s c a l e s was n o t s i g n i f i c a n t f o r any one i n t e r p r e t e r . The i n f l u e n c e o f d i f f e r e n t s c a l e s on h e i g h t measurement by p a r a l l a x b a r was t e s t e d by Losee (1953).  He used 1:1,200 and 1:7,200 RF  photographs o f e a s t e r n Canada and o b t a i n e d an average o f 2.1+0.5 f e e t and 0.6+2.1 f e e t r e s p e c t i v e l y a t 95 p e r c e n t p r o b a b i l i t y .  F i f t e e n t o twenty  32. measurements were u s e d and the s y s t e m a t i c e r r o r were - 1 . 5 t o +1.8 f e e t and -10 t o -16  feet respectively.  L a n d i s et, a l .  (1954)  s t u d i e d the  e r r o r o f s c a l e s and gave 3 p e r c e n t f o r 1:20,000 and 2 p e r c e n t 1:12,000 RF p h o t o g r a p h s .  A l l i s o n (1956)  for  s t u d i e d seventeen s e t s of  d i f f e r e n t photographs and r e p o r t e d * t h a t t h e h i g h e r t r e e s have g r e a t e r e r r o r and t h a t h i g h e r f l y i n g h e i g h t and/or s h o r t e r f o c a l l e n g t h and/or g r e a t e r degree o f enlargement, made t h e h e i g h t measurement l e s s  precise.  The q u a l i t i e s o f a e r i a l photographs a l s o g r e a t l y i n f l u e n c e d t h e  accuracy  o f measurements. Moessner and Rogers (1957)  a l s o concluded t h a t d i f f e r e n c e of  s c a l e o f photographs i n f l u e n c e d h e i g h t measurements. d i f f e r e n c e of  For  elevation  +636 f e e t t o -543 f e e t from t h e mean datum the s t a n d a r d  e r r o r was 10 f e e t without adjustment but a f t e r adjustment the e r r o r was reduced t o 3 . 5 f e e t .  They a l s o developed a t a b l e and a graph  from which p a r a l l a x f a c t o r s c o u l d be determined f o r d i f f e r e n t h e i g h t and base l e n g t h s .  standard  Johnson (1958b)  flying  studied four d i f f e r e n t  scales  ( 1 : 5 , 0 0 0 , 1 : 1 0 , 0 0 0 , 1:15,000 and 1:20,000 RF photographs) found t h a t h e i g h t measurements was n o t e f f e c t e d by s c a l e , and e r r o r s may be a s s o c i a t e d p r o b a b l y w i t h crown shape and t r e e s i z e .  However,  errors of  t r e e h e i g h t e s t i m a t i o n were d e f i n i t e l y a s s o c i a t e d w i t h o p e r a t o r s . Avery (1958)  conducted h e i g h t measurements on h e l i c o p t e r s  s t e r e o - p h o t o g r a p h y a t 200 and 300 f e e t f l y i n g h e i g h t , w i t h 1:20,000 RF p h o t o g r a p h s . a r e shown below:  and compared them  The r e s u l t s from t h r e e e x p e r i e n c e d o p e r a t o r s  33. T a b l e 9 - H e i g h t r e s u l t s by t h r e e o p e r a t o r s on 200 and 300 f e e t f l y i n g h e i g h t , and 1:20,000 RF p h o t o g r a p h s . Flying height (ft.)  Operators  R 1 ?  **  Mean difference  SD  (ft.)  (ft.)  1 2 3  200  2.5 1.8 1.2  + 2.1 + 2.9 + 1.8  1 2 3  300  1.3 1.3 8.0  1 .7 + 1.3 + 1.7  1 2 3  1:20,000  - 6.8 - 5.5 -13.0  + 6.3 + 3.2 + 5.9  He c o n c l u d e d t h a t H e l i c o p t e r stereograms were o n l y s l i g h t l y b e t t e r  than  1:20,000 RF photographs f o r h e i g h t measurements. Comparisons o f d i f f e r e n c e o f s c a l e s were made by Rogers e t , a l . (1959a)  with three d i f f e r e n t scales  photographs).  The t e s t s  ( 1 : 1 , 0 0 0 , 1:5,000 and 1:15,840 RF  showed t h a t e r r o r s i n t r e e h e i g h t e s t i m a t i o n were  s i g n i f i c a n t l y d i f f e r e n t among s c a l e s and among i n t e r p r e t e r s but i n t e r a c t i o n o f s c a l e s and i n t e r p r e t e r s was n o t s i g n i f i c a n t .  the  The mean  photo h e i g h t and ground h e i g h t were s i g n i f i c a n t l y d i f f e r e n t w i t h a negative value f o r a l l h e i g h t s were  44.56,  s c a l e s and i n t e r p r e t e r s  (photo measured mean  4 8 . 1 4 and 43.61 f e e t i n r e s p e c t t o s c a l e s and t h e  ground h e i g h t was 53.33 f e e t ) . D i f f e r e n t s c a l e s and f o c a l l e n g t h s were t e s t e d by 10 o p e r a t o r s t o measure 15 permanent p l o t s , w i t h average dominant and codominant h e i g h t r a n g i n g from 93 t o 138 f e e t o p e r a t o r s s e c u r e d r e s u l t s as l i s t e d  (Smith e t . a l . 1 9 6 0 ) . below:  The f o u r b e s t  34 T a b l e 10 - H e i g h t r e s u l t s o f f o u r b e s t Average _  . SD  A  120.70  15.60  B  132.80  9.56  E  125.90  L4.23  F  130.33  26.70  rw„„4.„,.  Operator  H  e  g  h  t  Q r  A l l trees ^ . h  g  g  h  t  118.27  operators Five ^  SD c  n  13.09  F i v e d i f f e r e n t s c a l e s and 2 d i f f e r e n t f o c a l l e n g t h s  h  trees  e  i  g  h  SD  t  131.40  11.64  ( 1 : 1 5 , 6 0 0 and  1:15,900 RF photographs w i t h 12 i n c h f o c a l l e n g t h , and 1 : 1 4 , 0 0 0 , and 1:28,800 RF photographs w i t h 6 i n c h f o c a l l e n g t h )  1:14,400  were used and  it  was found t h a t 1:14,000 photographs was b e t t e r than 1:28,800 and 1:15,600 photographs.  The r e s u l t s a l s o showed t h a t i n t e r p r e t e r s were the most  important source of  variation.  Moessner (1961) r e p o r t e d on two d i f f e r e n t  scales  1:20,000 RF photographs) t h a t the mean d i f f e r e n c e o f f o u r  (1:12,000 and skilled  i n t e r p r e t e r s were 1 . 5 4 , 1 . 5 3 , 4 « 6 and 4.73 f e e t r e s p e c t i v e l y f o r  1:20,000  p h o t o g r a p h s , b u t f o r 1:12,000 photographs t h e d i f f e r e n c e were 2 . 4 1 , 2 . 2 1 , 8.62  and 8.21 f e e t r e s p e c t i v e l y .  Pope (1957)  gave a l i s t  of nine points  as a p o s s i b l e s o u r c e o f e r r o r i n t r e e h e i g h t measurement. (1)  A c c i d e n t a l errors of i n t e r p r e t e r  and i n s t r u m e n t .  (2)  E r r o r s o f photo s c a l e d e t e r m i n a t i o n .  (3)  D i f f e r e n c e i n a l t i t u d e o f p l a n e between camera s t a t i o n s .  (4)  F a i l u r e of tree t i p to r e s o l v e .  (5)  Wind movement o f t r e e t o p .  (6)  Tree crowns o b s c u r i n g g r o u n d .  (7)  Brush o r o t h e r v e g e t a t i o n o b s c u r i n g g r o u n d .  (8)  F a l s e s t e r e o on ground p o i n t .  (9)  T i p and t i l t o f p h o t o g r a p h s .  35. The f i r s t f o u r c o n t r i b u t e d about 20 t o 25 f e e t e r r o r s ,  the f i f t h  did  n o t cause much e r r o r s but t h e s i x t h t o e i g h t h caused wrong p a r a l l a x reading.  Thus as l a r g e as 50 f e e t  e r r o r i n mature stands c o u l d o c c u r .  He c o n c l u d e d t h a t t h e d i f f e r e n c e o f s c a l e s and types o f photographs had l i t t l e e f f e c t on h e i g h t measurement. In c o n c l u s i o n i t  seems t h a t the p a r a l l a x b a r and wedge can  be u s e d w i t h e q u a l e f f i c i e n c y and c o n s i s t e n t e s t i m a t e s can be made by e x p e r i e n c e d i n t e r p r e t e r s who w i l l t a k e i n t o account a l l t h e that contribute to tree height error.  factors  The i n f l u e n c e o f s c a l e s seem  t o be i n c o n c l u s i v e due t o the f a c t t h a t many a u t h o r s s a i d i t  was  s i g n i f i c a n t l y d i f f e r e n t w h i l e o t h e r s s a i d i t was n o t .  reasonable  It  is  t o say t h a t s c a l e does i n f l u e n c e h e i g h t measurement, however i t  is  o n l y t h e degree o f i n f l u e n c e t h a t d i f f e r l i k e b i g g e r s c a l e tends t o have s m a l l e r e r r o r s t h a n s m a l l e r C o n v e n t i o n a l measurements  scale.  of:  Stocking F o r e s t r y Terminology ( S o c i e t y o f American f o r e s t e r s , 1950) d e f i n e d s t o c k i n g as " . . .  an i n d i c a t i o n o f t h e number o f t r e e s i n a  s t a n d as compared t o the d e s i r a b l e number f o r b e s t growth and management: s u c h as w e l l s t o c k e d , o v e r - s t o c k e d , and p a r t l y - s t o c k e d ..."  Smith e t » a l . ( 1 9 6 1 )  emphasized t h a t t h e term s t o c k i n g s h o u l d a l s o  be used t o d e s c r i b e t h e degree o f occupancy o f an a r e a o r i t s by t r e e crowns o r s t o c k e d q u a d r a t s .  The number o f t r e e s i n  coverage  "open"  and " d e n s e " stands d i s c u s s e d r e p r e s e n t e d complete o c c u p a t i o n o f  the  a r e a w i t h t r e e crowns and t h e r e f o r e f u l l coverage o r s t o c k i n g , but v a r y i n g d e n s i t y by numbers o f t r e e s .  F o r e s t managers must have f u l l  36. knowledge o f t h e growing s t o c k and the a r e a o c c u p i e d by t r e e s  in  t h e f o r e s t under management, i n o r d e r t o execute p l a n n i n g  efficiently.  W i t h s t o c k i n g , volume can a l s o be c a l c u l a t e d w i t h average  diameter  and t r e e h e i g h t .  It  n o t o n l y g i v e s growing s t o c k s and volume but  a l s o i n d i c a t e s t o t h e management whether the l a n d i s f u l l y  utilized  or n o t . S t o c k i n g had been s t u d i e d by many a u t h o r s , Meyer  (1928)  r e p o r t e d t h a t the t o t a l number o f t r e e s was n o t a s a t i s f a c t o r y o f s t o c k i n g and t h a t b a s a l a r e a was t h e most r e l i a b l e stocking.  index  index of  The t r a n s i t i o n i n d i c a t e d by an u n d e r - s t o c k e d s t a n d t o a  f u l l y - s t o c k e d o r normal c o n d i t i o n were about 2 p e r c e n t .  Again i n  1933 he assumed t h a t i n u n d e r - s t o c k e d stands l e s s t r e e s would d i e o f s u p p r e s s i o n and the growth was a l s o f a s t e r t h a n normal s t a n d s . he l o g i c a l l y c o n c l u d e d t h a t t r u e n o r m a l i t y was the b a l a n c e  Thus  between  the a c c e l e r a t e d n e t increment o f u n d e r - s t o c k e d stands t o b r i n g them up g r a d u a l l y t o n o r m a l i t y ,  and o v e r - s t o c k e d stands which s h o u l d be  r e t a r d e d i n n e t increment t o b r i n g them back t o n o r m a l i t y .  The age  o f s t a n d s were from 38 t o 88 y e a r s w i t h s i t e i n d e x o f 110 t o 202 f t . The change i n n o r m a l i t y f o r number o f t r e e s had no r e l a t i o n w i t h normality percentages -.153 +.132).  (an i n s i g n i f i c a n t c o r r e l a t i o n c o e f f i c i e n t  of  No m a t t e r what t h e i n i t i a l degree o f s t o c k i n g an  average i n c r e a s e o f 3.3 p e r c e n t f o r each f i v e y e a r s p e r i o d must be chosen.  B a s a l a r e a had a h i g h e r but i n s i g n i f i c a n t c o r r e l a t i o n ,  - . 1 9 8 +.132, than the number o f t r e e s w i t h an i n c r e a s e d o f 1.5 each f i v e y e a r s .  Volume v a l u e s seemed t o be d e f i n i t e l y r e l a t e d  of percent to  37. initial  s t o c k i n g ; u n d e r - s t o c k e d stand tended t o have a h i g h e r r a t e  o f change i n the p o s i t i v e d i r e c t i o n , f o r 100 and 120 p e r c e n t o f n o r m a l i t y t h e change was v e r y i n d e f i n i t e and s m a l l , and f o r s t o c k e d stands the change was on t h e whole n e g a t i v e .  over-  The t o t a l  volume c u b i c measure o f s t o c k i n g p e r c e n t a g e towards n o r m a l i t y  is  l i s t e d below:I n c r e a s e d 4 p e r c e n t a t 80 p e r c e n t and 1 p e r c e n t a t 100 p e r c e n t  (Meyer)  I n c r e a s e d 5 p e r c e n t a t 80 p e r c e n t and 1 p e r c e n t a t 106 p e r c e n t ( I n t e r n a t i o n a l r u l e board measure) I n c r e a s e d 5 p e r c e n t a t 80 p e r c e n t and 1 p e r c e n t a t 105 p e r c e n t ( S c r i b n e r r u l e board measure) There was l i t t l e  d i f f e r e n c e between the t h r e e but t h e s e were t h e  average t e n d e n c i e s b e s t a p p l i c a b l e t o stands between 4O and 80 y e a r s w i t h s i t e q u a l i t i e s o f I, II  and I I I  o f above 125 s i t e i n d i c e s .  The  t r e n d s toward n o r m a l i t y does n o t s t o p as t h e average t e n d e n c i e s above but w i l l c o n t i n u e upwards near t o 110-115 p e r c e n t . Briegleb  (1942) a g a i n c o n f i r m e d the r e p o r t s o f Meyer  (1928, 1933) t h a t t r e n d s towards n o r m a l i t y i n c r e a s e d r a p i d l y when t h e stands were u n d e r - s t o c k e d , young and t h e lower t h e percentage o f n o r m a l i t y was, the f a s t e r would t h e n o r m a l i t y p e r c e n t a g e i n c r e a s e d . But the o p p o s i t e was t r u e f o r o v e r - s t o c k e d s t a n d s , o l d stands and t h e h i g h e r t h e degree o f n o r m a l i t y .  The b a s i s f o r measurement o f n o r m a l i t y  a f f e c t e d the t r e n d o f n o r m a l i t y p e r c e n t a g e ( b a s a l a r e a , than c u b i c measures and l a s t board measures) i n f l u e n c e d by m o r t a l i t y .  and t h i s t r e n d was s t r o n g l y  38. N o r m a l i t y o f s t o c k i n g c o n d i t i o n does n o t remain i n nature  (Wellwood 194-3).  stationary  I n c o m p a r i s o n , u n d e r - s t o c k e d stands would  have a l o w e r r a t e o f m o r t a l i t y b u t a g r e a t e r r a t e o f diameter t h a n normal s t a n d s .  Alternatively  growth  o v e r - s t o c k e d stands would have  g r e a t e r m o r t a l i t y from s u p p r e s s i o n and a lower r a t e o f d i a m e t e r growth.  Thus i t seemed both t h e u n d e r - s t o c k e d and o v e r - s t o c k e d  s t a n d s moved toward n o r m a l i t y ,  each i n i t s own way.  The t r e n d s t o  n o r m a l i t y o f u n d e r - s t o c k e d stands were found from t h e permanent sample p l o t s . I t was found t h a t t h e age o f Douglas f i r was an i m p o r t a n t f a c t o r i n d e t e r m i n i n g the r a t e o f i n c r e a s e towards n o r m a l i t y and G i r a r d 194-3).  (Briegleb  Young stands o f a g i v e n d e n s i t y i n c r e a s e d toward  n o r m a l i t y were r a p i d l y than o l d e r s t a n d s .  Bell  (1964.) c o n f i r m e d  B r i e g l e b and G i r a r d ' s 194-3 r e p o r t b y s t u d y i n g 7 1 ^ a c r e p l o t s o f Douglas f i r from 1953-62.  He c o n c l u d e d t h a t young p o o r l y stocked  stands i n c r e a s e d r a p i d l y towards n o r m a l i t y , f o r more r a p i d l y  than  past studies i n d i c a t e d . Gevorkiantz  (1944) s t a t e d t h a t the t r e n d o f f o r e s t stands  towards n o r m a l i t y had g a i n e d g r e a t e r r e c o g n i t i o n .  Many s t u d i e s have  shown t h a t number o f t r e e s i s r e l a t e d t o average stand diameter and v a r i e d w i t h d i f f e r e n t u n i t s o f measurements. s t r u c t u r e which r e f l e c t s  However a d e f i n i t e  t h e i r normal development' c o u l d be d e t e c t e d .  B i e k f o r d et.al.(1957) gave two approaches t o i d e a l s t o c k i n g : ( l )  the  c a p a c i t y o f an a c r e t o support t r e e s , which was t h e r e l a t i v e o c c u p a t i o n o f t r e e s w i t h a p p r o p r i a t e adjustment f o r m i x t u r e by s p e c i e s and a g e .  39. (2)  the s t o c k i n g t h a t r e s u l t e d i n maximum y i e l d , which was  b e s t s t o c k i n g , e v e r y f o r e s t manager would l i k e t o h a v e .  the  The f i r s t  approach was w i d e l y used and c o u l d be e a s i l y r e c o g n i z e d on the ground w h i l e the second, was more v a l u a b l e but f a r more complex. The concept o f a normal f o r e s t was d e v e l o p e d i n Europe as an i d e a l g u i d e f o r f o r e s t managers.  It  was based on normal i n c r e m e n t ,  d i s t r i b u t i o n o f age c l a s s e s and normal growing s t o c k . stand was the same as a f u l l y - s t o c k e d stand where a l l utilized,  above and below the  normal  Thus a normal the s i t e  was  soil.  Chapman and Meyer (194-9) s t a t e d t h a t d e n s i t y o f s t o c k i n g v a r i e d v e r y w i d e l y due t o t h e f a c t t h a t the stand had passed t h r o u g h a l o n g p e r i o d under the i n f l u e n c e d o f n a t u r a l f a c t o r s .  Volume d i d  not a d e q u a t e l y p o r t r a y t h e growing s t o c k because new growth p o t e n t i a l was based upon b o l e a r e a and not volume (Leren Gill t h r e e ways:  (a)  1943).  (1950) e x p l a i n e d the d i s t r i b u t i o n o f r e g e n e r a t i o n I n s y s t e m a t i c d i s t r i b u t i o n can be shown by newly  p l a n t a t i o n s where the t r e e s are e v e n l y spaced b u t t h i s cannot be f o u n d i n n a t u r a l after planting,  (b)  planted  condition  stands o r even i n p l a n t a t i o n s sometime  chance o r random d i s t r i b u t i o n i s p o s s i b l e  n a t u r a l f o r e s t stands but w i t h v a r y i n g degree o f p r o b a b i l i t y . h i g h e r t h e number of t r e e s t h e g r e a t e r i t  in The  i s f o r the quadrat t o be  s t o c k e d and (c) Heterogeneous d i s t r i b u t i o n i s a l s o o f t e n f o u n d i n n a t u r a l f o r e s t because o f seed source and s i t e .  These v a r y i n g  d i s t r i b u t i o n would a f f e c t the degree o f s t o c k i n g as w e l l as d e n s i t y of  stands.  40. Gingrich  (1964) d e f i n e d s t o c k i n g as a q u a l i t a t i v e term  r e f e r r i n g t o t h e degree of adequacy o f a stand c o n d i t i o n t o meet a t i m b e r management o b j e c t i v e .  It  c o u l d e i t h e r be s p e c i f i e d as  degree o f o c c u p a t i o n o f s i t e o r growth. determine o c c u p a t i o n , f i r s t l y , et.al.(1940) the t r e e ,  the  Two methods were used t o  by t r e e a r e a r a t i o used by Chrisman  t h a t the growing space of t r e e depended on t h e s i z e o f  thus b e i n g r e l a t e d t o d . b . h . by a second p a r a b o l a . Tree-area  where:- a , b , c ,  =  '/  2  aN + b £ D ' + c2D  are r e g r e s s i o n c o n s t a n t s , N i s t h e number o f  trees  2 per a c r e ,  ZD i s t h e sum o f i n d i v i d u a l d . b . h . and £D  i s the  squares  of the d . b . h . Crown d i a m e t e r s c o u l d a l s o be s u b s t i t u t e d f o r d . b . h . because h i g h c o r r e l a t i o n o f crown w i d t h and d . b . h . had been found by many a u t h o r s . The second concept o f measurement o f s t o c k i n g by growth was perhaps more i m p o r t a n t because t h e space o c c u p i e d and u t i l i z e d by a t r e e o f a given d . b . h . varied greatly,  and the number o f t r e e s a l s o  w i t h t h e same crown c l o s u r e p e r c e n t a g e .  The a v a i l a b l e  varied  growing space  can g r e a t l y i n f l u e n c e growth r a t e o f an i n d i v i d u a l t r e e .  He found t h a t  f u l l y open grown oaks and h i s k o r y s w e l l d e f i n e d t h e l i m i t s o f growing space and independent o f s i t e and age as found by K r a j i c e k It  was a l s o found t h a t the average  et.al.(I96l).  stand s t r u c t u r e v a r y g r e a t l y  had l i t t l e e f f e c t on s t o c k i n g t h u s t h e y c o n c l u d e d t h a t stand can be i g n o r e d i n t h e a p p r a i s a l o f s t o c k i n g except i n a few  structure specific  c a s e s and t h e problem o f u n d e r - s t o c k i n g i n young stands was n o t i f m o r t a l i t y was w e l l d i s t r i b u t e d .  but  serious  4l. The p o s s i b l e use o f G e h r h a r d t ' s f o r m u l a was d i s c u s s e d by G e v o r k i a n t z (1937) The two f o r m u l a e  and he t e s t e d i t  are:-  Z r = bZ(2-b)  (tolerant  Zr = bZ(l.7-0.7b) where:- Z r i s  out i n 1937 w i t h hardwood s t a n d s .  species)  (intolerant  species)  the p e r i o d i c growth o f the u n d e r - s t o c k e d stands f o r  the n e x t decade, b i s t h e p r e s e n t degree o f ( r a t i o o f a c t u a l and normal b a s a l a r e a s ) ,  stocking  and Z the  c o r r e s p o n d i n g growth as shown by a normal y i e l d The numbers i n p a r e n t h e s e s a r e e m p i r i c a l  table.  constants  determined by s p e c i a l s t u d i e s which showed a  definite  r e l a t i o n s h i p between growth p e r c e n t and d e n s i t y o f stocking. He a l s o found t h a t the c o n s t a n t f o r t o l e r a n t  s p e c i e s c a l c u l a t e d was  t h e same as G e h r h a r d t ' s by t h e f o r m u l a b e l o w : ~  -  Pu + Pb "p  where:- Pu i s t h e growth p e r c e n t o f a c t u a l  stands.  P  i s t h e growth p e r c e n t of normal s t a n d s .  b  i s t h e degree o f s t o c k i n g ( r a t i o o f a c t u a l t o normal basal area). It  i s i m p o r t a n t t o note t h a t G e h r h a r d t ' s formulae do n o t t a k e  age as a c o n t r o l l i n g f a c t o r t o d e n s i t y o f s t o c k i n g , t h e r e f o r e i t  can  be u s e d f o r un-even aged stands t o o . Duerr (1938)  experimented f u r t h e r w i t h G e h r h a r d t ' s  by u s i n g t h e f o r m u l a below-to determine the P K  *  P -  P (1-b)  constant:-  formulae  42 where: - s m a l l p and l a r g e P a r e growth p e r c e n t f o r the next 10 y e a r s o f u n d e r - s t o c k e d and normal-stocked stands respectively,  and b i s the  density.  He found t h e c o n s t a n t f o r i n t o l e r a n t  s p e c i e s t o be 0 . 6 t o 0 . 7 ,  I n t e r m e d i a t e s p e c i e s 0 . 8 t o 0 . 9 and t o l e r a n t  s p e c i e s 1.0 t o 1 . 1 ,  thus  showing t h a t growth towards n o r m a l i t y b e i n g more r a p i d among t o l e r a n t species.  He suggested t h a t where a c t u a l d e t e r m i n a t i o n o f  Gehrhardt's  c o n s t a n t cannot be done, t h e f o r m u l a can use K f o r t h e known degree of tolerance of species concerned.  G e h r h a r d t ' s f o r m u l a can be  a p p l i c a b l e t o any t y p e o f y i e l d t a b l e p r o v i d e d t h e p r o p e r c o n s t a n t i s u s e d , but when a p p l i e d t o n e t gtowth t h e e f f e c t o f m o r t a l i t y upon t h e f o r m u l a must be d e t e r m i n e d . In g e n e r a l c o n c l u s i o n i t  can be s a i d t h a t two methods a r e  w i d e l y used t o measure d e n s i t y i n t h e p a s t , one i s by number o f i n r e l a t i o n t o d . b . h . and t h e o t h e r i s t h e growth.  It  trees  i s a l s o agreed  t h a t t h e u n d e r - s t o c k e d stands w i l l c o n t i n u e t o t r e n d towards  normality  and o v e r - s t o c k e d stands w i l l be r e t a r d e d by m o r t a l i t y back t o normal stocking.  Other methods of s t o c k i n g d e t e r m i n a t i o n w i l l be d i s c u s s e d  later. Stand  density S t a n d d e n s i t y was d e f i n e d by the F o r e s t r y Terminology  ( S o c i e t y o f American F o r e s t e r s 1950) as t h e d e n s i t y o f s t o c k i n g i n terms o f number o f t r e e s , a per-acre b a s i s . accurate,  b a s a l a r e a , volume and o t h e r c r i t e r i a ,  The q u a n t i t a t i v e  expression of stand d e n s i t y  simple and u s e f u l terms has l o n g b a f f l e d f o r e s t  on in  43. measurationists.  Obviously i t  cannot be s i m p l y the number o f  trees  p e r u n i t a r e a , because a c e r t a i n number i n a young s t a n d may represent c o n d i t i o n s of incomplete u t i l i z a t i o n o f the a r e a ,  while  the same number i n an o l d s t a n d may r e p r e s e n t complete u t i l i z a t i o n . Czarnowski (1961)  and Smith (1966) u s e d crowding t o d e s c r i b e  stand  d e n s i t y measurement. Many a u t h o r s have t r i e d t o f i n d t h e most s u i t a b l e way r e p r e s e n t d e n s i t y and v a r i o u s methods were r e p o r t e d . i n d e x was proposed by Reineke  (1933)  Stand  f o r even-aged s t a n d s .  density He u s e d  t h e r e l a t i o n o f l o g a r i t h m o f number o f t r e e s p e r a c r e t o t h e i r d.b.h.  The shape o f t h e curve o f maximum number of t r e e s p e r  over average d . b . h . i s  average acre  concave upwards, r a p i d l y f a l l i n g f o r medium  d i a m e t e r s and f l a t t e n i n g  as the l a r g e r d . b . h . a r e r e a c h e d .  r e p l a c e d conventional p l o t t i n g with use of l o g a r i t h m i c paper thus making t h e l i n e s be used  to  Reineke  cross-section  s t r a i g h t and t h e f o r m u l a below can thus  easily. LogN  =  -1.605 l o g D + K  where:- N i s the number o f t r e e s p e r a c r e , D i s t h e i r d.b.h.,  and K i s  average  a constant varying with s p e c i e s .  The r e f e r e n c e c u r v e d e f i n i n g t h e maximum K i s 4 . 6 0 5 , t h e c u r v e  passes  t h r o u g h t h e p o i n t r e p r e s e n t i n g 10 i n c h e s average d . b . h . and 1,000 per a c r e .  The s t a n d d e n s i t y i n d e x p e r m i t s t h e d i r e c t  between s p e c i e s by u s i n g t h e r e f e r e n c e c u r v e . construct,  It  is  comparison a l s o easy  i n d e p e n d e n t l y o f age and s i t e i n d e x , and good f o r  applicability.  trees  Stand d e n s i t y i n d e x has proven t o be u s e f u l .  to  general Stand  44. b o l e i n d e x ( S . B . T . ) which i s t h e m u l t i p l i c a t i o n o f d . b . h . , and number o f t r e e s d i v i d e d by a c o n s t a n t , advantages t o M u l l o y (1944) Spurr  (1952)  seemed t o have some  but t h e s e have y e t t o be p r o v e n .  confirmed Reineke's  (1933) r e p o r t t h a t  d e n s i t y i s u n r e l a t e d t o age and s i t e q u a l i t y o f s t a n d . et,al.(1957)  height  stand  Bickford  c o n c l u d e d t h a t crown c l o s u r e and o t h e r crown  variables  were not u s e d t o measure s t a n d d e n s i t y because t h e y o n l y show t h e a r e a o c c u p i e d but t h i s w i l l be proved o t h e r w i s e here i n a r e v i e w o f more r e c e n t l i t e r a t u r e .  The b a s i c v a r i a b l e s used w e r e : - d . b . h . ,  h e i g h t , form and number o f t r e e s p e r a c r e expressed as b a s a l a r e a , number o f t r e e s p e r a c r e ,  volume o r o t h e r c r i t e r i a .  d i f f e r e n t methods have t o be used t o s u i t d i f f e r e n t  It  seemed t h a t  silvicultural  systems and stand c o m p o s i t i o n s but t h e measurements must be c l e a r , consistent, objective  and easy t o a p p l y .  When number o f t r e e s  r e l a t i o n t o d . b . h . i s used as an i n d i c a t o r o f stand d e n s i t y , u s e d i n the form o f stand d e n s i t y i n d e x .  Smith e t , a l . ( 1 9 6 1 )  is  T h i s method e l i m i n a t e d age  and s i t e as v a r i a b l e s and may be i n c o n s i s t e n t . appear t o be a good measure o f  it  in  Thus t h i s does n o t  density.  s t a t e d t h a t an advantage o f the  average  d . b . h . approach i n the e s t i m a t i o n o f y i e l d i s t h e f a c t t h a t n o r m a l i t y by number o f t r e e s i s the same as n o r m a l i t y by volume.  Volume i s  another measure o f stand d e n s i t y based on £he number o f t r e e s , h e i g h t and form ( B i c k f o r d that i t quality,  et„al.l957).  d.b.h.,  The d i s a d v a n t a g e o f volume  a l s o i n c l u d e s dead heartwood and does not i n d i c a t e the wood thus i t  does n o t seem t o be a good measure o f  density.  is  45. Caarnowski (1961)  d i s c u s s e d crovm d e n s i t y measurement and t o  measure s t a n d d e n s i t y he used a "crowding f a c t o r " which was  the  r a t i o o f the a c t u a l number o f t r e e s per u n i t a r e a t o t h e normal number.  The average d . b . h . of t h e stand i s p r o p o r t i o n a l t o  crowding f a c t o r .  this  Another measure o f d e n s i t y used by him was a  "compactness f a c t o r " ,  the r a t i o between the a c t u a l volume p e r  and the maximum volume a t t a i n a b l e f o r the a c r e .  acre  The f o l l o w i n g  f o r m u l a e were used t o c a l c u l a t e the maximum volume (Mmax) and compactness  factor:Mmax  =  K . H . N  w  where: K and w a r e c o n s t a n t v a l u e f o r the s p e c i e s , H i s the h e i g h t , and N w i l l be a c o n s t a n t number o f t r e e s f o r a g i v e n q u a l i t y and Mmax i s X  site  the maximum volume.  = Mmax  where: X i s the compactness f a c t o r and M i s the a c t u a l volume. B a s a l a r e a c o u l d be u s e d t o measure stand d e n s i t y b u t from b a s a l a r e a too l i t t l e i s known about t h e s t a n d .  Howard  (1957)  suggested t h a t t h e s t a n d s h o u l d be s p l i t i n t o diameter c l a s s e s o f s a p l i n g s , p o l e s , and sawtimber f o r b e t t e r b a s a l a r e a measurement. B a s a l a r e a seemed t o be t h e b e s t measure o f s t a n d d e n s i t y which was w i d e l y u s e d i n Europe ( B i c k f o r d e t a l . l 9 5 7 ) . t  It  i s easy t o use and  when m u l t i p l i e d by average h e i g h t and form f a c t o r g i v e s c u b i c volume. However,  t h e r e are the problems o f g i v i n g e q u a l weight t o o l d and  young t r e e s , square i s  t o suppressed and dominant t r e e s ,  and a l s o whether  the  e q u a l t o the exponent o f d . b . h . Tree h e i g h t i s a l s o i g n o r e d  46. h e r e , and i t a l s o g i v e s e q u a l weight t o heartwood which may n o t be sound and t o sapwood which i s i n d i c a t e d by t h e growth o f t h e cambium. The 10 f a c t o r angle guage was found t o be b e s t f o r measurement o f s t a n d d e n s i t y o f Ponderosa p i n e o f d . b . h . from 1 2 . 8 t o 1 8 . 7 i n c h e s (Lemmon and Schumacher I960) and t h e y used t h e f o r m u l a below t o c a l c u l a t e basal area f a c t o r . B.A.F.  =  43560/(4d)  2  where: d i s t h e s t u d i e d t r e e ' s d . b . h . i n f e e t . Moessner (1964) c o n s t r u c t e d two b a s a l a r e a t a b l e s w i t h a e r i a l photo measurements.  One i s f o r mixed s p e c i e s i n t h e N o r t h e r n  Rocky mountains w i t h t h e e q u a t i o n : B.A.  = 0.24701H - 0.77068C + 0.02116HC + 0 . 0 0 0 1 4 H +'0.00231C  2  + 15.92380  2  and t h e o t h e r f o r ponderosa p i n e i n t h e southwest w i t h t h e e q u a t i o n below:B.A.  = 0.816205 - 0.83765C + 0.01902HC + 0 . 0 0 5 4 5 H  2  + 0 . 0 1 8 3 1 C + 55.32472 2  He used average stand h e i g h t (average v i s i b l e height, w i t h a ground check)  crown c l o s u r e and crown d i a m e t e r , a l l from a e r i a l p h o t o g r a p h s . Nelson et^al.. (1963) s t u d i e d a number o f s t a n d d e n s i t y  measures; number o f t r e e s , s t a n d d e n s i t y i n d e x , and b a s a l a r e a o f l o b l o l l y p i n e and recommended t h a t b a s a l a r e a be used f o r f u t u r e c u b i c f e e t growth a n a l y s i s . Crown c o m p e t i t i o n f a c t o r density.  (CCF) i s another measure o f s t a n d  T h i s was i n t r o d u c e d by K r a j i c e k  et.al.(1961).  T h i s i s made  47 by u s i n g t h e a r e a o f crowns o f open t r e e s t o e x p r e s s t h e crowns o f the s t a n d as i f  t h e y were f u l l y opened t o g i v e a p e r c e n t a g e o f an  a c r e c a l l e d Maximum crown a r e a ( M . C . A . ) .  The sum o f a l l M . C . A . on  an a c r e g i v e s the crown c o m p e t i t i o n f a c t o r and t h e minimum s t o c k i n g for f u l l  s i t e u t i l i z a t i o n a t open d e n s i t y .  The denser the s t a n d the  g r e a t e r i s the CCF, w i t h 100 r e p r e s e n t i n g f u l l o c c u p a t i o n by t h e i r open crowns.  It  seemed t h a t s i t e and age d i d n o t i n f l u e n c e CCF much.  V e z i n a (1963b) a g a i n r e p o r t e d on crown c o m p e t i t i o n f a c t o r  (CCF)  c o n c l u d e d t h a t l i t t l e c o r r e l a t i o n e x i s t e d between CCF and s i t e but t h e r e was a s i g n i f i c a n t d e c r e a s e of CCF w i t h a g e .  and index  Plots with the  same CCF c o u l d have d i f f e r e n t s t a n d d e n s i t y i n d e x and v i c e v e r s a .  The  number o f t r e e s v a r i e d c u r v i l i n e a r l y f o r any g i v e n CCF and l i n e a r l y index values. Spurr  (1962) demonstrated t h e use o f p o i n t d e n s i t y f o r  experimental purposes.  T h i s measure u t i l i z e s the a n g l e subtended by  a l l t h e t r e e s s u r r o u n d i n g the t e s t p o i n t r a t h e r than a p o i n t sample t o d e f i n e stand d e n s i t y .  \  The b a s a l a r e a formulae a r e shown below:-  = U-£)75.625(^)  2  where: D i s t h e d i a m e t e r a t p r e s e n t h e i g h t and L i s t h e d i s t a n c e from the centre p o i n t .  The c o n s t a n t  75.625 i s the q u o t i e n t o f  43560 ( s q . f t . p e r a c r e ) d i v i d e d by 576, t h e p r o d u c t o f t h e 144 n e c e s s a r y t o c o n v e r t square i n c h e s t o square f e e t and t h e 4 r e p r e s e n t i n g the square o f 2 t o c o n v e r t r a d i u s t o  diameter.  48.  Bn  = (n-i)75.625 (g^)  2  where: n i s t h e n t h t r e e . T h e r e f o r e t h e mean b a s a l a r e a f o r m u l a becomes Bn = 75.625 &&) 2  * 3/2&)  £(5n) _7 2  2  + ... • n -  Thus a p r e c i s e s t a n d d e n s i t y measurement c a n be made around a apecific point i n a forest stand. W i t t g e n s t e i n and A l d r e d (1967) s t u d i e d t h e e s t i m a t i o n o f t r e e volumes and they a l s o used o v e r l a p p i n g p r o p o r t i o n o f t r e e crowns t o express t h e s u p p r e s s i o n o f one t r e e by i t s n e i g h b o u r s . However,  t h i s i s an e s t i m a t e t h a t i s dependent on t h e i n t e r p r e t e r s  judgement.  They e x p r e s s e d t h e degree o f crowding by t h e number o f  t r e e s growing i n a c i r c u l a r a r e a , w i t h r a d i u s e q u a l t o t h e sample tree height.  Another v a r i a b l e  expressing the r e l a t i o n s h i p o f a tree  t o i t s n e i g h b o u r s was measured by t h e number o f t r e e s n e a r e s t and taller  than t h e sample t r e e . The above r e v i e w o f s t a n d d e n s i t y i s m a i n l y based on t h e  number o f t r e e s ,  volume, b a s a l a r e a and crown c o m p e t i t i o n f a c t o r  and a r e v i e w o f t h e i n f l u e n c e o f v a r i o u s crown v a r i a b l e s , and h e i g h t w i l l f o l l o w l a t e r .  diameter  That b a s a l a r e a p e r a c r e i s t h e b e s t  f o r measurement o f s t a n d d e n s i t y was shown by t h e s e a u t h o r s . B i c k f o r d et,al.(1957) mentioned t h a t b a s a l a r e a was u s e d f o r European S c o t s p i n e b u t t h e y d i d n o t e x p l a i n why.  effectively  The main r e a s o n  f o r t h i s i s t h a t b a s a l a r e a can o n l y measure stand d e n s i t y  effectively  under r e l a t i v e l y s t a n d a r d c o n d i t i o n s o f s t o c k i n g and crowding e . g . i n even-aged, normal stands o r i n normal p l a n t a t i o n s and i t i s i n e f f i c i e n t i n n a t u r a l f o r e s t s o r w i t h abnormal s t a n d s .  49. Crown v a r i a b l e s and t r e e v a r i a b l e s used t o determine  stand  d e n s i t y and s t o c k i n g H e i g h t , d . b . h . , crown w i d t h , crown c l o s u r e , crown l e n g t h , and t h e i r r a t i o s are b e i n g adopted as measures o f s t a n d d e n s i t y and s t o c k i n g , more f r e q u e n t l y a t p r e s e n t .  T h i s i s because o f the h i g h  c o r r e l a t i o n between them, e . g . p r e v i o u s i n v e s t i g a t i o n s  revealed  t h a t crown w i d t h i s h i g h l y c o r r e l a t e d w i t h diameter a t  breast  height  (Minor 1951,  Warrack 1959,  & 1963,  Krajick _ _ . _ l . 1 9 6 l ,  F e r e e 1953,  Smith 1958,  1966,  Enle  1959,  Smith e t . _ l .  The i n c l u s i o n o f t r e e h e i g h t improves t h e c o r r e l a t i o n w i t h  1961). d.b.h.  V e z i n a 1952  (Nash  Thus i t  1948, G l o e s s a l o 1950, W i l l i n g h a m 1957 and S p u r r I960).  seems t h a t we a r e t u r n i n g towards the b i o l o g i c a l a s p e c t  because a l l t h e above v a r i a b l e s a r e a f f e c t e d by environment and inherent  characteristics. The use o f h e i g h t r e l a t i o n s t o d e n s i t y has been r e p o r t e d  by a number o f a u t h o r s ; GevorkLantz  (1944) s t u d i e d h e i g h t and d . b . h .  r e l a t i o n s f o r d e t e r m i n a t i o n o f n o r m a l i t y by t h e f o r m u l a below:  where: A i s t h e age o f s t a n d , H i s the h e i g h t , D i s the d . b . h . , and C and d a r e c o n s t a n t s , v a r y i n g w i t h s p e c i e s o r t o l e r a n c e . He t h e n t r a n s f o r m e d t h e above f o r m u l a i n t o l o g a r i t h m i c forms representing a straight log(AD) where:  'C  is  equal to  the  intercept.  line.  = b log(AH) 'a',  - a  ' b ' i s t h e s l o p e o f the l i n e and  'a  1  50. He found t h a t the h i g h e r the  ' b ' and ' a ' v a l u e s the more  i n t o l e r a n t and v i c e v e r s a f o r t o l e r a n t s p e c i e s . seemed t o have an ' a ' v a l u e o f 1.011 o v e r - s t o c k e d stands  Normal stands  and ' b ' o f 1.032, and an  ' b ' was 0.982 and ' a  1  was 0.943.  G e v o r k i a n t z (1947) r e p o r t e d t h a t i n J a v a , Ferguson i n 1933  used h e i g h t t o express s t o c k i n g o f teak  (Tectona g r a n d i s  S.F.)  stands by the f o r m u l a below: SH = 10745.7 x =±r v n where: H i s the upper h e i g h t o r average h e i g h t o f 100  tallest  t r e e s p e r h e c t a r e i n m e t e r s , S i s t h e s p a c i n g o f the upper h e i g h t , and n i s the number o f t r e e s p e r h e c t a r e . The r e d u c t i o n o f the above f o r m u l a t o an a c r e b a s i s w i l l take same form as W i l s o n ' s f o r m u l a i n N  the  1946  -43560 "  (SH)2  The o n l y d i f f e r e n c e i s t h a t W i l s o n u s e d average h e i g h t i n s t e a d o f upper h e i g h t .  G e v o r k i a n t z suggested t h a t  'S* o r s p a c i n g should be  used as a percentage o f average h e i g h t w i t h o r w i t h o u t  consideration  o f suppressed t r e e s due t o the f a c t t h a t t h e s e t r e e s w i l l not  last  t o the end o f t h e r o t a t i o n . Briegleb  (1952) proposed t h e use o f diameter h e i g h t  r e l a t i o n s as a measure o f d e n s i t y , he d e s c r i b e d t h r e e Douglas stands i n Denmark as shown i n t a b l e  11.  fir  51. T a b l e 11 - D e n s i t y , by v a r i o u s measures, o f t h r e e Douglas f i r stands a f t e r  thinning  Stand H 1st thinning 20 y e a r s 6th t h i n n i n g 35 y e a r s  Measure  contrasting  Stand B  1st thinning 55 y e a r s  Stand C 1st thinning 20 y e a r s 12th t h i n n i n g 55 y e a r s  Average dbh ( i n . )  10  10  17  Average  60  90  93  ht.(ft.)  Average cw ( f t . )  12.6  8.6  19.2  Average space trees (ft.)  14.6  10.8  22.6  37.3  31.7  58.4  206  203  142  between  Average crown l e n g t h Density  (per a c r e  (ft.)  basis)  No. o f t r e e s Volume Cubic f e e t Bole area  (m.cu.ft.) (m.sq.ft.)  Stand i n t e n s i t y *  (sq.ft.)  Crown p r o j e c t i o n  (m.sq.ft.)  Crovm s u r f a c e  (m.sq.ft.)  * stand i n t e n s i t y  2.9  7.9  4.9  17.7  47.8  13.8  4.8  88  53  25.7  21.6  24.6  304  319  299  i s stem volume i n c u . f t . d i v i d e d by average  The o n l y two v a r i a b l e s  s i m i l a r i n a l l t h e t h r e e stands were crown  p r o j e c t i o n ( a r e a o f crovm p r o j e c t e d onto a h o r i z o n t a l s u r f a c e ) surface  stand h e i g h t .  and crown  ( s u r f a c e o f crown p a r a b o l o i d ) which a r e p r o b a b l y r e l a t e d t o  photosynthetic area.  Thus B r i e g l e b c o n c l u d e d t h a t volume growth i s b e s t  as a normal d e n s i t y i n d i c a t o r . '  He f u r t h e r made a h y p o t h e s i s t h a t  crown  w i d t h and l e n g t h i s r e l a t e d t o t r e e diameter and h e i g h t , u s i n g t h e formulae below:Crown w i d t h  (ft.)  Crown l e n g t h ( f t . )  =  5.88 + 1 . 4 6 ( d b h ( i n . ) ) - 0.184 ( h e i g h t  = 12.0  + 3 . 6 3 ( d b h ( i n . ) ) - 0.184 ( h e i g h t  (ft.)) (ft.))  52. The m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t s were 0.91 and O . 8 4 r e s p e c t i v e l y highly  both  significant. B r i e g l e b a l s o measured d e n s i t y by u s i n g the average dbh, and  average h e i g h t f o r s e t t i n g standards f o r number, b a s a l a r e a o r growing s p a c e . He found t h a t t h e number o f t r e e s expressed as a p e r c e n t o f normal f o r d.b.h.  average  e q u a l s - 34.62 + 1.24.5 times stand h e i g h t expressed as a percentage o f  normal h e i g h t f o r average d . b . h . o f 0.59 was o b t a i n e d but i t number o f t r e e s per  A highly significant correlation  coefficient  o n l y accounted f o r 3 5 p e r c e n t of the v a r i a t i o n  in  acre.  Aspsey ( I 9 6 l ) ,  Pearson (1962),  Johnson (1962)  s t u d i e d the crown width o f open- and f o r e s t - g r o w n t r e e s . w i d t h ' s r e l a t i o n s h i p to other t r e e v a r i a b l e s  and G i l p i n  (1965)  They a n a l y s e d crown  and came t o s i m i l a r c o n c l u s i o n s  as l i s t e d i n t a b l e 1 2 . T a b l e 12 - Simple c o r r e l a t i o n c o e f f i c i e n t determination (r  (r)  and c o e f f i c i e n t  of  ) for•crown w i d t h on DBH and Height  o f f o r e s t and open s t a n d s .  Author  Species  Tree Variables  open-grown r  2 r 68.5 30.4  13.0  68.5  .853** .578**  72.8 33.2  .937**  .864**  87.8 74.7  .853** .722**  72.8 52.1  DBH Ht.  .729** .431**  53.1 18.6  .567** .440*  32.1  DBH Ht.  .926** .823**  85.7 67.8  .896** . .758**  80.3 57.5  DBH Ht.  .920** .779**  Pearson  B l a c k Cottonwood  DBH Ht.  .816** .361**  Johnson  Douglas  'DBH Ht.  Engelmann spruce  Sitka  spruce  r  2  .818** .551**  Red a l d e r  Gilpin  r  84.6  Aspsey  fir  dens e-grown(forest)  61.5  ( T a b u l a t e d v a l u e s o n l y show two o f the most s i g n i f i c a n t  values)  19.4  53. From t h e t a b l e above i t  can be seen t h a t diameter a t b r e a s t  f o r a l l f o u r a u t h o r s e x p l a i n e d most o f the v a r i a t i o n s ,  and h e i g h t  i s t h e second b e s t t o e x p l a i n v a r i a t i o n i n crown w i d t h . Bailey  height  Smith and  (1964.) r e p o r t e d t h a t i n c r e a s e o f crown w i d t h was c l o s e l y  a s s o c i a t e d with stand d e n s i t y .  They suggested t h a t  stand d e n s i t y  s h o u l d be c o n s i d e r e d t o g e t h e r w i t h s t o c k i n g when crown w i d t h i s t o e s t i m a t e number o f t r e e s per a c r e o f e i t h e r Douglas f i r lodgepole p i n e .  There i s a l s o a s i g n i f i c a n t d i f f e r e n c e  crown w i d t h o f open-and f o r e s t - g r o w n Bonnor  used  or  between  trees.  (1964) s t u d i e d t h e c o r r e l a t i o n o f d . b . h . w i t h crovm  w i d t h and h e i g h t t o determine t h e i r i n f l u e n c e s on s t a n d d e n s i t y expressed by number o f t r e e s p e r a c r e .  Diameter a t b r e a s t  height  was e s t i m a t e d by the f o r m u l a b e l o w : D = a + bWH where: D i s d . b . h . , a i s i n t e r c e p t , regression,  b i s the c o e f f i c i e n t  of  H i s h e i g h t and W i s crown w i d t h .  He found t h a t the r e g r e s s i o n o f d . b . h . on crown w i d t h and h e i g h t was not s i g n i f i c a n t l y a f f e c t e d by s t a n d d e n s i t y and gave two r e a s o n s f o r this.  A first  p o s s i b i l i t y was t h a t i n f u l l y  s t o c k e d stands  variations  i n stand d e n s i t y a f f e c t e d b o t h d . b . h . and crown w i d t h and t o some extent h e i g h t .  A second p o s s i b i l i t y was t h a t number o f t r e e s  per  a c r e c o n s t i t u t e a s t a n d parameter, whereas d . b . h . , crown w i d t h and height c o n s t i t u t e t r e e parameters. R a t i o o f crown w i d t h t o diameter a t b r e a s t h e i g h t (CW/D) were d e f i n e d by Van S l y k e  (1964) as the r a t i o o f average diameter  i n f e e t o f t h e crovm a t i t s w i d e s t p a r t  (CW)  t o t r e e diameter  (in  inches)  54. at breast height  (dbh = D ) .  R a t i o o f Height t o crown width (H/CW)  was d e f i n e d as the a b s o l u t e r a t i o o f t o t a l t r e e h e i g h t width  (H)  to  crown  (CW).  H e i g h t crown w i d t h r a t i o  (H/CW)  Height/crown w i d t h r a t i o was f i r s t used by Count o f Denmark d u r i n g 1800-1827.  Hummel used h e i g h t / s p a c i n g r a t i o  s p a c i n g arrangement o f t r e e s t o the upper h e i g h t (H) ( V e z i n a 1963a). was a r b i t r a r i l y  of  with  stand  The s t a n d a r d d e n s i t y o f 20 p e r c e n t o f upper h e i g h t a s s i g n e d an i n d e x o f 1.0 and a l l  other  densities  were e x p r e s s e d by the number of t r e e s i n r e l a t i o n t o t h e density.  Reventlow  This i s  c a l l e d Hummel's stand d e n s i t y i n d e x ,  standard  calculated  by the f o r m u l a below:H  where:  =  -m.  o  r  d  =  J & &  d i s the d . b . h . and N i s t h e number o f  Another i n d e x was t h e B e c k i n g ' s  trees.  spacing f a c t o r using  triangular  s p a c i n g t o c a l c u l a t e number o f t r e e s and t h e s p a c i n g was e x p r e s s e d as a p e r c e n t a g e o f upper h e i g h t by t h e f o l l o w i n g f o r m u l a e : -  ^ Dittmar  S F  =  diioo)  (I960) ^found t h a t t h e o l d e r t h e  stand the h i g h e r was  s p a c i n g f a c t o r f o r a r e l a t i v e b a s a l a r e a and c o n c l u d e d t h a t  the Becking*s  method was v e r y i n g e n i o u s f o r c a r r y i n g out t h i n n i n g on a n u m e r i c a l basis.  55. Smith (1966) r e p o r t e d t h a t different densities.  H/CW can be c a l c u l a t e d  Open s t a n d s w i l l have H/CW about 3 normal  about 5, and dense about 8.  These v a l u e s have shown t o be u s e f u l  g u i d e s a t l e a s t f o r young Douglas f i r  and l o d g e p o l e p i n e s t a n d s .  Crown w i d t h diameter b r e a s t h e i g h t r a t i o  (CW/D)  Smith and Ker (i960) u s i n g 96 open grown Douglas found t h a t  for  fir  so much o f the v a r i a t i o n was accounted f o r by crown  w i d t h , d . b . h . and CW/D r a t i o t h a t a d d i t i o n o f o t h e r v a r i a b l e s little  merit.  Smith e t » a l . ( 1 9 6 1 )  had  s t u d i e d the i n d e x o f square  s p a c i n g d i s t a n c e o r crown w i d t h t o d . b . h . r a t i o as a measure o f d e n s i t y and s t o c k i n g .  T h i s method was c o n v e n i e n t l y u s e d w i t h  average d . b . h . t o a s s e s s stand d e n s i t y .  Stands w i l l t h e n v a r y  d e n s i t y from a CW/D r a t i o o f 0 . 7 f o r d e n s e , t o about one f o r  in  fully-  s t o c k e d o r normal s t a n d s , t o two o r more f o r n e a r l y open t o opengrown s t a n d s .  The H/CW r a t i o was a l s o s t u d i e d but from t h e  c o r r e l a t i o n c o e f f i c i e n t s computed w i t h v a r i o u s v a r i a b l e s i t t h a t CW/D r a t i o was b e t t e r .  However,  t h e two r a t i o s are  changeable by use o f the r e g r e s s i o n e q u a t i o n s .  They a l s o  seemed  interstated  t h a t f o r a g i v e n r a t i o the b a s a l a r e a p e r a c r e was c o n s t a n t and sometimes l e s s t h a n normal b a s a l a r e a w i l l p r o v i d e t h e optimum c o m b i n a t i o n o f growth and growing  stock.  Aspsey (1961) r e p o r t e d on the r e l a t i o n s h i p between crown w i d t h and d i a m e t e r b r e a s t h e i g h t f o r open- and dense-grown r e d alder.  He assumed t h a t crown w i d t h corresponded t o square s p a c i n g  t o e s t i m a t e t h e number o f t r e e s o f a g i v e n d . b . h . t h a t would  fully  56. occupy an a r e a .  The CU/D r a t i o o f w e l l s t o c k e d stands was about  1.5 and f o r open-grown stands about 2 . 5 .  Pearson (1962)  reported  t h a t CW/D r a t i o o f b l a c k cottonwood was 1.667 f o r open-grown t r e e s and 1.671 f o r f o r e s t - g r o w n t r e e s . the s i m i l a r r e s u l t s .  Firstly,  He gave two main reasons f o r  t h e sample t r e e s may be i n c o r r e c t l y  c a t e g o r i z e d , meaning t h a t t h e stand c o u l d have proceeded from an open c o n d i t i o n and s t i l l was not c l o s e d , a l t e r n a t i v e l y was d e v e l o p e d from the dense to the p r e s e n t open s t a g e .  the  stand  Secondly,  t h e n a t u r e o f b l a c k cottonwood may be such t h a t the open-grown would n o t grow l a r g e r crown than f o r e s t - g r o w n t r e e s , (iii)  Crown c l o s u r e Smith e t . a l . ( 1 9 6 1 )  showed t h a t t h e r e may be 100 p e r c e n t  crown c l o s u r e a t the open l e v e l o f stand d e n s i t y w i t h o n l y oneq u a r t e r o f the number o f t r e e s p e r a c r e found i n a normal s t a n d o f t h e same average diameter b r e a s t h e i g h t . on the measurement o f t r o p i c a l f o r e s t t r e e s ,  Dawkins (1963)  reported  suggested t h a t when  any k i n d o f d e f i n i t e r e l a t i o n can be d i s c o v e r e d between crown w i d t h ( d . k . ) and diameter b r e a s t h e i g h t (d)  t h e n the p r e d i c t i o n o f  b a s a l a r e a d e n s i t y was p o s s i b l e f o r any g i v e n crown d e n s i t y closure)  and v i c e v e r s a .  (crown  The f o r m u l a below was u s e d : -  A r e a o f u n i t X crown d e n s i t y + (dk/d r a t i o )  = Basal area d e n s i t y ,  where: dk/d r a t i o i s the crown width/dbh r a t i o . The a c c u r a c y depends on how a c c u r a t e l y crown w i d t h can be measured o r p r e d i c t e d from diameter b f e a s t h e i g h t and v i c e v e r s a f o r photo measurements o f crown w i d t h .  aerial  57. Smith and B a i l e y  (1964) s t u d i e d the i n f l u e n c e s o f  s t o c k i n g and stand d e n s i t y on crown w i d t h .  They s t a t e d t h a t  100 p e r c e n t crown c l o s u r e o r f u l l s t o c k i n g o f u n i f o r m l y spaced t r e e s grown from an i n i t i a l l y  open stand d e n s i t y , w i l l advance t o  any l e v e l o f stand d e n s i t y , from open through normal t o d e n s e . Because of t h i s i t  i s n e c e s s a r y t o s p e c i f y degree o f c r o w d i n g , o r  s t a n d d e n s i t y i n a d d i t i o n t o crown c l o s u r e when f o r m u l a t i n g i d e a s as t o how s t a n d s s h o u l d be grown.  When p l a n n i n g t o use crown  w i d t h s o f i n d i v i d u a l t r e e s as a guide t o t h e number o f t r e e s  per  a c r e o r y i e l d t h a t can be e x p e c t e d , the degree o f crowding s h o u l d be c o n s i d e r e d . Comparison between s t a n d d e n s i t y and crown c l o s u r e was made by V e z i n a  (1964) who a g a i n c o n f i r m e d S m i t h ' s 1961 and 1964  r e p o r t s t h a t crown c l o s u r e i 3 a measure o f p o r t i o n o f a r e a o c c u p i e d by the t r e e crowns which can r e p r e s e n t a wide range o f stand d e n s i t i e s . He used Dawkin's b a s a l a r e a d e n s i t y f o r m u l a and found a h i g h l y s i g n i f i c a n t c o r r e l a t i o n c o e f f i c i e n t between crown c l o s u r e and b a s a l a r e a f o r j a c k p i n e which was b e t t e r t h a n balsam f i r (jack pine)  and  0.560 (balsam f i r ) ) .  v a r i a b l e s o f number o f t r e e s ,  (r =  0.664  He c o n c l u d e d t h a t the  three  diameter and h e i g h t f o r stand d e n s i t y  measurement a r e too c o m p l i c a t e d f o r p r a c t i c a l f i e l d a p p l i c a t i o n b u t t h e s e d a t a can g i v e v a l u a b l e i n f o r m a t i o n on o t h e r m e n s u r a t i o n aspects.  Crown w i d t h d i a m e t e r a t b r e a s t h e i g h t r a t i o i s recommended  f o r p r e d i c t i o n o f crown c l o s u r e and s t a n d d e n s i t y . e x p r e s s e d by b a s a l a r e a i s more u s e f u l i f a r e added.  Stand  density  number o f t r e e s and d . b . h .  He a l s o recommended t h a t d i f f e r e n t s t a n d d e n s i t y measures  58 be compared w i t h growth o f crown c l o s u r e and o t h e r c r i t e r i a  which  would r e s u l t i n the development o f a s a t i s f a c t o r y method o f e x p r e s s i n g s t a n d d e n s i t y o r growing s t o c k l e v e l s f o r f o r e s t  growth  and y i e l d p r e d i c t i o n . L i v e crown l e n g t h and l i v e crown r a t i o S m i t h and Dubow (i960) r e p o r t e d t h a t the  correlation  c o e f f i c i e n t was 0.75 f o r t h e a s s o c i a t i o n o f d i a m e t e r growth and l i v e crown l e n g t h . t o stem l e n g t h .  Diameter growth was s l i g h t l y but p o s i t i v e l y  related  They i n t r o d u c e d t h e use o f compound v a r i a b l e s  such  as 3c + 5 = 2c + h ( t h r e e t i m e s the l i v e crown l e n g t h p l u s t h e  stem  l e n g t h e q u a l s two times t h e l i v e crown l e n g t h p l u s h e i g h t ) ,  which  weights-crown s i z e t h r e e times as h e a v i l y as stem l e n g t h .  They  concluded that r a t i o crown/total height i s a c t u a l l y not a  satisfactory  i n d e x o f d i a m e t e r growth because i t s use assumed n e g a t i v e  correlation  between diameter growth and stem l e n g t h . Czarnowski (1961)  s t a t e d t h a t a t r e e grox*ing i n the open  a l l i t s l i f e w i l l have t h e l i v e branches e x t e n d i n g almost a l l the b o l e , from t o p t o ground l e v e l .  along  A t the same time on a t r e e grown  i n the m i d s t o f o t h e r t r e e s l i k e a f o r e s t t r e e the l i v e crown w i l l be h i g h e r up t h e b o l e w i l l u s u a l l y be t w o - t h i r d s o r l e s s o f t o t a l  height.  Thus the r a t i o o f average l i v e crown l e n g t h t o average t r e e h e i g h t c o u l d be r e g a r d e d as a measure o f degree o f crowding o f a s t a n d . He a l s o gave an example o f European S c o t s p i n e , when t h e l i v e  crown  r a t i o averaged o n e - t h i r d , f o r a stand f u l l y s t o c k e d and a t normal  59. d e n s i t y f o r even-aged s t a n d s .  Smith et.al.(1961) a n a l y s e d  percentage o f l i v e crown i n r e l a t i o n t o d . b . h . , h e i g h t , a g e , s i t e i n d e x , crown w i d t h , b a s a l a r e a , CW/D, crown c l a s s , H/CW and l e n g t h o f l i v e crown.  They found t h a t o n l y b a s a l a r e a and H/CW were  s i g n i f i c a n t l y a s s o c i a t e d w i t h percentage l i v e crown.  Percentage  l i v e crown d e c r e a s e d w i t h i n c r e a s i n g b a s a l a r e a p e r a c r e and the H/CW r a t i o . Brown  (1962) suggested t h a t l i v e crown l e n g t h was the  i n d i c a t o r o f s t a n d d e n s i t y and proposed t h a t p r u n i n g degree be d e f i n e d by t h e crown r a t i o l e f t  a f t e r pruning, to the p o t e n t i a l  crowrt l e n g t h f o r t h e e x i s t i n g d e n s i t y .  Thus he a c c e p t e d t h e  h y p o t h e s i s t h a t on a g i v e n s i t e , d e n s i t y i s t h e predominant f a c t o r l i m i t i n g l i v e crown l e n g t h . Ward  (1964) s t u d i e d l i v e crown r a t i o and d e n s i t y o f r e d  oak stands and found t h a t an average o f 4 O t o 50 p e r c e n t o f t h e v a r i a t i o n i n l i v e crown r a t i o was e x p l a i n e d by v a r i a t i o n i n crown competition index.  (Crown c o m p e t i t i o n i n d e x was the sum o f the  r a t i o s o f a n u m e r i c a l e x p r e s s i o n o f the crown c l a s s o f each competing t r e e t o i t s h o r i z o n t a l d i s t a n c e from the i n d i v i d u a l sample  tree).  Thus he c o n c l u d e d t h a t f a c t o r s o t h e r than crown c o m p e t i t i o n e n t e r e d i n t o t h e d e t e r m i n a t i o n o f l i v e crown r a t i o .  Probably  inherited  v i g o r , m i c r o - s i t e d i f f e r e n c e s and v a r i a t i o n i n r o o t c o m p e t i t i o n not r e c o g n i z a b l e by above-ground c o n d i t i o n s were a l l i m p o r t a n t factors.  However,  crown c o m p e t i t i o n was the most  determinant o f l i v e crown r a t i o .  significant  60. 4.  IMPROVEMENTS IN METHODS OF MEASUREMENTS OF TREES AND STANDS Illustrations  A. (i)  o f how t r e e s and stands are measured.  V a r i a b l e s u s e d f o r s t o c k i n g and d e n s i t y measurement: Height There a r e t h r e e methods o f measuring t r e e h e i g h t s from a e r i a l photographs: (1)  D i r e c t measurement o f d i s p l a c e m e n t on s i n g l e photographs.  aerial  (2)  D i r e c t o r s t e r e o s c o p i c measurement o f t r e e shadows.  (3)  S t e r e o s c o p i c measurement o f p a r a l l a x d i s p l a c e m e n t w i t h p a r a l l a x b a r and p a r a l l a x wedge.  The f i r s t method i s not used much i n f o r e s t r y because i t t o measure t h e d i s p l a c e m e n t o f a t r e e i n a f o r e s t . t r e e s can be measured i n t h i s way.  i s not  easy  Only open-grown  T h e r e f o r e the d i s c u s s i o n here  will  be c o n c e n t r a t e d upon s t e r e o s c o p i c o b s e r v a t i o n o f the second and t h i r d methods which are f r e q u e n t l y used i n t r e e h e i g h t measurements. There are two most i m p o r t a n t c o n d i t i o n s t h a t must be f u l f i l l e d if  h e i g h t i s t o be measured from a e r i a l photographs by p a r a l l a x methods.  Both t h e t o p and ground l e v e l o f the t r e e must be v i s i b l e when viewed under the s t e r e o s c o p e .  The a c c u r a c y o f measurement o f t r e e h e i g h t  is  f u r t h e r a f f e c t e d by the r e s o l u t i o n o f p h o t o g r a p h i c d e t a i l and n o r m a l l y human eyes cannot r e c o g n i z e o b j e c t s l e s s t h a n 0 . 0 0 1 i n c h i n However, under s l i g h t m a g n i f i c a t i o n o b j e c t s o f can be f e c o g n i z e d .  0.0005  diameter.  inch i n  In a c t u a l e m p i r i c a l t e s t s the minimum s i z e o f  o b j e c t s t h a t c o u l d be r e c o g n i z e d i s f a r l e s s than the f i g u r e s above, i t  diameter  given  i s u s u a l l y 1 f o o t a t 1 : 6 , 0 0 0 ; 2 f e e t a t 1 : 1 2 , 0 0 0 ; 2^ f e e t  a t 1:16,000 and 3 f e e t a t 1:20,000 RF (Spurr 1 9 4 8 ) .  61 Shadow method The shadow method i s n o t as f r e q u e n t l y used as the methods but was found t o be r e l a t i v e l y  easy t o use and q u i t e  as l o n g as one knows t h e a n g u l a r e l e v a t i o n o f the s u n . shows how the shadow method i s  parallax accurate  Figure 3  applied:  ANGLE OF  SUN'S  ELEVATION  K- LENGTH OF SHADOW F i g u r e 3 - Angle o f the sun and shadow l e n g t h The a n g u l a r e l e v a t i o n o f t h e sun at a g i v e n time and a t a g i v e n p l a c e ( g i v e n l a t i t u d e and l o n g i t u d e )  2LQ '  . *.  ~  tree height shadow l e n g t h  tree height  =  shadow l e n g t h x 2£ &  The o n l y i n s t r u m e n t needed i s a shadow o r micrometer wedge.  The measurement can be done by p l a c i n g the wedge such t h a t  one s i d e o f t h e wedge c u t s t h r o u g h the c e n t r e o f the t r e e crown ( a c t u a l l y at the centre of the butt) where t h e shadow e n d s .  and t h e o t h e r s i d e a t the p o i n t  A t t h e same time the shadow must a l s o be a t  r i g h t angle t o t h e a x i s o f the wedge as shown i n f i g u r e 4 .  62.  WEDGE F i g u r e 4 - Measurement o f shadow l e n g t h T h i s can a l s o be done under a s t e r e o s c o p e which w i l l g i v e a better  view. T h i s method has many d i s a d v a n t a g e s : -  (1)  narrow crowned t r e e s do n o t produce d i s t i n c t shadows, o r t h e i r t o p s are n o t e a s i l y seen due t o l i g h t  shadows.  (2)  Any o b s t r u c t i o n s w i l l s h o r t e n t h e shadow.  (3)  The t r e e s on t h e s l o p e d o r u n d u l a t i n g l a n d w i l l have s h o r t e n e d o r l e n g t h e n e d shadows depending on t h e d i r e c t i o n of the sun s h i n i n g onto the s l o p e . suitable for f l a t  (4)  T h e r e f o r e t h i s method i s  only  terrain.  A l a r g e crowned t r e e w i l l c a s t a d i f f e r e n t a s m a l l crowned t r e e ,  shadow from t h a t  as the l a r g e crown tree-shadow i s  by t h e o u t e r branches making the shadow l o n g e r than i t (5)  of  cast should be.  U n l e s s the t r e e i s p e r f e c t l y s t r a i g h t the shadow l e n g t h w i l l be d i f f e r e n t , but when a t r e e i s l e a n i n g too much we can always detect i t  on the a e r i a l p h o t o g r a p h s .  63. (6)  D i s p l a c e m e n t o f t r e e image on one s e t o f a e r i a l photographs i s d i f f e r e n t from another and the d i s p l a c e m e n t outwards from t h e c e n t r e , t h e t a l l e r  increases  the t r e e the g r e a t e r  is  the displacement. The above d i s a d v a n t a g e s a r e shown by t h e f o l l o w i n g diagrams  in  f i g u r e 5»  LARGE  CROWN  TREE  LEANING  Figure 5 - I l l u s t r a t i o n s measurement.  TREE  of effectiveness  IMAGE  DISPLACEMENT  o f shadow l e n g t h  P a r a l l o x methods are more f r e q u e n t l y and f o r t r e e h e i g h t measurement because t h e y a r e easy to use and have many o t h e r advantages.  However,  some p r a c t i c e must be done b e f o r e one can use  64 it  efficiently.  S i n c e t h e above two c o n d i t i o n s o f  parallax  measurement must be f u l f i l l e d so t h e r e must be a t l e a s t  a small  opening near the t r e e o r f l a t t e r r a i n b e f o r e t h e h e i g h t can be measured more a c c u r a t e l y .  Under the s t e r e o s c o p e the r e s o l u t i o n o f  t r e e t o p (crown) s m a l l e r than a c e r t a i n diameter f o r c e r t a i n RF cannot be s e e n .  Thus t r e e s w i t h narrow crowns cannot be measured  as a c c u r a t e l y as l a r g e crowned t r e e s .  Two t y p e s o f e r r o r e x i s t  p a r a l l a x measurements, s y s t e m a t i c and random.  in  These c o n s i s t e n t  lower or h i g h e r measurement c o n s t i t u t e s y s t e m a t i c e r r o r s .  When more  t h a n one e s t i m a t e i s made o f t r e e h e i g h t , t h e e s t i m a t e s w i l l from one another a c c o r d i n g t o t h e laws o f random e r r o r s . o f e r r o r s o c c u r i n a c t u a l measurement t o some degree i f  vary  Both types the  measurements a r e r e p e a t e d . Parallax  bar A p a r a l l a x b a r i s a b a r w i t h a f i n e l y graduated micrometer  d e v i c e and two c o l o u r e d d o t s , e . g . one b l a c k and t h e o t h e r r e d , on two s m a l l sheets o f p l a s t i c  plates.  FLOATING DOT  F i g u r e 6 - Measurement of p a r a l l a x bar and e x p l a n a t i o n o f floating dot.  the  65. Under the s t e r e o s c o p e t r e e s w i t h narrow t o p cannot be accuratelymeasured as the t o p cannot be s e e n , thus t h e dot cannot be p l a c e d e x a c t l y on the t o p .  This i s  e s p e c i a l l y t r u e w i t h w e s t e r n hemlock s i n c e i t  has a d r o o p i n g  l e a d e r as shown by the diagrams i n f i g u r e s 7 and 8.  —*l 2.5 \<-  ROUND  RESOLVING  LIMIT  CROWN  CONICAL  2.5 'f-  CROWN  F i g u r e 7 - Diagrams showing n e g a t i v e b i a s based on RF 1 : 1 6 , 0 0 0 photographs due t o l i m i t a t i o n i n r e s o l v i n g power o f p h o t o g r a p h s .  BROAD  CROWN _7Z°)  Figure 8 -  MARROW  CROWN  (40°)  NARROW CROWN (27°)  ' L o s s o f h e i g h t ' due t o i m p e r f e c t i o n r e g i s t e r o f t r e e images on v e r t i c a l a e r i a l photographs (Andrew 1 9 3 6 ) .  66. Thus the t r e e h e i g h t i s u s u a l l y u n d e r - e s t i m a t e d and many a u t h o r s have suggested the use o f adjustments f o r t r e e h e i g h t measurements. The e x a c t ground l e v e l i s hard t o f i n d but the dot seems t o appear f l a t t e n e d when i t merges w i t h the ground o r o t h e r s o l i d c o v e r on t h e g r o u n d .  It  i s a l s o e a s i e r t o p l a c e the dot on a d a r k e r  s u r f a c e than a w h i t e s u r f a c e because the ground i s n o t as when w h i t e .  When u s i n g the p a r a l l a x b a r i t  r a t h e r than upwards as i t  visible  s h o u l d be moved downwards  i s u s u a l l y e a s i e r t o judge the ground l e v e l  by d o t merging w i t h t h e ground i n s t e a d o f emerging from under t h e ground.  As f o r the e s t i m a t i o n o f t r e e t o p i t  (upward o r downward).  i s as easy e i t h e r way  However, when the dot i s near t h e t o p i t  be moved from l e f t t o r i g h t o r v i c e v e r s a t o see i f of the t r e e o r n o t .  it  can  i s at the top  Another check i s t h a t the eyes s h o u l d be c l o s e d  i n t u r n t o make sure t h a t each d o t i s a t the t o p o f each t r e e image on t h e two v e r t i c a l a e r i a l p h o t o g r a p h s .  The d o t must never be put  i n t o the image o f t h e t r e e b u t a t t h e s i d e o f i t d e s i r e o f the  depending on t h e  interpreter.  The e s t i m a t i o n has t o be made u n t i l t h e r e a r e two i d e n t i c a l values value  (dp)  (dp)  o r 6 t o 10 measurements can be averages as t h e  c a l c u l a t i o n o f t r e e h e i g h t i s than made by t h e p a r a l l a x  formula below:n  where: h  Q  _ o "  H x, dp P + dp  o  r  o ~  (H-h) x dp P + dp  i s t h e c a l c u l a t e d t r e e h e i g h t , h i s the e l e v a t i o n o f t h e  s i t e on which the t r e e s t a n d s , H i s the f l y i n g h e i g h t , P i s t h e base l e n g t h o f photographs ( d i s t a n c e between the two p r i n c i p a l p o i n t s ) , and dp i s the d i f f e r e n c e i n p a r a l l a x .  67 Parallax  wedge The p a r a l l a x wedge was i n t r o d u c e d by S p u r r  (1945) and  t h e d e s i g n v a r i e s from l i n e s , rows o f d o t s o r c i r c l e s on g l a s s p l a t e s or p l a s t i c  sheets.  Rogers  (1946) suggested the use o f r e d  l i n e s i n s t e a d o f b l a c k l i n e s as t h e r e d l i n e f u r n i s h e s good c o n t r a s t and w i l l c u t t h r o u g h t h e f o r e s t t r e e s t o t h o s e ground areas t h a t  are  v i s i b l e through s m a l l o p e n i n g s . P a r a l l a x wedges i n use today u s u a l l y c o n s i s t of two c o n v e r g i n g l i n e s o r tows o f d o t s on t r a n s p a r a n t p l a s t i c  material.  There a r e two c l a s s e s o f wedge, t h e s t a n d a r d model w i t h image s e p a r a t i o n o f 2.0 o f 2.3  i n c h e s and the wide model w i t h image s e p a r a t i o n  i n c h e s a t the c e n t r e o f the wedge.  When p l a c e d under the  s t e r e o s c o p e o f p r o p e r l y o r i e n t e d photographs the two l i n e s merge f o r m i n g a t h r e e - d i m e n s i o n a l l i n e and t h i s l i n e when moved can be made t o r e s t on t h e ground o r on the t r e e t o p .  A g a i n w i t h the c o n d i t i o n s  and l i m i t a t i o n s imposted above, the same problems a r i s e here as w i t h p a r a l l a x b a r f o r measurement o f t r e e t o p and ground l e v e l , by t h e diagrams i n f i g u r e  as shown  9.  F i g u r e 9 - P a r a l l a x wedge measurement and t h e i n f l u e n c e of r e s o l v i n g power o f p h o t o g r a p h s .  68. F o r t h e above two methods the f o l l o w i n g p r o c e d u r e s must be c o n s i d e r e d i n o r d e r t o secure b e t t e r (1)  estimates.  New s c a l e and f l y i n g h e i g h t must be c a l c u l a t e d f o r e s t i m a t e on rough t e r r a i n photographs because the o f s c a l e and f l y i n g h e i g h t i s  each difference  so g r e a t t h a t the use o f  average s c a l e o v e r t h e whole photograph i s n o t a p p r o p r i a t e . (2)  A f t e r c a r e f u l o r i e n t a t i o n and alignment under the s t e r e o s c o p e , t h e p a i r o f a e r i a l photographs must be f a s t e n e d so t h a t  they  w i l l n o t move t o g i v e erroneous r e a d i n g s o f t o p o r ground l e v e l of (3)  tree.  S i n c e t h e e s t i m a t i o n o f t r e e h e i g h t i s h i g h l y v a r i a b l e due t o inaccurate  e s t i m a t e o f ground l e v e l  and t r e e t o p , i t  is  always  a d v i s a b l e t o t a k e an average v a l u e from s e v e r a l measurements. (4.)  The a x i s o f t h e p a r a l l a x wedge must be a t r i g h t a n g l e s t o f l i g h t l i n e and as the p a r a l l a x b a r must be a l o n g o r to the f l i g h t  the  parallel  line.  The p r e f e r e n c e f o r any o f t h e t h r e e methods depends on t h e i n d i v i d u a l . The p a r a l l a x wedge and b a r a r e w i d e l y u s e d and q u i t e c o n s i s t e n t can be o b t a i n e d .  The w r i t e r  results  used t h e p a r a l l a x wedge as he found  t o be most c o n v e n i e n t and e a s i e r t o use than t h e p a r a l l a x b a r . Crown w i d t h There a r e two ways o f measuring crown w i d t h from photographs. (1)  Dot wedge  (2)  Micrometer wedge  aerial  it  69 Both methods are commonly u s e d .  They can e s t i m a t e crovm w i d t h on  s i n g l e photograph o r under a s t e r e o s c o p e . more o f t e n u s e d as i t  The l a t t e r method i s  g i v e s a b e t t e r view o f the t r e e crown t h a n  does n o n - s t e r e o s c o p i c o b s e r v a t i o n . Dot wedge A d o t wedge c o n s i s t s o f a , s e r i e s by 0.0025 i n c h s u c c e s s i v e l y .  It  of dots d i f f e r i n g i n  size  was i n t r o d u c e d by Jensen (194-8).  T h i s wedge i s m o s t l y used under the s t e r e o s c o p e and sometimes two d o t wedges may be used t o g e t h e r t o p r o v i d e a t h r e e - d i m e n s i o n a l dot which a few a u t h o r s c o n c l u d e d t o be b e t t e r t h a n s i n g l e d o t . wedge i s  The d o t  s l i d a l o n g t h e t r e e image u n t i l the same s i z e d o t i s matched  w i t h t h e crown image.  Crown w i d t h e s t i m a t e d on t h e a e r i a l  photographs  i s n o t d i r e c t l y comparable t o t h a t measured on the ground because p r o t r u d i n g branches cannot be seen from h i g h e r u p . width i s u s u a l l y under-estimated.  T h e r e f o r e crown  The w r i t e r found t h a t  after  matching t h e crown s i z e w i t h the dot t h e n e x t l a r g e r dot should be t a k e n and t h i s g i v e s a more a c c u r a t e r e s u l t of crown w i d t h  estimation.  U s i n g o f the l a r g e r d o t above i s l i k e adding a c o r r e c t i o n f a c t o r 0.0025 i n c h t o each r e a d i n g b e f o r e the crown w i d t h i s T h i s method i s  of  calculated.  e a s i e r t o use than the micrometer wedge.  Micrometer wedge o r shadow wedge The micrometer wedge c o n s i s t s o f two c o n v e r g i n g l i n e s graduated t o t h e n e a r e s t thousand of an i n c h . Wilson  (1948).  It  It  was d e s i g n e d by  can be used on a s i n g l e photograph but the images  o f t r e e s a r e n o t so c l e a r l y  s e e n , so t h r e e - d i m e n s i o n a l images under  the stereoscope are u s u a l l y used t o f a c i l i t a t e  more a c c u r a t e  estimation.  70. Two r e a d i n g s a t r i g h t a n g l e t o each o t h e r must be t a k e n and the average v a l u e i s the crown w i d t h .  The wedge i s o f t e n i n a c c u r a t e  due t o t h e convergence o f t h e wedge l i n e s w i t h the crown w i d t h , g i v i n g an o v e r - e s t i m a t e o f crown w i d t h . S i n c e the d i s t o r t i o n o f t r e e image near the c e n t r e o f a photo i s l e s s t h a n t h a t f a r t h e r t o t h e edge o f p h o t o g r a p h , the crown w i d t h must be measured a t r i g h t a n g l e s t o the  radial  line  from t h e p r i n c i p a l p o i n t t h r o u g h t h e image o f t r e e .  The method o f  p l a c i n g the micrometer and d o t wedge a r e shown i n f i g u r e 1 0 .  F i g u r e 10 - Diagram o f micrometer and d o t wedge measurements o f crown w i d t h . The measurement o f crown w i d t h by t h e s e two methods must bear the f o l l o w i n g c o n d i t i o n s i n mind so t h a t b e t t e r r e s u l t s  can  be o b t a i n e d . (l)  The s c a l e o f photographs must be c o n s i d e r e d , as a l a r g e r s c a l e photograph g i v e s a c l e a r e r view o f the crown than a s m a l l s c a l e p h o t o g r a p h , thus g i v i n g c l o s e r e s t i m a t e comparison w i t h ground measurement.  in  However, t o o l a r g e  scales,  71. l i k e those i n stereograms taken by h e l i c o p t e r s a t 300 t o 500  feet  above ground w i l l o n l y g i v e a c c u r a t e measurements o f t h e few  trees  i n the c e n t r e and a l o n g the f l i g h t l i n e  (base l i n e between  Otherwise the d i s p l a c e m e n t o f t r e e images are so g r e a t measurements are i m p o s s i b l e .  camera).  that  The stereograms and the diagram i n  f i g u r e 11 and 12 w i l l i l l u s t r a t e  this  point.  F i g u r e 11 - H e l i c o p t e r stereogram 350 f t . Douglas f i r .  flying  height  F i g u r e 12 - H e l i c o p t e r stereogram 350 f t . Lodgepole p i n e .  flying  height  72. (2)  The o r i e n t a t i o n and a l i g n m e n t under s t e r e o s c o p e and o t h e r t r e a t m e n t s o f photographs must be the same as when making p a r a l l a x h e i g h t measurements.  (3)  I r r e g u l a r crovms o f hardwoods a r e more a c c u r a t e l y measured by a micrometer wedge than a dot wedge because two measurements can be t a k e n a t r i g h t a n g l e t o each o t h e r , and t h e average o f t h e w i d e s t and narrowest estimates.  sides gives a better  However, more r e g u l a r crowns of c o n i f e r s  are  e a s i e r t o measure and g i v e b e t t e r r e s u l t s when the dot wedge is (4)  used.  On rough t e r r a i n ,  e l e v a t i o n o f t r e e s must be i n d i v i d u a l l y  determined because a l a r g e d i f f e r e n c e of s c a l e can g i v e  an  i n a c c u r a t e c a l c u l a t i o n o f crown w i d t h . (5)  M u l t i p l e stem t r e e s , all  (iii)  i n t e r l o c k i n g crowns and shadow  variations  c o n t r i b u t e t o the d i s c r e p a n c i e s o f crown w i d t h measurements.  Crown c l o s u r e Crown c l o s u r e may be measured by the t h r e e main methods below from a e r i a l p h o t o g r a p h s . (1)  Ocular estimation.  (2)  T r a n s p a r e n t dot g r i d .  (3)  Crown d e n s i t y  Ocular  scale.  estimation O c u l a r e s t i m a t i o n can o n l y be made by e x p e r i e n c e d  interpreters.  T h i s i s because much p r a c t i c e must be made b e f o r e  one can a c c u r a t e l y  e s t i m a t e crown c l o s u r e by the o c u l a r method.  73. An i n e x p e r i e n c e d i n t e r p r e t e r tends t o o v e r - e s t i m a t e crown c l o s u r e . T h i s method i s f r e q u e n t l y used because i t  i s the  simplest.  T r a n s p a r e n t dot g r i d A t r a n s p a r e n t dot g r i d i s a d e v i c e c o n s i s t i n g o f a number o f s y s t e m a t i c a l l y d i s t r i b u t e d d o t s u s u a l l y 20 t o 30 p e r  acre.  The dot g r i d i s p l a c e d over the a r e a t o be measured and the d o t s f a l l i n g on t o the t r e e crown are c o u n t e d . f a l l on t r e e crown i n the stand i t  If  15 o u t o f 30 d o t s  has 50 p e r c e n t crown c l o s u r e .  T h i s method cannot be used r a p i d l y and e a s i l y . Crown d e n s i t y  scale  A crown d e n s i t y s c a l e i s a l s o f r e q u e n t l y used because i s easy t o a p p l y .  It  c o n s i s t s o f random o r s y s t e m a t i c  o f d o t s , and the s i z e o f d o t s are a l s o d i f f e r e n t f o r s i z e crowns and d i f f e r e n t p h o t o - s c a l e .  distribution  different  The percentage crown c l o s u r e  on the s c a l e i s from 5 p e r c e n t t o 95 p e r c e n t . a c r e s i z e p h o t o , square o r r o u n d .  it  It  i s u s u a l l y i n one  The use o f two s e t s o f s c a l e s  to  produce a t h r e e - d i m e n s i o n e f f e c t was a l s o p r a c t i s e d by a few a u t h o r s . The s c a l e i s put under the s t e r e o s c o p e onto p r e p e r l y o r i e n t e d and a l i g n e d photographs and s l i d up and down a l o n g the p l o t u n t i l one t h a t f i t s b e s t i s  the  found.  Pseudoscopic images Pseudoscopic images are c r e a t e d when the r i g h t - and l e f t hand photographs a r e r e v e r s e d under the s t e r e o s c o p e , t h e r e l i e f the ground s u r f a c e w i l l appear t o be r e v e r s e d .  Objects  on  standing  u p r i g h t w i l l appear t o be c a v i t i e s i n t h e ground, e . g . h i l l s  will  appear as v a l l e y s , appear as c a v i t i e s . all  v a l l e y s w i l l appear as r i d g e s and t r e e s E x c a v a t i o n s w i l l appear as mounds.  because we are used t o o b s e r v i n g t h e shadow f a l l i n g  us and u s u a l l y cannot see the shadow away from u s , e . g . b e h i n d the o b j e c t . shadows c a s t ,  will  This  is  towards shadow  T h e r e f o r e we tend t o judge the o b j e c t s by the  g i v i n g the p s e u d o s c o p i c images.  This e f f e c t i s often u s e f u l f o r  photo-interpretation  e s p e c i a l l y f o r measurement o f crown c l o s u r e because t h e  small  openings appear as s p i r e s s t i c k i n g up towards the o b s e r v e r and thus t h e i r a r e a s can be e s t i m a t e d . The problems t h a t a r i s e from the t h r e e methods o f closure estimation (1)  crown  are:-  The r e s o l v i n g power o f photographs w i l l g r e a t l y h i n d e r crown c l o s u r e e s t i m a t i o n because a t a c e r t a i n s c a l e t h e r e i s a c e r t a i n l i m i t a t i o n t o r e s o l v i n g power.  If  also  RF o f 1:16,000  photographs i s t a k e n t o measure crown c l o s u r e a l l  the openings  o f the f o r e s t t h a t are l e s s than 2% f e e t w i l l not be v i s i b l e , so the crown c l o s u r e w i l l be o v e r - e s t i m a t e d no matter t h e r e i s any o t h e r a d d i t i o n a l e r r o r o r n o t .  whether  So the s c a l e  is  an i m p o r t a n t f a c t o r f o r s c r o w n : c l o s u r e . d e t e r m i n a t i o n . (2)  The e s t i m a t i o n o f crown c l o s u r e may be the whole crown c l o s u r e w i t h a l l  forest  the t r e e s p r e s e n t o r o n l y t h e t o p  crown c l o s u r e c o n s i s t i n g o f dominant and codominant t r e e s . When one t r i e s  t o determine the t o p crown c l o s u r e , i t  easy t o o v e r - e s t i m a t e i t lower  vegetations.  is  very  by i n c l u d i n g the crown c l o s u r e o f  7 5 .  (3)  S m a l l openings and shadows can i n f l u e n c e crown c l o s u r e causing i t  (4)  estimation  t o be o v e r - e s t i m a t e d .  Crown c l o s u r e o f areas on t h e edge o f the a e r i a l photographs a r e u s u a l l y o v e r - e s t i m a t e d because of h i g h d i s p l a c e m e n t and the vertical  openings cannot be s e e n .  A l l the problems are of o v e r - e s t i m a t i o n o f crown c l o s u r e t h e r e f o r e we must be c a r e f u l and keep these f a c t o r s i n mind when e s t i m a t i n g crown c l o s u r e . There are a l s o o t h e r methods used t o measure crown c l o s u r e . A cramming method was used by Pope (i960) and he termed i t type o f o c u l a r e s t i m a t i o n .  as  another  The whole p l o t i s c a r e f u l l y p l o t t e d w i t h  a l l t h e v i s i b l e t r e e crowns and the crown c l o s u r e i s  a s s e s s e d by  p u t t i n g t h e crowns t o g e t h e r but t h i s method i s v e r y t e d i o u s .  By  method t h e d i s t r i b u t i o n o f t r e e s w i t h i n the p l o t can be shown.  this This  method and the above method are used i n t h i s s t u d y because they w i l l a good v i s u a l view o f s t o c k i n g . B.  S t o c k i n g and d e n s i t y c o n d i t i o n s under which t r e e s  (a)  Stocking Stocking i s description.  grow:  one o f the most i m p o r t a n t a s p e c t s o f  stand  A f o r e s t i s a u n i t a r e a o f l a n d covered w i t h  trees  growing t o g e t h e r .  The c o n d i t i o n s under which these t r e e s grow v a r y  enormously, e s p e c i a l l y i n n a t u r a l stands because of the non-uniform site quality,  from v e r y poor t o v e r y good.  T h e r e f o r e the e s t a b l i s h -  ment o f t r e e s are l i m i t e d , and the d i s t r i b u t i o n o f t r e e s are uneven on any g i v e n l a n d s u r f a c e ,  often  and thus c r e a t i n g open-grown t r e e s ,  normal-grown t r e e s and dense-grown t r e e s  ( f o r e s t grown  trees).  give  76. Open-grown t r e e s and u n d e r - s t o c k e d stands The use o f an open-grown t r e e o r i n d i v i d u a l t r e e as a b a s i c u n i t f o r s t u d y i n g o f t r e e growth was r e v i v e d v e r y  recently.  T h i s i s based on the concept t h a t open-grown t r e e s have a l l space a v a i l a b l e  t o express t h e i r g e n e t i c c h a r a c t e r i s t i c s  i s a l s o no c o m p e t i t i o n from n e i g h b o u r i n g t r e e s . dimension can spread t o i t s g r e a t e s t  a l s o o c c u r a l l a l o n g the stem, from t i p t o ground l e v e l , surface area f o r • photesynthetic a c t i v i t i e s growth.  crown branches g i v i n g more  and p r o d u c i n g the  fastest  S i n c e the open-grown t r e e s are spaced a p a r t from each o t h e r  t h e r e f o r e the number o f t r e e s p e r u n i t a r e a w i l l be v e r y However,  and t h e r e  Thus the  e x t e n t and the l i v e  the  small.  open-grown t r e e s are u s u a l l y found on adverse s i t e s ,  r o c k y and/or poor wet p l a c e s , d u e t o f a c t o r s l i m i t i n g of seedlings.  Wherever  establishment  t h e r e are p o c k e t s o f s o i l t o s u p p o r t t r e e  growth, a t r e e may grow w i t h no o t h e r s around i t .  Another  i s t h a t when n a t u r a l r e g e n e r a t i o n i s v e r y poor o n l y a few t r e e s may e x i s t and grow f a r a p a r t . r a r e i n most n a t u r a l Krajicek  e.g.  situation scattered  These t y p e s o f t r e e s are  rather  forests.  et.al.(1961)  used t h e f o l l o w i n g  specifications  f o r s e l e c t i o n o f open-grown t r e e s : (1)  Crown f r e e o f c o m p e t i t i o n on a l l  (2)  Limbs e x t e n d i n g t o the ground on s m a l l t r e e s and n e a r l y so on larger  (3)  sides.  trees.  Lowest branches t h e l o n g e s t o r a t l e a s t as l o n g as t h o s e above. ( T h i s e l i m i n a t e d t r e e s t h a t had been r e l e a s e d from c o m p e t i t i o n  77 i n t h e p a s t and on which t h e lower p o r t i o n o f the crown o r i g i n a t e d from e p i c o r m i c If  (4)  branches).  t h e open-grown t r e e i s used as a sample t r e e the  c o n d i t i o n s are u s u a l l y For small trees  present  following  attached.  ( l e s s t h a n 16 f e e t t a l l )  no f o r k i n g i n  the  e n t i r e l e n g t h , and f o r l a r g e t r e e s no f o r k i n g o f base below 16 f e e t  ( t h i s l i m i t s t h e sample t o t r e e s t h a t were o f  t y p e t h a t would be f a v o u r e d i n t h e f o r e s t l i m b i n e s s and e x c e s s i v e (5)  the  s t a n d , except f o r  taper).  No e v i d e n c e o f p r u n i n g , s h e a r i n g , b r o w s i n g , decadence, storm damage o r s e r i o u s i n s e c t damage.  (6)  Tree a p p a r e n t l y n o t o f s p r o u t  origin.  These above c o n d i t i o n s f o r sample t r e e s are o n l y s u i t a b l e f o r ground o b s e r v a t i o n but on the a e r i a l photographs t h e s e f a c t o r s cannot be r e c o g n i z e d due t o i t s  orthographic view.  When an a r e a i s t a k e n i n t o c o n s i d e r a t i o n , t h e open-grown t r e e s become an u n d e r - s t o c k e d s t a n d .  But t h i s t y p e o f s t a n d i s  not  t h e optimum c o n d i t i o n f o r any f o r e s t except perhaps on i r r e g u l a r l y adverse s i t e because i t  does not f u l l y u t i l i z e the s i t e .  The  d i s t r i b u t i o n o f open-grown t r e e s i n u n d e r - s t o c k e d stands v a r i e s  in  c o m p o s i t i o n and s t r u c t u r e .  is  The d i f f e r e n c e s are so wide t h a t i t  o f t e n d i f f i c u l t t o use a d e s c r i p t i v e c h a r a c t e r i s t i c under-stocked s t a n d s . to i t s  characteristic  However,  distribution.  stand d e n s i t y and s t o c k i n g .  the  a s i n g l e stand may be d e s c r i b a b l e as T h i s i s v e r y i m p o r t a n t because  u n l e s s one can d e s c r i b e t h e s t r u c t u r e i t its  to s u i t a l l  i s n o t easy t o determine  78 Normal-grown t r e e s and f u l l y  s t o c k e d stands  Normal-grown t r e e s are t r e e s growing i n a f u l l y - s t o c k e d c o n d i t i o n where the crowns are t o u c h i n g but n o t o v e r l a p p i n g and t h e number o f t r e e s p e r u n i t a r e a w i l l a l s o be the normal number expected f o r t h i s s t a n d by comparison w i t h normal y i e l d t a b l e .  The number o f  stems p e r u n i t a r e a v a r i e s from s p e c i e s t o s p e c i e s as t h e crown s i z e s a r e n o t t h e same, e . g . i t w i l l have l e s s Douglas f i r  t r e e s per  acre  than lodgepole p i n e . When an a r e a i s taken i n t o c o n s i d e r a t i o n t h i s t y p e o f normal-grown t r e e s may form a f u l l y - s t o c k e d s t a n d . c o n d i t i o n i s o n l y a p a s s i n g stage i n most f o r e s t  However  this  s t a n d s , meaning t h a t  a f o r e s t s t a n d does n o t s t a y at normal d e n s i t y f o r v e r y l o n g .  The  u n d e r - s t o c k e d s t a n d may advance t o u n d e r - f u l l y - s t o c k e d s t a n d , t h e n t o f u l l y - s t o c k e d s t a n d and p a s t n o r m a l i t y t o o v e r - s t o c k e d s t a n d i f adjustment i s made by management.  no  T h i n n i n g w i l l u s u a l l y keep the  f u l l y - s t o c k e d s t a n d i n a normal c o n d i t i o n but when the f o r e s t i s  too  dense n a t u r a l m o r t a l i t y w i l l a l s o b r i n g t h e stand back t o n o r m a l i t y again.  If  stocked i t  a stand i s e v e n l y s p a c e d , e . g . p l a n t a t i o n , and i s always p o s s i b l e f o r i t  t o normal a t an o l d e r a g e . under-stocked stands, i t  sufficiently  t o advance from open when young  However as s t r e s s e d i n the s e c t i o n on  i s almost i m p o s s i b l e t o have a u n i f o r m f o r e s t  o f f u l l y - s t o c k e d stands as the s i t e f a c t o r s are d i f f e r e n t from p l a c e to place.  So f u l l y - s t o c k e d stands can o n l y be found i n patches o r  on good s i t e s o f even s o i l d i s t r i b u t i o n .  Therefore fully-stocked  stands are u s u a l l y found i n p l a n t a t i o n s under p r o p e r management.  79. F u l l y - s t o c k e d stands r e s u l t i n g from u n d e r - s t o c k e d stands have almost s i m i l a r growth, except t h a t any f u r t h e r expansion w i l l cause t h e crowns t o o v e r l a p , and thus p r o c e e d p a s t n o r m a l i t y . condition i s that i f  Another  a f u l l y - s t o c k e d stand i s o b t a i n e d by r e l e a s e  of  a dense- o r o v e r - s t o c k e d s t a n d , t h e n the growth c o n d i t i o n s w i l l be different.  The crovm w i d t h o f t h i s  stand w i l l be s m a l l e r due t o  p a s t c o m p e t i t i o n and the l i v e crown i s a l s o s h o r t e r . h e r e w i l l be s l o w e r , stocked stands.  So t h e  growth  e s p e c i a l l y i n diameter i n comparison w i t h u n d e r -  But the t r e e s are t a l l e r  and have l e s s t a p e r .  The  r a t e o f growth o f f u l l y - s t o c k e d stands has been viewed as the optimum f o r managed f o r e s t i n the p a s t , because the f u l l y - s t o c k e d stands  fully  u t i l i z e the s i t e .  in  However,  f u l l u t i l i z a t i o n of s i t e ,  especially  a d v e r s e o r suboptimum s i t e s where t h e growth may be normal b u t the d i s t r i b u t i o n o f t r e e s s t i l l wide a p a r t l i k e open-grown t r e e s , (iii)  Dense-grown t r e e s and o v e r - s t o c k e d  stands  Dense-grown t r e e s a r e t r e e s growing a t a denser c o n d i t i o n than normal-grown t r e e s ,  t h i s means t h a t t h e y have o v e r l a p p i n g crowns  and are growing c l o s e r t o g e t h e r .  T h i s may a l s o mean t h a t t h e r e  many s t o r i e s o f c a n o p i e s , one above the o t h e r .  When a r e a s are  are taken  i n t o c o n s i d e r a t i o n t h e dense-grown t r e e s becomes o v e r - s t o c k e d s t a n d s . T h i s type o f c o n d i t i o n i s more f r e q u e n t l y found i n young s t a n d s about 25 t o 35 y e a r s i n western hemlock o r mixed stands o f  natural  f o r e s t , p a r t l y due t o the d i f f e r e n t degree o f t o l e r a n c e o f the It  e.g.  species.  can a l s o be found i n pure even-aged stands o f e x t e n s i v e l y managed  forest.  Here the c o m p e t i t i o n w i l l be s t r o n g between t r e e s as  they  80. are o f t h e same s i z e and a l l w i l l t a l l trees.  eventually s u f f e r , producing t h i n  However t h e c o m p e t i t i o n  w i t h i n t h e same s p e c i e s  v a r i e s w i t h s p e c i e s and even  and age, because d i f f e r e n t i n h e r e n t  c h a r a c t e r i s t i c s may p l a y an i m p o r t a n t p a r t i n t h e growth o f t r e e s w i t h i n the s t a n d s . superior inherent stand  T h i s means t h a t some o f t h e t r e e s t h a t have c h a r a c t e r i s t i c s w i l l dominate and codominate t h e  and suppress t h e i n f e r i o r ones.  But i n t h e n a t u r a l f o r e s t  where t h e ages a r e d i f f e r e n t some o f t h e more v i g o r o u s  and o l d e r  t r e e s w i l l become dominant and codominant l e a v i n g t h e slow growing t r e e s as suppressed t r e e s , which w i l l e v e n t u a l l y d i e . stocked  The o v e r -  stands u s u a l l y o c c u r i n young stands and as the stand  grows o l d e r t h e n a t u r a l m o r t a l i t y w i l l have d e p l e t e d s t o c k i n g t h a t i t w i l l become a f u l l y - s t o c k e d stand  so much o f t h e again.  Dense-grown t r e e s u s u a l l y have a s m a l l e r crown w i d t h and s h o r t e r l i v e crown because due t o t h e l a c k o f space t h e crown w i d t h growth i s r e t a r d e d The  by c o m p e t i t i o n  and a l s o broken o f f by f r i c t i o n .  s h o r t l i v e crown i s a l s o m a i n l y due t o c o m p e t i t i o n .  s i n c e t h e t r e e s a r e i n a dense c o n d i t i o n t h e h e i g h t a l s o i n c r e a s i n g but a t a slower r a t e . stand i s h i g h e r Stand  than i n f u l l y - s t o c k e d  Furthermore,  and d.b.h. a r e  The m o r t a l i t y o f t h i s t y p e o f stand.  density Stand d e n s i t y i s t h e degree o f crowding w i t h i n a stand and  t h i s type o f c o n d i t i o n d i f f e r s w i t h i n any g i v e n area, one  thus making i t  o f t h e most d i f f i c u l t problems i n f o r e s t m e n s u r a t i o n .  c o n d i t i o n s a l s o v a r y w i d e l y w i t h i n any g i v e n a r e a .  Stocking  Even w i t h t h e same  d e n s i t y t h e s t o c k i n g i s n o t t h e same and depends upon t h e s i z e and  81.  species of t r e e s . must be f u r t h e r  It  seems t h a t the b i o l o g i c a l a s p e c t o f the  s t u d i e d b e f o r e we can b e t t e r understand t h e  o f crowding and growth o f f o r e s t  forest  basis  trees.  Open s t a n d d e n s i t y Open stand d e n s i t y i n d i c a t e s t h a t the t r e e s are relatively  spaced  f a r a p a r t from each o t h e r e . g . i n open-grown s t a n d s .  C o n s i d e r i n g o l d growth o n l y ,  s m a l l patches o f o l d growth i n open  d e n s i t y s t a n d s can be found i n areas o f 100 p e r c e n t crown c l o s u r e o r f u l l y - s t o c k e d , which g e n e r a l l y appears l i k e dense-grown t r e e s when viewed under the s t e r e o s c o p e . i s i n the f i r s t  The e x i s t e n c e of t h i s t y p e of  i n s t a n c e due t o e s t a b l i s h m e n t and adverse  which can o n l y be found i n n a t u r a l f o r e s t s t a n d s .  stands  sites,  The second i n s t a n c e  due t o o l d age and s i z e i s found b o t h i n n a t u r a l and p l a n t a t i o n  stands.  S i n c e t h e d i s t r i b u t i o n o f t r e e s d i f f e r s w i d e l y i n open-grown c o n d i t i o n s , , the open stand d e n s i t i e s a l s o d i f f e r . a r e f u r t h e r a t t r i b u t e d t o s t o c k i n g which v a r i e s  These  variations  enormously w i t h t h e  s i z e and d i s t r i b u t i o n of t r e e s w i t h i n any s p e c i f i c a r e a .  The open  s t a n d d e n s i t y may c o n s i s t o f one t r e e p e r a c r e of v e r y open s t a n d d e n s i t y up t o the maximum number, the square s p a c i n g d i s t a n c e o r  size  o f crown would a l l o w a t open stand d e n s i t y . S i n c e t h e t r e e s are growing i n open c o n d i t i o n s the o f crown diameter i s u n l i m i t e d , i . e .  the maximum crown d i a m e t e r s t h a t  can be grown without any c o m p e t i t i o n from o t h e r t r e e s . time, the diameters  spread  ( d . b . h . ) a r e a l s o growing v e r y f a s t ,  t h o s e of c l o s e stands of the same a g e .  Therefore i t  A t t h e same faster  than  can be assumed  82 t h a t t h i s t y p e o f stand d e n s i t y p r o v i d e s the f a s t e s t  individual  t r e e growth due to the enormous crown a r e a a v a i l a b l e f o r photos y n t h e s i s , and abundant s o i l space f o r r o o t spread and n u t r i e n t absorption. The CW/dbh r a t i o i s u s u a l l y g r e a t e r t h a n two and may even r e a c h as h i g h as t h r e e o r f o u r , and the H/CW r a t i o i s about t h r e e . T h i s i s because the crown expands l a t e r a l l y u n l i m i t e d space, w h i l s t  v e r y r a p i d l y due t o  the d . b . h . , and to a c e r t a i n e x t e n t  a r e a l s o growing but n o t a t such a f a s t r a t e ,  the  height,  so g i v i n g a l a r g e r  CW/dbh r a t i o and a s m a l l e r H/CW r a t i o . T h e o r e t i c a l models are a t t a c h e d i n appendix 1. Open-normal stand d e n s i t y Open-normal stand d e n s i t y i s a stage between t h e open and normal s t a n d d e n s i t i e s .  The s t a n d h e r e i s more crowded than t h a t  open-stand d e n s i t y but l e s s t h a n t h a t o f normal stand d e n s i t y .  of  This  means t h a t t h e s t o c k i n g i s a l s o b e t t e r than the open s t a n d d e n s i t y of t h e same average d . b . h . , but i f stocked with trees i t  the  stand i s s u f f i c i e n t l y  well  can advance towards normal s t a n d d e n s i t y .  normal s t a n d d e n s i t y i s found more f r e q u e n t l y i n n a t u r a l f o r e s t i n w e l l managed p l a n t a t i o n s because the s i t e v a r i e s  so much i n  Openthan natural  f o r e s t and the m o r t a l i t y i s more i r r e g u l a r . S i n c e the open-normal stand d e n s i t y i s l i k e t h a t o f open s t a n d d e n s i t y w i t h r e g a r d t o space a v a i l a b l e is  also similar.  Therefore i t  f o r growth, the  growth  seems a b e t t e r p r o p o s i t i o n t o grow  83. s t a n d s a t open-normal stand d e n s i t y . plantations  The p r e s e n t t r e n d s o f  seem t o be moving towards more open  (open-normal)  stands because many a u t h o r s p o i n t e d out the f a c t t h a t t r e e s i n open-normal stands grow r e l a t i v e l y normal s t a n d s . the r e v e r s e .  individual  f a s t e r than t h o s e  in  However the a b s o l u t e growth o f a dense stand i s  just  The t h i n n i n g regimes a l s o f o l l o w t h i s l i n e of t h i n k i n g .  S i n c e t h e crown d i a m e t e r , d . b . h . and h e i g h t a r e s i m i l a r t o t h a t o f open s t a n d d e n s i t y t h e r e f o r e the CW/dbh, and H/CW r a t i o s w i l l a l s o be t h e same.  The o n l y d i f f e r e n c e t h a t e x i s t s here i s t h e  o f more t r e e s p e r u n i t  distribution  area.  T h e o r e t i c a l models are a t t a c h e d i n appendix 1. (iii)  Normal s t a n d d e n s i t y Normal s t a n d d e n s i t y s i g n i f i e s a stage when a l l the i n a stand are growing n o r m a l l y , w i t h each o t h e r .  However t h i s i s o n l y a v e r y s h o r t phase  older,  in  A stand can grow from open and open-normal s t a n d d e n s i t i e s  t o normal s t a n d d e n s i t y i f stocked.  of t h e s e a r e i n c o m p e t i t i o n  T h e i r crowns are c l o s e d (100 p e r c e n t crown c l o s u r e ) ,  and almost o v e r l a p p i n g . any s t a n d .  and a l l  trees  the stand i s  s u f f i c i e n t l y and u n i f o r m a l l y  A young stand may be at open s t a n d d e n s i t y but as i t  t h e stand d e n s i t y o r crowding i n c r e a s e s a c c o r d i n g t o i t s  grows d.b.h.  and crown w i d t h growth, t o open-normal than normal and may be t o dense stand d e n s i t y .  The r e v e r s e may be c r e a t e d by n a t u r e and man, e . g .  in  a dense stand the m o r t a l i t y w i l l be r a t h e r h i g h due t o c o m p e t i t i o n and s u p p r e s s i o n thus b r i n g i n g the s t a n d back t o normal stand d e n s i t y a g a i n .  84.  T h i s u s u a l l y happens as a s t a n d grows o l d e r and thus each t r e e needs more space t o grow.  Man can a l s o b r i n g a dense stand back t o normal  stand d e n s i t y by t h i n n i n g . In n a t u r a l f o r e s t stands the d i s t r i b u t i o n and crowding c o n d i t i o n s v a r y so v a s t l y t h a t normal s t a n d d e n s i t y can o n l y be found i n s m a l l p a t c h e s u n l i k e t h a t o f p l a n t a t i o n s where the t r e e s  are  even-aged and normal stand d e n s i t y may be encountered throughout the s t a n d .  T h i s i s why t h e European f o r e s t e r s used normal y i e l d  s t a n d t a b l e s and many p e o p l e i n t h e p a s t a l s o a c c e p t e d and used t h i s t a b l e w i t h o u t knowing the concept o f the normal s t a n d s , w i t h r e g a r d t o both normal s t o c k i n g and d e n s i t y . known as a f u l l y  A normal stand i s a l s o  s t o c k e d stand because the a r e a i s  usually  completely  u t i l i z e d o r f u l l o c c u p a t i o n o f s i t e e x i s t s s i n c e t h e r e i s 100 p e r c e n t crown c l o s u r e .  The number o f t r e e s a r e d i f f e r e n t  even w i t h i n  fully  s t o c k e d s t a n d s , depending on the s i z e of d . b . h . and crown width of the t r e e s p r e s e n t .  T h i s i s why t h e number of t r e e s i s n o t a good  i n d i c a t o r o f s t o c k i n g w i t h o u t adding average d . b . h . and crown c l o s u r e . The h e i g h t o f t h i s type o f s t a n d d i f f e r s depending upon the towards n o r m a l i t y .  If  it  trends  i s from open- o r open-normal s t a n d d e n s i t y  towards normal stand d e n s i t y the h e i g h t f o r a g i v e n d . b . h . w i l l be shorter, taller  and i f  it  i s from dense stand d e n s i t y the h e i g h t w i l l be  because the f i r s t  i s younger and t h e second i s  older.  The growth o f d . b . h . and crown w i d t h i s almost i n  similar  p r o p o r t i o n t h e r e f o r e the CW/dbh r a t i o used f o r normal stand d e n s i t y i s one and the H/CW r a t i o i s about  five.  85 T h e o r e t i c a l models are p r e s e n t e d i n appendix 1. Normal-dense s t a n d d e n s i t y When a f o r e s t stand p r o c e e d s p a s t normal stand d e n s i t y reaches a l e v e l  o f normal-dense stand d e n s i t y .  it  Here the c o m p e t i t i o n  has s t a r t e d and t r e e s compete w i t h each o t h e r t o g e t as much s u n l i g h t as p o s s i b l e , thus p u t t i n g on r e l a t i v e l y d i a m e t e r growth.  more h e i g h t growth than  A t t h e same time the crowns w i l l o v e r l a p one another  and the lower branches w i l l d i e . as c o m p e t i t i o n i n c r e a s e s .  The c l e a r b o l e l e n g t h w i l l  On the o t h e r hand, i f  a stand i s brought  back to normal-dense c o n d i t i o n from dense c o n d i t i o n s by  natural  m o r t a l i t y o r man, the growth w i l l be d i f f e r e n t as t h e lower are a l r e a d y dead,  so i t  increase  branches  has a h i g h e r c l e a n b o l e than those advancing  from normal stand d e n s i t y .  The crown w i d t h w i l l a l s o be s m a l l e r due  t o p a s t c o m p e t i t i o n and the growth o f t h i s t y p e o f stand may be a c c e l e r a t e d due t o t h e r e l e a s e .  Normal-dense stand d e n s i t i e s  u s u a l l y found i n young n a t u r a l stands o r p l a n t a t i o n s .  are  Again, t h i s  u s u a l l y o n l y f o u n d i n patches i n n a t u r a l f o r e s t c o n d i t i o n s as  is  the  r e g e n e r a t i o n i s d i s t r i b u t e d r a t h e r u n e v e n l y due t o v a r y i n g s i t e  and  mortality. The s t o c k i n g i n t h i s t y p e o f stand i s u s u a l l y above normal o r o v e r - s t o c k e d as the number of t r e e s exceeds the number t h a t can n o r m a l l y be grown i n such a s i t e .  Normal-dense s t a n d d e n s i t y may  t r e n d towards dense stand d e n s i t y o r back t o normal d e n s i t y by mortality.  The growth i n normal-dense stands w i l l a l s o be slower  t h a t o f normal stands because the t r e e s are a l l  than  crowded t o g e t h e r and  the crown w i d t h cannot d e v e l o p due t o l a c k o f space and the young  86.  s h o o t s w i l l a l s o be broken o f f by f r i c t i o n , thus g i v i n g a s m a l l e r crown w i d t h .  The d . b . h . and h e i g h t growth a t the same time  i n c r e a s i n g a l t h o u g h a t a slower r a t e ,  are  so t h e CW/dbh r a t i o o f normal-  dense stands w i l l be below one and t h e H/CW r a t i o w i l l be l a r g e r , about e i g h t .  The crown c l o s u r e of normal-dense s t a n d d e n s i t y  always 100 p e r c e n t and i t  can a l s o be observed from t h e  photographs t h a t the crown d e n s i t y  (compactness)  is  aerial  i s h i g h e r than t h a t  o f normal crown d e n s i t y . T h e o r e t i c a l models are a t t a c h e d i n appendix 1. Dense s t a n d d e n s i t y Dense s t a n d d e n s i t y i s not v e r y common i n f o r e s t e i t h e r n a t u r a l o r p l a n t a t i o n s u n l e s s the s t a n d i s stocked.  extremely  stands, over-  Otherwise dense stand d e n s i t y can o n l y be found i n v e r y  small  p a t c h e s i n n a t u r a l f o r e s t s and v e r y seldom i n p l a n t a t i o n s because o f t h e systematic spacing of t r e e s .  The c o n d i t i o n o f t r e e s e x i s t i n g i n  t y p e o f d e n s i t y i s v e r y compact (densed o r crowded), are so c l o s e t o g e t h e r .  since the  this  trees  The c o m p e t i t i o n i s v e r y g r e a t between them  thus r e s u l t i n g i n h i g h m o r t a l i t y due t o s u p p r e s s i o n o f the weaker  trees.  D e n s i t y extremes o c c u r because n a t u r a l m o r t a l i t y i s i r r e g u l a r and o f t e n associated with periodic climatic  extremes.  A t extreme d e n s i t i e s as i n s t a g n a t e d o r l o c k e d l o d g e p o l e p i n e s t a n d s , the h e i g h t growth i s f a r s l o w e r .  Due t o c o m p e t i t i o n each  t r e e w i l l n o t get as much n u t r i t i o n as t h e t r e e s i n open s t a n d d e n s i t y and t h e a r e a f o r p h o t o s y n t h e s i s i s a l s o s m a l l e r . although i t  The d . b . h . growth,  i s i n c r e a s i n g , i s alow and the crowns due t o t h e c l o s e n e s s  87. o f n e i g h b o u r i n g t r e e s w i l l not be a b l e t o expand.  At the same time  some o f the o u t e r young shoots may be broken o f f by crown f r i c t i o n caused by wind a c t i o n . grown t r e e s .  So crown w i d t h i s f a r below t h a t o f open-  The c l e a r b o l e l e n g t h i s a l s o l o n g e r , o r a t l e a s t  same as t h o s e of normal-dense grown t r e e s . ratio is  the  T h e r e f o r e the CW/dbh  s m a l l e r about 0 . 7 and t h e r e are l a r g e r H/CW r a t i o s ,  8 or  more. T h e o r e t i c a l models are a t t a c h e d i n appendix 1. The i n f l u e n c e o f crown c l o s u r e on s t a n d d e n s i t y A e r i a l photographs, can be used t o measure a c e r t a i n p a r t of t h e growing s t o c k w i t h i n any f o r e s t s t a n d s , t h a t i s o f i n t e r e s t particular investigator.  D i r e c t e s t i m a t i o n o f crown c l o s u r e , s i z e of  crown, and t r e e h e i g h t i s p o s s i b l e and t h e s e v a r i a b l e s  can be u s e d  i n d i r e c t l y t o c a l c u l a t e d . b . h . , b a s a l a r e a and number o f t r e e s acre.  With these d i r e c t l y  variables  t o any  e s t i m a t e d , and i n d i r e c t l y  per  calculated,  the e v a l u a t i o n o f s t a n d d e n s i t y and s t o c k i n g i s p o s s i b l e . Crown c l o s u r e ,  s i z e of crown, h e i g h t , d . b . h . , b a s a l a r e a  and number o f t r e e s per a c r e are the most i m p o r t a n t v a r i a b l e s  to  evaluate  When  stand d e n s i t y and s t o c k i n g from a e r i a l p h o t o g r a p h s .  crown c l o s u r e i s n o t used i n stand d e n s i t y and s t o c k i n g e s t i m a t i o n , r e s u l t s are sometimes v e r y m i s l e a d i n g because w i t h o u t p e r c e n t a g e of crown c l o s u r e the stand d e n s i t y and s t o c k i n g cannot be separated.  accurately  The d i s t r i b u t i o n o f crown c l o s u r e i s a l s o an i m p o r t a n t  f a c t o r to be c o n s i d e r e d , e . g . the same percentage o f crown c l o s u r e may be i n one b l o c k , l i n e o r d i s p e r s e d clumps. c r e a t e d i f f e r e n t stand s t r u c t u r e ,  A l l these f a c t o r s  can  thus g i v i n g d i f f e r e n t stand d e n s i t y  and s t o c k i n g .  Even w i t h the same percentage crown c l o s u r e and  s i m i l a r d i s t r i b u t i o n , the crown c l o s u r e may be dense o r sparse which a g a i n shows d i f f e r e n c e s i n stand d e n s i t y and s t o c k i n g . two d i f f e r e n t crown c l o s u r e s t h a t are e x a c t l y a l i k e i n f o r e s t s o r even i n  There a r e no natural  plantations.  Crown c l o s u r e i s q u i t e d i f f e r e n t from t h a t o f density,  stand  e . g . 50 p e r c e n t crown c l o s u r e o f a u n i t a r e a may come from  a few v e r y l a r g e t r e e s , many l a r g e t r e e s ,  o r v e r y many s m a l l  trees.  S i n c e the number o f t r e e s w i t h i n a u n i t a r e a i s d i f f e r e n t the i s also different.  density  The v a r i a t i o n o f d e n s i t i e s may take many forms  because the d i s t r i b u t i o n o f the t r e e s w i l l i n f l u e n c e the crowding o f the stands w i t h t h e same crown c l o s u r e .  The stand d e n s i t y  therefore  depends on the s i z e o f t r e e crowns and t h e i r d i s t r i b u t i o n . T h e o r e t i c a l l y i t may be t r u e t h a t i n p r o p e r l y managed p l a n t a t i o n s the t r e e s are r e g u l a r l y d i s t r i b u t e d u n l e s s t h e r e has been clumped m o r t a l i t y (v&i))  subsequent to  establishment.  The i n f l u e n c e o f stand d e n s i t y on growth and o t h e r t r e e and stand variables Growth can be measured as t o t a l c u b i c volume growth o r merchantable growth y i e l d . the f i r s t  The d i f f e r e n c e between these two i s  one c o n s i d e r e d the t o t a l volume growth e . g . a l l  t r e e s i n the standj  that  complete  and t h e second one o n l y measured the p o r t i o n o f  merchantable growth which i s dependent upon diameter growth r a t e ,  and  o t h e r s p e c i f i c a t i o n o f the p r o d u c t s d e s i r e d . Hawley and Smith (1954)  stated that,  i n theory,  the  g r e a t e s t c u b i c volume o f wood i s produced i n t h o s e p l a n t a t i o n s are f i r s t  dense enough t o a c h i e v e f u l l occupancy o f the s i t e as  that early  89 as p o s s i b l e w i t h o u t b e i n g so d e n s e l y spaced t h a t t h e y d i m i n u t i o n of h e i g h t growth.  suffer  As the s p a c i n g i s widened beyond t h i s  optimum, p r o d u c t i o n o f c u b i c volume i s l o s t because a l l u n d e r s t o c k e d u n t i l crowns o r r o o t systems c l o s e . that after f u l l  stands remain  They f u r t h e r  s t o c k i n g has been a t t a i n e d , p r o d u c t i o n o f  stated  total  c u b i c volume tends t o be c o n s t a n t and optimum over a r e l a t i v e l y range of stand d e n s i t i e s and t h a t i t  can be d e c r e a s e d , but n o t  i n c r e a s e d , by a l t e r i n g the amount o f growing s t o c k t o l e v e l s this  wide  outside  range. The i n f l u e n c e o f s t a n d d e n s i t i e s on t r e e and s t a n d  characteristics (1)  can be s t a t e d as f o l l o w s :  Diameter - i n c r e a s e s w i t h s p a c i n g f o r a g i v e n age.  T h i s means  t h a t t r e e s grow f a s t e r i n open stand d e n s i t y than dense stand density. (2)  Height - i s a f f e c t e d by s p a c i n g depending upon the s p e c i e s . The Wind R i v e r Experiment showed s u b s t a n t i a l i n c r e a s e i n h e i g h t o f Douglas f i r  total  but Alabama A g r i c u l t u r a l Experiment  S t a t i o n showed r e s u l t s of s l a s h , l o b l o l l y and l o n g l e a f p i n e were l i t t l e a f f e c t e d by s p a c i n g .  Height growth i s reduced a t  the  extremes o f s p a c i n g , e s p e c i a l l y i n c l o s e l y - s p a c e d s t a n d s on poor s i t e (3)  (Hawley and S m i t h , 1954) •  Crown d i a m e t e r , l i v e crown l e n g t h and crown r a t i o i n c r e a s e w i t h open s p a c i n g . available  per  T h i s i s due t o t h e g r e a t e r amount o f tree.  space  90. B a s a l a r e a - d e c r e a s e s w i t h an i n c r e a s e i n s p a c i n g when the whole s t a n d i s  c o n s i d e r e d but f o r l a r g e r d i a m e t e r t r e e s i n  the  stand b a s a l area increases with s p a c i n g . Volume - v a r i e s w i t h s p a c i n g a c c o r d i n g t o the minimum merchantable diameter l i m i t s .  Volume g e n e r a l l y d e c r e a s e s when  a l l t r e e s a r e i n c l u d e d but i n d i v i d u a l t r e e volume tends t o increase with spacing. Stem t a p e r - i n c r e a s e s w i t h s p a c i n g . Number o f stems per a c r e - n a t u r a l l y d e c r e a s e s w i t h s p a c i n g . But the f i n a l c r o p t r e e s do n o t i n c r e a s e as much i n the c l o s e r s p a c i n g due t o s u p p r e s s i o n and m o r t a l i t y . M o r t a l i t y - i s d i r e c t l y r e l a t e d t o s p a c i n g because more t r e e s w i l l d i e o f s u p p r e s s i o n i n dense stands than i n open s t a n d s , but m o r t a l i t y from d i s e a s e i s n o t n e c e s s a r i l y r e l a t e d .  91 5.  DESCRIPTION AND LOCATION OF STANDS STUDIED The U n i v e r s i t y of B r i t i s h Columbia Research F o r e s t  is  s i t u a t e d on the lower m a i n l a n d t o the n o r t h o f Haney, i n the l o w e r Fraser V a l l e y of B r i t i s h Columbia.  It  c o n s i s t s o f an a r e a o f about  10,000 a c r e s , w i t h an e l e v a t i o n r a n g i n g from sea l e v e l t o 2 , 6 0 0 f e e t . There a r e a wide v a r i e t y o f c o n i f e r s and hardwoods but the  three  c o n i f e r s p e c i e s t h a t c o n s t i t u t e t h e most v a l u a b l e and l a r g e s t volumes a r e w e s t e r n r e d c e d a r , western hemlock and Douglas f i r .  The  Research F o r e s t i s i n t h e c o a s t a l Western Hemlock Zone ( K r a j i n a 1 9 5 9 ) . F u l l b i o l o g i c a l d e t a i l s o f t h i s zone were g i v e n by O r l o c i ( i n  Krajina,  1 9 6 5 ) ; summaries o f c l i m a t e , geology p e d o l o g y , v e g e t a t i o n and l a n d use were g i v e n by K r a j i n a given i n  (1965).  A b r i e f h i s t o r y o f the f o r e s t was  'The F i r s t Decade o f Management and Research o f U . B . C .  Forest  (1949-1958)'. A l l the d a t a h e r e i n were c o l l e c t e d on the U n i v e r s i t y Research F o r e s t .  The sample p l o t s were d i s t r i b u t e d throughout the  c e n t r a l p o r t i o n o f the f o r e s t and ranged from 500 f e e t t o 1,875 f e e t above sea l e v e l , as shown on the mosaic (appendix 4 ) .  The sample  p l o t s were t a k e n i n f o u r d i f f e r e n t age c l a s s stands (average age o f 30, 60, 90 and 120 y e a r s ) , s i t e classes  on f i v e d i f f e r e n t s u b j e c t i v e l y  selected  (poor d r y , poor wet, medium,good, and v e r y good s i t e s ) ,  and f i v e d i f f e r e n t stand d e n s i t i e s s u b j e c t i v e l y s e l e c t e d by b a s a l a r e a p e r a c r e (open, open-normal, n o r m a l , normal-dense, and dense stand d e n s i t i e s ) .  The young stands sampled were a l l  r e g e n e r a t e d and r e l a t i v e l y  naturally  even-aged (the range may be about 5 y e a r s )  92 western hemlock stands w i t h a s l i g h t m i x t u r e o f Douglas western r e d c e d a r , b l a c k cottonwood and v i n e maple.  fir,  As t h e  became o l d e r the m i x t u r e o f western hemlock, Douglas f i r r e d cedar became more homogeneous and Douglas f i r dominant s p e c i e s .  stands  and western  i s usually  the  T h e r e f o r e the sample p l o t s were never l o c a t e d  in  a b s o l u t e l y pure western hemlock stands and the range of ages was sometimes v e r y w i d e ,  e s p e c i a l l y i n older stands.  The method o f  s e l e c t i o n o f d e n s i t y an t h e ground was by u s i n g b a s a l a r e a p e r  acre.  Thus the more open s t a n d s , e . g . open s t a n d d e n s i t y o f 60 square  feet  b a s a l ' a r e a were n e c e s s a r i l y measured i n clumps r a t h e r than i n  evenly  spaced s t a n d s .  windfall  stands,  Some o f the clumps were remnants of l o g g e d o r  e s p e c i a l l y i n o l d e r and lower d e n s i t y s t a n d s .  T h i s type o f  s t a n d s were chosen because t h e y have the r i g h t d e n s i t i e s by b a s a l a r e a ( p r i s m sweep),  t h u s t h e y may not be as good as s t a n d s growing  under n a t u r a l c o n d i t i o n s . determination of subjective  There was a l s o no c l e a r f e a t u r e s f o r s i t e c l a s s e s and t h u s some of t h e  p l o t s may f a l l o u t s i d e t h e i r c l a s s e s due t o b i a s e d f i e l d based on i n s u f f i c i e n t e x p e r i e n c e i n t h e s e  stands.  the  sample  judgements  93 METHOD OF DATA COLLECTION C o l l e c t i o n o f f i e l d d a t a and making of ground stereograms A t o t a l o f 47 sample p l o t s were measured on the o f B r i t i s h Columbia Research F o r e s t .  University  W i t h i n each sample p l o t a  s e l e c t i o n o f dominant, codominant, i n t e r m e d i a t e and suppressed t r e e s was made and t h e b a s a l a r e a , number o f t r e e s p e r p l o t , d . b . h . , h e i g h t , crown w i d t h , crown c l o s u r e , l i v e crown l e n g t h and age were measured. The b a s a l a r e a at b r e a s t h e i g h t around each sample t r e e was  estimated  by p r i s m sweeps w i t h prisms h a v i n g 10 and 20 b a s a l a r e a f a c t o r s . The number o f t r e e s i n each 360-degree sweep were r e c o r d e d and a count of t h e number o f t r e e s above 4 . 5 f e e t i n a 1/50 a c r e p l o t was a l s o r e c o r d e d by s p e c i e s and d . b . h . abney l e v e l t o t h e n e a r e s t one f o o t .  The h e i g h t was measured w i t h an It  was found by a c t u a l measure-  ments taken on the few t r e e s f a l l e n f o r c o l l e c t i o n o f f o l i a g e the measurements were always w i t h i n o n e - h a l f f o o t . l e n g t h was a l s o e s t i m a t e d by t h e abney l e v e l .  The l i v e  height.  crown  The crown w i d t h was  measured w i t h a diameter t a p e and the crown c l o s u r e was ocularly.  that  estimated  An increment b o r e r was used t o f i n d the age at  breast  A n a l y s e s were made u s i n g age at b r e a s t h e i g h t , e x c e p t f o r  estimation of  s i t e i n d e x which had t h e age t o b r e a s t h e i g h t added.  The s i t e i n d e x was e s t i m a t e d from t h e " a l i g n m e n t c h a r t f o r of s i t e i n d e x f o r western hemlock" by Barnes  determination  (1962).  Four competing t r e e s on the n o r t h , e a s t ,  s o u t h and west  quadrants around each sample t r e e w i t h i n each p l o t were a l s o chosen and measurements of d . b . h . , crown w i d t h and d i s t a n c e away from the  94.. i n d i v i d u a l sample t r e e were r e c o r d e d .  S i n c e the s t a t u s o f competing  t r e e s was n o t easy t o d e f i n e some o f the t r e e s measured may o r may not be c o n s i d e r e d as a c t u a l l y competing t r e e s , sample t r e e o r n o t as c l o s e o r t o o c l o s e  e . g . not as l a r g e  as  together.  Ground stereograms were taken on most o f the sample p l o t s , u s u a l l y around the dominant and/or codominant t r e e s .  The i d e n t i f i c a t i o n  o f dominant, codominant, i n t e r m e d i a t e and suppressed t r e e s was made e a s i e r by a p i e c e o f w h i t e c l o t h a t t a c h e d to each t r e e w i t h v a r y i n g w i d t h , w i t h t h e dominant t r e e h a v i n g the w i d e s t p i e c e o f c l o t h . d i s t a n c e o f the stereograms was about 20 f e e t  away and s i n c e  The  the  camera was h e l d by hand the d i s t a n c e s moved (photo base) were n o t c o n s t a n t but a l l were about h a l f a f o o t .  These stereograms were  t a k e n f o r d e n s i t y s t u d i e s ; t h a t i s to show how t h e t r e e s are d i s t r i buted i n each s t a n d .  Some o f the p l o t s were without  stereograms  because t h o s e p l o t s were sampled on r a i n y days making photography impossible.  A few o f the stereograms were n o t v e r y c l e a r because t h e  camera was s l i g h t l y shaken d u r i n g t h e slow exposure o f the f i l m s . Two s p e c i a l s e t s o f stereograms were a l s o t a k e n t o show t h e  effects  o f d i s t a n c e s moved between exposures from two i n c h e s t o one f o o t a t d i s t a n c e o f 20 and 4-0 f e e t from t h e stand edge (Appendix  a  3).  Crown c l o s u r e photographs were t a k e n between the sample t r e e and the n e a r e s t competing t r e e t o study the crown c l o s u r e . wide angle l e n s on a Pentax camera was u s e d .  A 63 degrees  These photographs are  a l s o shown w i t h the a c t u a l crown c l o s u r e m o d e l s .  95. Measurements o f p h o t o - d a t a and c o n s t r u c t i o n o f crovm c l o s u r e models The sample p l o t s were c a r e f u l l y l o c a t e d on the photographs a f t e r t h e ground measurements were t a k e n .  aerial  The photographs  used were t a k e n i n J u l y , 1965 w i t h an average RF o f 1:15,000 and a 1 2 - i n c h f o c a l l e n g t h by Lockwood Survey C o r p o r a t i o n L i m i t e d .  After  the l o c a t i o n o f the p l o t s t r e e v a r i a b l e s w i t h i n the s t a n d were measured, e . g . h e i g h t , crown w i d t h and crown c l o s u r e were e s t i m a t e d . The h e i g h t was e s t i m a t e d w i t h a p a r a l l a x wedge as d e s c r i b e d i n 4.  section  The measurement o f h e i g h t i n c l u d e d o n l y dominant and codominant  t r e e s and f o u r e s t i m a t i o n s were t a k e n f o r each t r e e .  The crown w i d t h  was e s t i m a t e d w i t h a dot wedge as d e s c r i b e d i n s e c t i o n 5, a l s o o n l y on t h e dominant and codominant t r e e s w i t h the same number o f measurements as h e i g h t .  In o r d e r t o p r e v e n t b i a s , t h e e s t i m a t i o n s o f the  above  two v a r i a b l e s were made i n f o u r d i f f e r e n t s e r i e s w i t h each s e r i e s s e p a r a t e d by a few d a y s .  The crown c l o s u r e was e s t i m a t e d by a Moessner  d e n s i t y s c a l e as d e s c r i b e d i n s e c t i o n 4, u s i n g o n l y two d i f f e r e n t e s t i m a t e d on s e p a r a t e d a y s .  The average v a l u e s o f a l l  the above  series three  v a r i a b l e s were used as the mean o f each v a r i a b l e f o r computation p u r p o s e s . Models o f crown c l o s u r e i n each l o c a l i t y  s t u d i e d were  p r e p a r e d from the a e r i a l photographs t o r e p r e s e n t 1/5 a c r e p l o t s . T h i s was a l a b o r i o u s and t e d i o u s t a s k c a u s i n g much eye  strain.  R e p r e s e n t a t i o n o f each p l o t t o o k an average o f 25 minutes and o n l y a few p l o t s c o u l d be drawn at any one time because o f the eye involved.  strain  A round p l o t w i t h an a r e a e q u i v a l e n t t o 1/5 a c r e on the  1:15,000 RF photographs was made on a sheet o f p l a s t i c .  The  96. directions  (north, northeast,  west and northwest)  east,  southeast,  south,  southwest,  were a l s o drawn onto t h e s i d e s o f the p l o t so  t h a t the crown w i d t h of i n d i v i d u a l t r e e can be p l o t t e d more accurately,  under t h e s t e r e o s c o p e , onto the m o d e l s .  However  since  the t r e e s were n o t e v e n l y spaced and the number o f t r e e s cannot be a c c u r a t e l y counted on t h e a e r i a l photographs o f 1:15,000 RF, average crown w i d t h was o f t e n u s e d . the w r i t e r  T h i s method was e a s i e r  the because  has n o t e d the ground c o n d i t i o n s when samples were taken  on the g r o u n d .  Another f a c t o r t h a t may n o t be v e r y a c c u r a t e was  o v e r l a p o f i n d i v i d u a l t r e e s c o n s t r u c t e d i n the model because f a c t o r cannot be seen c l e a r l y from the a e r i a l p h o t o g r a p h s .  the  this The  a c c u r a c y o f b o t h the above f a c t o r s f o r the model c o n s t r u c t i o n w i l l be dependent upon i n d i v i d u a l judgements. The models o f crown c l o s u r e are a t t a c h e d i n appendix 2.  97. 7.  INTERPRETATION OF PHOTO-MENSURATION DATA  A.  D e s c r i p t i o n o f crown c l o s u r e models D e s c r i p t i o n s o f crown c l o s u r e models i n d i v i d u a l l y were t a b u l a t e d i n c o n j u n c t i o n w i t h the models i n appendix 2. 31 v a r i a b l e s , listed  A total  photo and ground, were used t o d e s c r i b e each model as  below:-  Model number Photo d a t a Date o f photography Representative Focal Flying  fraction  length height  Plot size Elevation of  of  plot  T o t a l h e i g h t o f dominant t r e e Average h e i g h t o f dominant and codominant  trees  Dominant crown w i d t h Average crown w i d t h o f dominant and codominant Height/Crown w i d t h  ratio  Average h e i g h t / a v e r a g e crown w i d t h Grown c l o s u r e ( i n Adjusted basal  decimal)  area  1  2 A d j u s t e d number o f t r e e s per  acre  Ground d a t a Age c l a s s 1  A c t u a l b a s a l a r e a p e r a c r e d i v i d e d by d e c i m a l crown c l o s u r e .  2  A c t u a l stems per a c r e d i v i d e d by d e c i m a l crown c l o s u r e .  98. Site  class  S i t e index B a s a l a r e a per  acre  Number of t r e e s p e r  acre  T o t a l h e i g h t o f dominant t r e e Crovm w i d t h o f dominant t r e e Diameter a t b r e a s t h e i g h t o f dominant t r e e Average d i a m e t e r a t b r e a s t  height  L i v e crown l e n g t h Crown w i d t h / d i a m e t e r Height/crown w i d t h  breast height  ratio  ratio  Normal number o f t r e e s p e r  acre  Crowding f a c t o r A d j u s t e d crowding f a c t o r ^ M o r t a l i t y per  acre  Discussion How w e l l do photo models agree w i t h t h o s e t h e o r e t i c a l  models?  The comparison o f t h e o r e t i c a l and photo crown models can be d i s c u s s e d under t h e f o l l o w i n g headings D i s t r i b u t i o n of  trees  Crown w i d t h s i z e s H e i g h t f of  trees  Crown c l o s u r e L i v e crown l e n g t h and r a t i o s Trend towards  3  normality  A c t u a l stem p e r a c r e d i v i d e d by d e c i m a l crown c l o s u r e and normal stems p e r a c r e .  99. In t h e t h e o r e t i c a l models the s p a c i n g and d i s t r i b u t i o n o f t r e e s are v e r y r e g u l a r and u n i f o r m .  They r e p r e s e n t the  ideal  d i s t r i b u t i o n o f open, open-normal, n o r m a l , normal-dense, and dense s t a n d d e n s i t i e s as w e l l as s t o c k i n g . representative  These c o n d i t i o n s are more  of p l a n t a t i o n s than n a t u r a l f o r e s t stands.  models are r e p r e s e n t a t i o n s o f t r u e n a t u r a l f o r e s t  The photo  stands, thus  d i s t r i b u t i o n s o f t r e e s are i n i r r e g u l a r arrangements.  the  Some o f them  a r e q u i t e e v e n l y d i s t r i b u t e d w h i l e o t h e r s are n o t , and some are s c a t t e r e d , i n clumps o r even i n l i n e s . within i t s e l f ,  Each one o f the above  varies  e . g . a clump may be formed by c l o s e l y grown t r e e s  or  t r e e s growing a p a r t from each o t h e r o r a m i x t u r e o f b o t h on a s m a l l a r e a w i t h open spaces around i t .  In n a t u r a l f o r e s t clumps, growth  is  most common because o f m i c r o - s i t e i n f l u e n c e s on s e e d l i n g e s t a b l i s h m e n t . The s i z e o f t r e e crowns i n i n d i v i d u a l t h e o r e t i c a l models  is  the same and t h e i n c r e m e n t s a r e a l s o assumed t o be a t t h e same r a t e . Thus t h e r e are n e g l i g i b l e d i f f e r e n c e s i n crown s i z e s as w e l l as i n t r e e heights, therefore i t the crown c l o s u r e i s  i s o n l y l o g i c a l t o make another assumption t h a t o n l y a t one h e i g h t l e v e l .  These assumptions  a g a i n are o n l y a p p l i c a b l e t o even-aged p l a n t a t i o n s t a n d s .  The s i z e s  o f t r e e s i n a n a t u r a l s t a n d (photo crown models) v a r y g r e a t l y  e.g.  t h e r e may be t r e e s as s m a l l as 4" d . b . h . o r s m a l l e r up t o 1 0 " d . b . h . o r l a r g e r i n the s t a n d .  Even i n even-aged n a t u r a l stands  (a  difference  o f 5 y e a r s o r more may be c o n s i d e r e d as even-aged depending on the age o f the stand) w i t h i n the stands.  t h e s i z e s may v a r y because o f the range o f ages T h i s means t h a t d i f f e r e n t s i z e s o f crown d i a m e t e r  and h e i g h t a r e p r e s e n t which w i l l g i v e r i s e t o d i f f e r e n t  stories  of  100. crown c l o s u r e w i t h i n the s t a n d s . The l i v e crown l e n g t h and r a t i o o f the i n d i v i d u a l model can be e s t i m a t e d e a s i l y and q u i t e a c c u r a t e l y  theoretical  as the sequence o f  models shows v e r y open towards v e r y dense s t a n d d e n s i t y and a l s o stocking.  Even i f  the stand i s r e l e a s e d from dense back t o open o r  normal some e s t i m a t i o n can be made.  T h i s i s not the case w i t h n a t u r a l  s t a n d s because t h e y had passed through a l o n g p e r i o d under the of n a t u r a l c o n d i t i o n s .  The c o n d i t i o n s o f each s p e c i f i c t y p e o f  s t a n d i s d i f f e r e n t from a n o t h e r , thus making i t u n d e r s t a n d i n g o f the n a t u r a l f o r e s t difficulties it  influence  stands.  natural  complicated f o r  Because o f the  full  above  i s v e r y hard t o e s t i m a t e t h e l i v e crovm l e n g t h and r a t i o  from the appearance o f the i n d i v i d u a l model w i t h o u t f u l l  information  o f stand h i s t o r y as w e l l as ground s a m p l i n g . It  i s n o t hard t o see from the t h e o r e t i c a l models how an open  s t a n d t r e n d s toward n o r m a l i t y because o f the s i m i l a r growth r a t e assumption.  However,  it  i s v e r y h a r d t o v i s u a l i z e from t h e s i n g l e phase,  exposed t o v a r i o u s n a t u r a l c o n d i t i o n s , o f such a t r e n d on the photo m o d e l s . T h i s needs c a r e f u l a c c u m u l a t i o n o f d a t a on t h e stands i n v o l v e d . In  conclusion i t  can be s a i d t h a t the t h e o r e t i c a l and photo  models are q u i t e d i f f e r e n t from each o t h e r because t h e r e i s no i d e a l d e n s i t i e s i n n a t u r a l f o r e s t that could represent the t r u e  theoretical  densities, (ii)  Ground stereograms Two s e t s o f ground stereograms were t a k e n to determine d i s t a n c e between exposures t h a t was most d e s i r a b l e at 20 and AO from the stand edge.  W i t h t h e h e l p o f t h e s e i t was found t h a t  the feet  at  101. 20 f e e t t h e b e s t d i s t a n c e between exposures (photo-base) was 6 inches.  within  When the camera i s 4-0 f e e t away the b e s t d i s t a n c e between  exposures was w i t h i n 12 i n c h e s . t o the l e f t  The movement o f the camera may be  o r r i g h t as l o n g as both photographs c o v e r e d the same  a r e a (100 p e r c e n t c o v e r a g e ) .  The d i s t a n c e between exposure a l s o  i n f l u e n c e d the depth p r e c e p t i o n , e . g . t h e depth p r e c e p t i o n i n c r e a s e s w i t h the l e n g t h o f p h o t o - b a s e , u n t i l the s e p a r a t i o n i s two images w i l l no l o n g e r be merged.  so f a r t h a t  the  T h i s means t h a t the p o s i t i o n o f  the two photo are so f a r a p a r t t h a t t h e y do not r e c o r d the same images (two t o t a l d i f f e r e n t views) o f the same o b j e c t s as shown i n f i g u r e 1 3 .  DIST.  k-  PHOTO -4 BASE  r — P H O T O BASE—*  F i g u r e 13 - The d i f f e r e n c e s o f photo-base on ground stereograms.  0  102 8.  TEST OF PHOTO-INTERPRETATION FIELD DATA  AND PHOTO-MENSURATION RESULTS AGAINST  A n a l y s i s o f photo-mensuration d a t a and ground d a t a .  A l l t h e a n a l y s e s were made by r e g r e s s i o n a n a l y s i s computed on an IBM 704-0 computer. variables  Simple a n a l y s e s o f r e g r e s s i o n between two  and m u l t i p l e r e g r e s s i o n of one dependent v a r i a b l e  number o f o t h e r independent v a r i a b l e s were u s e d . a m u l t i p l e l i n e a r r e g r e s s i o n equation i s t h a t ,  on a  The advantages  of  i t measures the combined  i n f l u e n c e o f a l l independent v a r i a b l e s on the dependent v a r i a b l e . f o l l o w i n g twenty-four  v a r i a b l e s were used but each a n a l y s i s may c o n s i s t  o f l e s s than t h i s t o t a l number.  The v a r i a b l e s l i s t e d below are not  i n sequence because t h e s e v a r i a b l e s were o n l y p a r t o f the d a t a c o l l e c t e d d u r i n g the summer o f 1966. other variables  M r . Osborn w i l l analysec'  i n h i s study o f growth.  XI  == Diameter a t b r e a s t h e i g h t  X2  == t o t a l h e i g h t ground ( H t , G ) .  X3  ==  X5  == crown w i d t h (CW,G)  X6  == l i v e crown l e n g t h  X7  == l i v e crown r a t i o  age at b r e a s t h e i g h t  (D).  (Age)  (LCL) (LCR)  X13 == b a s a l a r e a o f i n d i v i d u a l t r e e X14- == X15  -=  X16 ==  t o t a l height/crown w i d t h r a t i o crown w i d t h / d i a m e t e r  (BA,T) (Ht/CW,G)  at b r e a s t h e i g h t r a t i o  (CW/D)  b a s a l a r e a w i t h a t e n BAF f a c t o r p r i s m (BA,10)  X17 == number o f t r e e s per a c r e X19 ==  The  (SPA)  crown c l o s u r e photo ( i n decimal)  (CC,P)  the  103 X21  =  b a s a l a r e a a d j u s t e d per a c r e  (Adj.BA)  X23  =  t o t a l h e i g h t photo (Ht,P)  X33  =  crown s u r f a c e a r e a  X34-  =  crown volume  X38  =  average t o p h e i g h t o f codominant and dominant t r e e s the p l o t photo ( A v . H t , P )  X39  =  average crown width of codominant and dominant t r e e s t h e p l o t photo (Av.CW,P)  X4O  =  crown w i d t h photo (CW,P)  X4I  =  s i t e index  X45  =  t o p height/crown width photo (Ht/CW,P)  X46  =  average h e i g h t / a v e r a g e crown w i d t h r a t i o photo (Av.Ht/Av.CW,P)  X73  =  crowding f a c t o r  X74-  =  crowding f a c t o r a d j u s t e d  (CSA)  (GV) in in  (SI)  (OF) (Adj.CF)  The mean, standard d e v i a t i o n , c o e f f i c i e n t o f  variation,  maximum and minimum f o r each o f t h e s e v a r i a b l e s are shown i n Table 1 3 . Simple c o r r e l a t i o n c o e f f i c i e n t s o f 9 dependent v a r i a b l e s the 24 independent v a r i a b l e s are l i s t e d i n T a b l e s 14- and 1 5 . seen from t h e t a b l e s t h a t more independent v a r i a b l e s w i t h CW/D(X15),  are  It  can be  correlated  Ht/CW,G(Xl4), Ht/CW,P(X45) and Av.Ht/CW,P(X46) than  BA(X16), C C , P ( X 1 9 ) ,  A d j . B A ( X 2 l ) , CF(X73) and A d j . C F ( X 7 4 ) .  Although  t h e r e a r e many h i g h l y s i g n i f i c a n t c o r r e l a t i o n s they d i d not account f o r a l a r g e percentage o f the t o t a l sum o f s q u a r e s .  The r a t i o s  of  XL4, X15» X45 and X46 seems t o be h i g h l y c o r r e l a t e d w i t h each o t h e r and e x p l a i n e d a g r e a t e r amount o f v a r i a t i o n than t h a t between the other  variables.  on  104 Simple l i n e a r r e g r e s s i o n e q u a t i o n s were a l s o computed f o r v a r i o u s dependent and independent v a r i a b l e s  as l i s t e d i n T a b l e 1 6 .  These e q u a t i o n s were used f o r g r a p h i c a l p u r p o s e s , so t h a t the  relation  of any two v a r i a b l e s p r e s e n t i n each e q u a t i o n may be b e t t e r u n d e r s t o o d . The e q u a t i o n s were p l o t t e d as shown i n F i g u r e s 14- t o 2 7 , a d e s c r i p t i o n o f each f i g u r e i s a l s o a t t a c h e d . The m u l t i p l e r e g r e s s i o n program used was d e s c r i b e d by Kozak and Smith (1965), and Munro, Kozak and H e j j a s (1965). program i n c o r p o r a t e d the M i l l e r ' s  This  (1965) t-prime c r i t e r i o n i n t o  the  e a r l i e r program; t h a t c o u l d c a r r y out the t e s t o f s i g n i f i c a n c e at any stage o f t h e e l i m i n a t i o n and when the v a r i a n c e r a t i o i s the e l i m i n a t i o n c o u l d be s t o p p e d .  Earlier  ending w i t h the most important v a r i a b l e ,  significant,  programs d i d not ensure  thus the adding o f  Miller's  t-prime goes a l o n g way toward c o r r e c t i n g f o r the commonly observed s i t u a t i o n , where t h e r e seldom i s t r u e independence among the independent variables.  M i l l e r ' s t-prime c r i t e r i o n i n v o l v e s a p p l i c a t i o n o f a  weighing f a c t o r t o supplement t h e use o f p a r t i a l c o e f f i c i e n t s o f d e t e r m i n a t i o n f o r s e l e c t i o n o f v a r i a b l e s t o be e l i m i n a t e d .  The use of  t h i s new c r i t e r i o n s h o u l d improve the p r o b a b i l i t y t h a t the most important v a r i a b l e s w i l l be r e t a i n e d at a l l CW/D r a t i o  (X15)  and Ht/CW.G r a t i o  stages o f the  analysis.  (X14)  M u l t i p l e r e g r e s s i o n a n a l y s e s u s i n g the program d e s c r i b e d above were made f o r CW/D and Ht/CW,G r a t i o s on 14 independent (Xl(DBH), X 2 ( H t , G ) , X3(Age), X5(CW,G), X 6 ( L C L ) , X16(BA,10), X41(SI)).  X17(SPA), X 1 9 ( C C , P ) ,  X21(Adj.BA),  X7(LCR),  variables  X13(BA,T),  X33(CSA), X34(CV) and  T a b l e s 17 and 18 g i v e the v a r i a n c e r a t i o s o f each  105. independent v a r i a b l e a t each stage i n the stepwise r e g r e s s i o n a n a l y s i s f o r each dependent v a r i a b l e .  The c r i t e r i o n f o r r e j e c t i o n  of each independent v a r i a b l e was d i s c u s s e d e a r l i e r .  The b e s t  c o m b i n a t i o n s f o r t h r e e , two and one independent v a r i a b l e s were a l s o a n a l y s e d and the r e g r e s s i o n e q u a t i o n s o f t h r e e v a r i a b l e s are g i v e n i n Table 3 1 . A n a l y s i s o f GW/D(X15) and X5(GW,G), and Ht/CW,G(XL4)  as the dependent v a r i a b l e on Xl(DBH) on X2(Ht,G) and X5(CW,G) were a l s o made  t o determine t h e e f f e c t i v e n e s s o f t h e s e v a r i a b l e s on t h e i r  ratios  (Table 3 6 ) . Ht/CW.P r a t i o  (XA5)  and Av.Ht/Av.CW.P r a t i o  (XA6)  Ht/CW,P and Av.Ht/Av.CW,P r a t i o s were a l s o a n a l y s e d w i t h 14 independent v a r i a b l e s , but the Ht/CU,P r a t i o i n c l u d e d X23(Ht,P) and X40(CW,P) X39(Av.CW,P)  w h i l e the Av.Ht/Av.CW,P r a t i o i n c l u d e d X38(Av.Ht,P) and a l s o the same o t h e r independent v a r i a b l e s  X 3 ( A g e ) , X 6 ( L C L ) , X7(LCR), X 1 3 ( B A , T ) , X l 6 ( B A , 1 0 ) , X2l(Adj.BA),  X33(CSA), X34-(CV) and X 4 1 ( S I ) ) .  and  (Xl(DBH),  X17(SPA),  X19(CC,P),  The v a r i a n c e r a t i o s o f  each independent v a r i a b l e a t each stage i n the s t e p w i s e r e g r e s s i o n a n a l y s i s f o r each dependent v a r i a b l e are g i v e n i n T a b l e s 19 and 2 0 . The b e s t c o m b i n a t i o n f o r t h r e e , two and one independent v a r i a b l e s were a l s o a n a l y s e d and t h e r e g r e s s i o n e q u a t i o n s o f t h r e e v a r i a b l e s  are  l i s t e d i n Table 31. A n a l y s e s o f Ht/CW,P ( X 4 5 ) and Av.Ht/Av.CW,P(X4.6) independent v a r i a b l e s X 2 3 ( H t , P ) ,  on the  X 4 0 ( C W , P ) and X 3 8 ( A v . H t , P ) ,  X39(Av.CW,P)  r e s p e c t i v e l y were made to determine the u s e f u l n e s s o f t h e s e v a r i a b l e s (Table  36).  106. The e f f e c t s upon c o r r e l a t i o n c o e f f i c i e n t ,  coefficient  of  d e t e r m i n a t i o n and s t a n d a r d e r r o r of e s t i m a t e o f the r e g r e s s i o n e q u a t i o n s caused by r e j e c t i n g or r e d u c i n g the number o f independent v a r i a b l e s f o r the v a r i o u s dependent v a r i a b l e s  (X15(CW/D), X14  ( H t / C ¥ , G ) , X45(Ht/CW,P) and X46 (Av.Ht/Av.CW,P)) are l i s t e d  in  T a b l e 36. (iii)  Basal area ( X l 6 ) . Ad.i.BA(X2l).  CC.P(X19).  CF(X73) and Adi.CF(X7A)  These v a r i a b l e s were a l s o used as dependent v a r i a b l e s a n a l y s e d i n d i v i d u a l l y on v a r i o u s independent v a r i a b l e s The v a r i o u s r a t i o s o f each independent v a r i a b l e  and  as above.  a t each s t a g e i n  the  stepwise r e g r e s s i o n , a n a l y s i s f o r each dependent v a r i a b l e a r e  listed  i n T a b l e s 21 t o 3 0 .  are  The b e s t combinations o f t h r e e v a r i a b l e s  a l s o g i v e n i n T a b l e 31•  107. Table 13 - Mean, standard d e v i a t i o n (SD), c o e f f i c i e n t o f v a r i a t i o n p e r c e n t (CV %), minimum and maximum f o r a l l v a r i a b l e s of 4-7 western hemlock. Variables  Mean  Standard deviation  Minimum  Maximum  cv(#)  Units  XI  DBH  13.99  5.71  5.50  27.80  40.82  inches  X2  Ht,G  91.51  32.19  38.00  150.00  35.18  feet  X3  Age  61.26  32.69  20.00  133.00  53.36  years  X5  CW,G  20.83  5.57  10.00  32.00  26.74  feet  X6  LGL  59.75  20.77  21.00  99.00  34.76  feet  X7  LCR  67.48  16.41  35.71  100.00  24.32  X13  BA,T  1.24  0.99  0.17  4.22  80.60  XU  H/CW  4.44  1.19  2.11  26.80  X15  CW/D  1.60  0.38  1.06  6.94 2.53  23.50  X16  BA,10  185.11  85.34  50.00  370.00  X17  SPA  834.00  923. U  100.00  X19  CC,P  57.06  0.1689  X21  Ad'ij.BA  336.57  X23  Ht,P  X33  square  feet  46.10  square  feet  3950.00  110.68  Number  0.0500  0.8500  29.61  Percent  165.76  142.86  1200.00  49.25  square  91.81  32.66  39.20  152.40  35.58  feet  CSA  8089.18  6283.14  647.93  26274.00  77.67  square  X34  CV  2117.05  1155.85  375.08  5040.70  54.60  cubic  X38  Av.Ht,P  88.35  32.26  39.20  152.40  36.52  feet  X39  Av.CWjP  18.63  6.23  8.00  31.00  33.41  feet  X4O  CW,P  19.58  6.23  8.00  32.10  31.83  feet  X41  SI  122.49  22.68  80.00  160.00  18.52  feet  X45  Ht/CW,P  4.83  1.37  2.49  8.01  28.36  X46  Av.Ht/ Av.CW,P  4.86  1.26  2.66  8.01  25.97  X73  CF  0.80  0.50  0.11  2.22  63.19  X74  Adj.CF  1.38  0.74  0.35  3.03  53.65  feet feet feet  and c o e f f i c i e n t s o f T a b l e 14 - Simple c o r r e l a t i o n c o e f f i c i e n t s d e t e r m i n a t i o n percentages between X14, X15, X45 and X46 on a l l the other independent v a r i a b l e s  Dep. In.  Var,  X14 (Ht/CW,G)  Var.  v (%)  X14 X15 X16 X17 X19 X21 X23 X33 X34 X38 X39 X40 X4I X45 X4-6 X73 X74  0.306» 0.614**  0.446**  (Ht/CW) (CW/DBH) (BA,10) (SPA) (CC,P) (Adj.BA) (Ht,P) (CSA) (CV) (Av.Ht,P) (Av.CWjP) (CW,P) (SI) (Ht/CW,P) (Av.Ht/Av.CW,P) (CF) (Adj.CF)  -0.121 0.326* -0.586** -0.249 1.000** -0.779** 0.529** -0.077 0.301 0.162 0.611** 0.049 0.127 0.608** 0.108 -0.0300 0.110 0.845** 0.762**  0.450** 0.425**  ** i n a l l tables indicates * in all  tables indicates  9.30  37.70 19.90  10.63 34.34  100.00 60.68 27.98 9.06 37.33 36.97  -0.731** -0.792** -0.732** -0.327* -0.587**  0.462**  -0.677** -0.779** 1.000** -0.268 0.314* -0.084 -0.148 -0.790** -0.467** -0.511** -0.775** -0.503**  58.06  20.25  18.06  0.057 -0.527** -0.438** -0.279 -0.353*  53.44 62.73 53.58  10.69  34.46 21.34  45.83  60.68  100.00 9.86  62.41 21.81  26.11 60.06  25.30 16.97  27.77 19.18  12.46  P  v (%)  2  0.086 0.371* 0.237-0.294*  0.59  -0.476** 0.070 0.845** -0.527** 0.608** 0.184 0.314* 0.221 0.376** -0.099 -0.038 0.378** -0.183 -0.331* 0.153 1.000 0.909** 0.483**  13.76  8.64 22.66 71.40 27.77 36.97 9.86 14.14 14.29 10.96 100.00  82.63  0.446**  23.33 19.39 = .372)  significance  at 1% p r o b a b i l i t y  l e v e l (0.01  significance  at %  l e v e l (0.05 = .288)  probability  X46 ( ^ [ _ S { )  r (%)  2  -0.412** 71.40  X45 (Ht/CW,P)  r (%)  2  XI (DBH) X2 (Ht,G) X3 (Age) X5 (CW,G) X6 (LCL) X7 (LCR)  X13 (BA,T)  X15 (CW/D)  2  0.046 0.329* 0.205 -0.281 0.089 -0.513** 0.035 0.762** -0.438** 0.650** 0.179 0.338* 0.257  10.82  26.32 58.06 18.18 42.25 11.42  0.336*  11.22  -0.066 0.342*  11.70  -0.112  -0.277 -0.317* 10.05 0.090 82.63 0.909** 1.000** 100.00 20.61 0.454** 17.56 0.419**  Table 15 - Simple c o r r e l a t i o n c o e f f i c i e n t s and c o e f f i c i e n t s o f d e t e r m i n a t i o n percentages between X16, X19, X21, X73, X74 on a l l t h e o t h e r independent v a r i a b l e s . Dep. In.  Var. Var.  XI (DBH) X2 (Ht,G) X3 (Age) X5 (CW,G) X6 (LCL) X7 (LCR)  X13(BA,T) Xl4(Ht/CW) X15(CW/DBH) Xl6(BA,10) X17(SPA) X19(CG,P) X2l(Adj.BA) X23(Ht,P) X33(CSA) X3*(CV) X38(Av.Ht,P) X39(Av.CW,P) X40(CW,P) X4l(Sl) X45(Ht/CW,P)  X46(Av.Ht/  Av.CW,P) X73(CF) X74(Adj.CF)  X16 r  -0.103 0.110 -0.047 -0.340* -0.201 -0.581** -0.091 0.529** -0.268 1.000** 0.393** 0.703** 0.329* 0.109 -0.230 -0.247 0.101 -0.287 -0.320* 0.137 0.608**  r (%) 2  r  r (%) 2  -0.226  -0.048  11.56 33.76 27.98 100.00 15.45 49.42 10.82  10.24  0.650**  36.97 42.25  0.485**  23.52  0.216  X19 (CC,P)  (BA,10)  -0.078 -0.362* -0.341* -0.538** -0.208 0.301* 0.084 0.703** 0.544** 1.000** -0.254 -0.064 -0.317* -0.351 -0.076 -0.295* -0.316* -0.048 0.314* 0.338* 0.523** 0.027  13.1 11.63 28.94  9.06 49.42 29.59 100.00 10.05 12.32 8.70 10.04  X21  (Adj.BA)  r 0.030 0.051 -0.072 -0.043 0.015 -0.084 0.011 0.162 -0.148 0.329* -0.015 -0.254 1.000** 0.057 -0.026 -0.014  r {%) 2  10.82 100.00  0.060  9.86 11.42  -0.085 -0.055 0.172 0.221 0.257  27.35  0.032  0.342*  11.70  X73 r -0.039 0.131 0.153 -0.238 0.059 -0.186 -0.072 0.450** -0.279 0.485** 0.474** 0.523** 0.032 0.128 -0.158 -0.107 0.136 -0.163 -0.237 -0.063 0.483** 0.454** 1.000** 0.823**  (CF) r (%) 2  X74 ( A d j . C F ) r  v (%) 2  0.138  0.260  20.25 23.52 22.47 27.35  23.33 20.61 100.00  67.73  0.269 -0.042 0.277 -0.058 0.081 0.425** -0.353* 0.216 0.196 0.027 0.342* 0.267 0.020 0.100 0.282 -0.001 -0.059 -0.007 0.446** 0.419** 0.823** 1.000**  18.06 12.46  11.70  19.89 17.56 67.73 100.00  110 T a b l e 16 - Simple l i n e a r r e g r e s s i o n e q u a t i o n s , w i t h c o r r e l a t i o n c o e f f i c i e n t , standard e r r o r and degrees o f freedom on v a r i o u s independent v a r i a b l e s by the dependent v a r i a b l e s X15, X14, X45, X46, X16, X21 and X19. Dep.Var. X15(CW/D)  In.Var.  a  b  r  vH%)  S E  E  df 1/45  X3 X16 X17 X19 X21 X73 X74  •2.114 . 1.818 1.493 1.705 1.712 1.765 I.846  -0.008 -0.001 0.0001 -0.186 -0.0003 -0.209 -0.179  -0.732** 0.268 0.314* 0.084 O.I48 0.279 0.353*  53.5 7.19 9.86 0.70 2.20 7.80 12.46  0.259 0.366 0.361 0.379 O.376 0.365 0.356  X3 X15 X16 X17 X19 X21 X45 X46 X73 X74  3.439 8.367 3.0700 4.513 3.222 4.041 0.891 0.945 3.586 3.490  0.016 -2.461 0.007 -0.0001 2.118 0.001 0.733 0.718 1.064 0.681  0.446** 0.779** 0.529** 0.077 0.301* 0.162 0.845** 0.762** 0.450** 0.425**  19.88 6O.64 27.93 0.59 9.08 2.61 71.43 58.08 20.23 18.06  1.075 0.753 1.019 1.197 1.145 1.185 0.642 0.778 1.073 1.087  X45(Ht/CW,P)  X3 X16 X17 X19 X21 X73 X74  4.222 3.023 4.603 3.380 4.215 3.783 3.691  0.010 0.010 0.0003 2.542 0.002 1.317 0.825  0.237 0.608** 0.184 0.314* 0.221 0.483** 0.446**  5.62 37.01 3.37 9.83 4.89 23.33 19.90  1.345 1.099 1.361 1.315 1.351 1.213 1.240  X46(Av.Ht/ Av.CW,P)  X3 X16 X17 X19 X21 X73 X74  4.371 3.078 4.652 3.416 4.199 3.949 3.870  0.008 0.010 0.0002 1.047 0.002 1.141 0.713  0.205 0.650** 0.179 0.338 0.257 0.454** 0.419**  4.20 42.25 3.19 11.42 6.58 20.64 17.57  1.248 0.969 1.254 1.200 1.232 1.136 1.157  X16(BA)  X3 X17 X19 X73 X74  192.573 154.813 -17.515 119.600 150.785  -0.122 0.036 355.078 82.430 24.849  0.047 0.393** 0.703 0.485** 0.216  0.22 15.44 49.42 23.53 4.66  86.184 79.339 61.359 75.446 84.245  X2l(Adj.BA)  X3 X17 X19 X73 X74  359.057 338.879 478.558 328.277 230.926  -0.367 -0.003 -248.828 104.318 76.483  0.072 0.015 0.254 0.032 0.342*  0.52 0.02 6.43 0.10 11.69  167.151 167.570 162.110 167.507 157.490  tt tt tt tt  X19(CC,P)  X17 X73 X74  0.488 0.431 0.562  0.544** 0.523** 0.027  29.59 27.32 0.07  0.143 0.146 0.171  n  Xl4(Ht/CW,G)  0.0001 0.176 0.006  11  n 11  n n 11 11  it it 11  n ti n tt it u it it tt tt tt n it it 11  tt it tt tt tt 11  it it it tt  tt  it 11  T a b l e 17 - V a r i a n c e r a t i o v a l u e s of independent v a r i a b l e s a t each stage i n t h e stepwise r e g r e s s i o n a n a l y s i s f o r f o u r t e e n v a r i a b l e s e q u a t i o n and f o r t h r e e s e l e c t e d v a r i a b l e s f o r a l l combinations are a l s o g i v e n f o r dependent v a r i a b l e X15(CW/D)  XI Variables  X2  X3  combination  X6  X7  X13  X16  X17  X19  X21  X33  X34  X41  VR  df  181.74 7.31 0.13  37.21 12.81 10.23 67.50 2.26 1.92 2.71 2.17 23.09 15.97 0.54 139.64 14/32  188.16 7.56  42.23 14.16 10.74 72.45 2.32 1.90 2.87 2.38 23.99 16.91 3.04 154.45 13/33  182.01 8.90  38.55 15.57 11.42 70.60  1.47 0.72 0.39 23.83 17.77 2.18 160.87 12/34  183.84 8.40  38.13 16.79 13.32 74.48  0.78  0.08 26.78 19.90 1.71 176.84 11/35  195.95  8.81  39.83 17.22 13.74 78.24  0.83  27.52 20.42 2.07 199.71 10/36  206.70  8.03  43.82 17.06 13.01 83.02  27.23 20.07 1.79 222.73  9/37  183.87  57.93  8.38  4.88 88.77  26.34 15.89 0.58 210.62  8/38  197.82  59.64  9.66  7.05 91.00  26.89 16.71  243.23  7/39  165.34  313.66  1.92 69.67  20.68 11.45  231.96  6/40  272.30  360.77  95.60  32.91 26.09  271.90  5/41  261.85  210.99  53.98  208.69  4/42  236.37  299.96  45.46  254.32  3/43  313.50  142.52  178.21  2/44  51.61  1/45  51.61 best  X5  4.78  0.03 8.55  3.02  27.13  3/43  15.13  3.44  41.59  2/44  75.65  1/45  75.65  T a b l e 18 - V a r i a n c e r a t i o v a l u e s o f independent v a r i a b l e s a t each stage i n t h e stepwise r e g r e s s i o n a n a l y s i s f o r f o u r t e e n v a r i a b l e e q u a t i o n and f o r t h r e e s e l e c t e d v a r i a b l e s f o r a l l combinations are a l s o g i v e n f o r dependent v a r i a b l e X14(Ht/CW,G) Equation '*  14  Variables  XI  X2  X3  X5  X6  X7  1 1 . 5 6 41.74 1 . 5 1 2 27.89 11.90 4 3 . 9 5 1 . 6 4 3 0 . 5 7 11.07 4 3 . 7 6 28.41 29.77 11.59 48.38 31.96 13.69 5 8 . 0 3 13.53 5 9 . 7 2  39.06 37.11 11.11  32.02 12.13 33.47 12.60 44.13 16.24 45.74 16.69 42.13 14.73 34.80 4 0 . 5 5 14.72 17.93  22.30  36.09 32.71  X13  X16  14.60  1.92  11.82  24.09 2.30  9.66  25.14  8.98  combinations  23.34 33.73 27.23  X33  X34  W  43.93 39.38 1.39 45.53 41.08 1.51 49.91 48.18 0.12 5 1 . 6 9 50.17 47.85 46.22 48.05 45.34 27.35 27.62  28.79  26.62  1 0 5 . 5 5 190.14 76.57 143.62 56.30 112.38  TO  230.37  df  1  14/32  255.35 1 3 / 3 3  271.43 1 2 / 3 4  303.77 11/35 322.33 10/36 345.74 9/37  291.23 8 / 3 8 321.80 7/39  242.57 6/40 5/41  239.47 131.46 26.60 23.48  4/42 3/43 2/44 1/45  9.86  22.31  3/43  23.20  31.93  2/44  27.23  1/45  155.00  42.89 23.48  1.84  X21  231.72  9.39  227.89 257.01  Best  X19  1.69 3.89 0.05 15.05 3 . 2 2 1 . 9 5 7 . 2 1 1 3 . 4 9 2.70 2 . 3 5 6 . 9 5 1 3 . 7 3 3 . 1 0 2.29 9.08 1 6 . 4 2 2.30 15.85 16.48 13.15  3 2 0 . 6 4 58.72 365.40 573.79 303.21 595.93 19.87  X17  T a b l e 19  XI Invariable s  V a r i a n c e r a t i o v a l u e s o f independent v a r i a b l e s at each stage i n the stepwise r e g r e s s i o n a n a l y s i s f o r f o u r t e e n v a r i a b l e e q u a t i o n and f o r t h r e e s e l e c t e d v a r i a b l e s f o r a l l combinations are a l s o g i v e n f o r dependent v a r i a b l e X45(Ht/CW,P)  X3  X6  X7  X19  X21  0.59  3.67  0.20  X13  X16  X17  0.001  3.44  X23  VR  df  X34  7.44  0.12  0.61 180.43  0.24  62.56  14/32  0.17 2.57  0.02  4.79  1.32 2.78  0.02  5.92  3.60  0.61  3.80  0.20  7.72  0.25  0.92 128.06  0.25  69.47  13/33  9.96  0.85  4 . 1 7 224.87  0.24  77.50  12/34  0.72  4 . 0 6 251.51 0.30  86.49  11/35  1.37  3.19  8.13  3.73  0.69  3.91 0.21  1.35  3.06  8.11  6.02  0.53  6.28  10.04  0.75  2.79  10.12  5.72  0.45  6.46  11.47  16.50 254.42  0.17  95.82  10/36  2.66  12.30  6.04  0.94  8.71  11.83  20.88 295.07  0.01 107.10  9/37  2.83  12.62  6.58 1.08  10.14  12.603  21.70 306.75  123.71  8/38  2.4-7  12.29  6.83  9.47  11.708  25.40 371.83  140.93  7/39  11.50  5.55  7.23  112.97  22.75 361.08  158.18  6/40  2.62  108.28  24.88 443.66  169.88  5/41  12.717  106.26  23.33 431.78  203.81  4/42  0.004  325.40  369.94  173.75  3/43  469.93  453.89  266.67  2/44  7.18  7.18  XA5  15.84  6.05  12.61  3/43  26.89  7.99  19.27  2/44  26.44  1/45  15.83  Best  combinations  X40  X41  X33  0.09  26.44  T a b l e 20 - V a r i a n c e r a t i o v a l u e s of independent v a r i a b l e s a t each stage i n the stepwise regression a n a l y s i s f o r fourteen v a r i a b l e equation a n d : f o r three selected v a r i a b l e s f o r a l l combinations are a l s o g i v e n f o r dependent v a r i a b l e X 4 6 (Av.Ht/Av.CW,P) XI 14 Variables  X3  X6  X7  X13  X16  X19  X21  X33  X34  X38  X39  X41  VR  df  0.27  0.11 0.36 3.11 0.22  5.25 0.17 3.01 0.92 0.02 0.06  3.48  91.80 0.05  37.83  14/32  0.33  0.10 0.90 3.31 0.34  5.47 0.17 3.09 0.94  0.36  4.76  94.60 0.05  41.99  13/33  5.11 0.29  5.54 0.13 3.09 0.93  0.32  20.74  94.14 0.02  46.72  12/34  0.29  5.76 0.11 3.27 0.96  0.32  21.73 111.32  52.431 11/35  0.28  22.31 119.36  10/36  0.26  I.48  0.24  1.54  0.37  1.80 5.31  0.49  5.80  3.63 0.88  0.603  6.83 6.77 1.20  6.03  3.99 0.90  25.27 166.34  66.97  9/37  6.33' 6.24 1.16  6.92  4.15 1.28  25.11 211.78  76.06  8/38  6.67 6.53  7.44  4.62 1.36  26.93 256.54  86.41  7/39  6.13 5.77  7.03  3.58  29.46 257.88  99.67  6/40  0.58  7.99  1.35  169.81 236.73  106.11  5/41  7.64  1.88  267.28 239.49  133.84  4/42  278.79 239.95  174.27  3/43  425.33 404.67  232.09  2/44  5.97  5.97  1/45  18.61  4.65  14.56  3/43  33.68  6.81  21.99  2/44  32.92  1/45  5.24  5.99  Best combinations  X17  0.34  32.92  T a b l e 21 - V a r i a n c e r a t i o v a l u e s o f independent v a r i a b l e s a t each s t a g e i n the stepwise r e g r e s s i o n a n a l y s i s f o r seventeen v a r i a b l e e q u a t i o n and f o r t h r e e s e l e c t e d v a r i a b l e s f o r a l l combinations are a l s o g i v e n f o r dependent b a r i a b l e s Xl6 (BA,10) p h o t o - d a t a . Equation  XI 17  Variables  X3  0.27 4.15  X6  2.38 5.64  1.36 4.30 3.34  1.41 4.41 1.40  3.45  X46  X73 X74  VR  1.26 3.84 1.09 0.04  6.21  4.29  5.37  6.91  17/29  2.28 4.09  6.63 4.41  5.64  2.58  16/30  1.13  10.37 4.54  5.80  8.34  15/31  6.43  15.41 I.64 2.26 2.66 4.77 1.23  10.65 4.77  5.93  9.21  14/32  9.88 4.44  5.61  9.69  13/33  X7 X13 X14 X17  5.81 6.01  4.50 4.27 6.51  0.04  3.48 0.06  X19 X33 X34 X38 X39  13.71  0.34  0.70  4.91  0.07 14.30  1.13 1.64  5.48  0.05  1.17  14.77  1.69 2.62 4.54  X41 X45  1.12 0.02  3.55 3.68  5.80  5.72  14.25  6.70  5.13  7.13  13.25 •  4.60 1.10 5.65  2.02  12/34  5.36 8.39 6.13  6.81  10.45 3.96 4.97 1 0 . a  13.05  5.39  4.91  1.99  10.53 3.68 4.62 11.23  11/35  3.37 4.66 2.36  3.56  25.88  3.37  1.93 0.74  6.83  1.25 11.15  10/36  4.70  2.07  3.11  26.21  3.21  1.22  6.19  1.06 12.40  9/37  3.90 3.46 0.96  3.30  24.91  4.46  7.79  1.09 13.72  8/38  4.03  3.06  24.15  5.02  7.75  0.94 15.56  7/39  2.26 1.69  29.40  2.52  25.33  0.67  16.78  6/40  2.29  32.70  0.84  23.26  0.13 19.47  2.22  33.35  0.82  5/41  29.42  24.81  4/42  1.51  34.13  28.74  32.95  3/43  36.99  26.93  46.12  2/44  43.97  1/45  3.61  31.52  3/43  26.93  48.12  2/44  43.97  1/45  5.40  4.43  4.40  1.01  1.71 1.71  4.83 1.14  43.97 Best  combinations  df  36.19 36.99 43.97  0.16  T a b l e 22 - V a r i a n c e r a t i o v a l u e s o f independent v a r i a b l e s a t each stage i n the stepwise r e g r e s s i o n a n a l y s i s f o r s i x t e e n v a r i a b l e e q u a t i o n and f o r t h r e e s e l e c t e d v a r i a b l e s f o r a l l combinations are a l s o g i v e n f o r dependent v a r i a b l e X l 6 (BA,10) ground-data. XI 16 Variables  X3  X5  X6  X7  X13  X14  X15  X17  X19  X33  X34  X41  X73  X74  VR  df  0.31  2.35 2.19 0.03 2.32 1.23 0.003  6.04 1.09 0.0000  8.94 1.17 1.80 0.18 2.03  3.18  5.21  16/30  0.32  2.45 2 . 3 3 0.03 2 . 5 9 1 . 3 3 0 . 0 0 3  6.45  9.58 1.29 1.97 0.19 2.11  3.30  5.74  15/31  1.15  2.76 2.53 2 . 4 6 0.09 3.45  1.56  7.11 2.37  10.29 2.73 3 . 2 6 0.22 2.27 3.58  6.35  14/32  2.85 2.78 2.44  3.77  1.55  9.02 2.37  10.82 2.98 3 . 6 7 0.17 2.26  3.61  7.03  13/33  2.76 3 . 0 0 4.63  4 . 1 8 1.70  9.16  2.27  11.15 3.29 4 . 0 4  2.27  3.62  7.79  12/34  3.88 5.03  2.85  7.42  2.86  10.77 1.75  2.31  0.83 1 . 9 2  8.18  11/35  2.66 3.47 5.05  3.47  7.16  2.41  23.30 1.87  2.55  2.56  8.96  10/36  0 . 9 4 1.74 4 . 0 2  2.85  7.16 0.90  22.39  2.31  2.25  9.52  9/37  0.11  0.85 3.81  3.84  10.72  21.56  3.10  2.25 1 0 . 6 2  8/38  0.78 4 . 2 3  5.61  10.86  22.67  4.91  2.37 1 2 . 4 1  7/39  5.14  4.85  18.78  22.46  5.23  2.36 1 4 . 4 3  6/40  3.43  12.74  29.08  0.46  0.65 14.94  5/41  3.96  12.47  30.74  0.58 18.88  4/42  3.80  16.84  30.51  25.11  3/43  12.27  36.18  33.62  2/44  43.97  43.97  1/45  6.32  24.35  22.53  3/43  12.27  36.18  33.62  2/44  43.97  43.97  1/45  3.12  Best combinations  X2  0.74  T a b l e 23 - V a r i a n c e r a t i o v a l u e s o f independent v a r i a b l e s at each stage i n t h e s t e p w i s e r e g r e s s i o n a n a l y s i s f o r seventeen v a r i a b l e e q u a t i o n and f o r t h r e e s e l e c t e d v a r i a b l e s f o r a l l combinations are a l s o given f o r dependent v a r i a b l e X21 (Adj.BA) p h o t o - d a t a Equation XI 17 Variables  X3  X6  0.83 6.31 3.55  X7  X13  XH  X17  X19  X33  X34  9.84 0.19 5.50 0.11 11.14 0.52 1.01  X38  X39  X4I  X45  2.12 6.30 2.78 0.06  X74  VR  df  6.50 23.54 29.03 3.56 17/29 31.41 4.28 15/31  1.10 7.13 3.65 10.42 0.28 6.10  12.90 0.45 0.94 2.47 6.69 3.01  8.92 25.07  3.10 7.34 6.05 10.65  8.96  13.45 2.61 3.28 4 . 4 9 6.97 3.17  8.91 25.59 32.74 4 . 6 8 14/32  1.85 9.68 5.80  7.92  7.77  10.54  2.57 8.14 5.07  9.00 22.67 29.09 4.61 13/33  5.16 9.63 5.64  6.14  7.30  9.15  3.90 8.80 4 . 6 6  10.49 20.72 26.90 4.76 12/34  3.61 8.02 6.59  6.28  4.42  7.54  4 . 5 5 3.92  5.01 4.18  3.99  2.19  5.61  5.87 2.75  6.38 14.67 19.26 4.25 10/36  3.51 2.14  1.87  3.65  3.70 1.55  5.17 12.12 16.59 4.34  9/37  1.76  1.83 1.19  3.83 10.72 15.62 4 . 5 4  8/38  3.65  2.94  1.56 1.35  3.60 12.86 17.32 5.24  7/39  4.38  2.74  0.06  2.14 12.55 16.45 5.78  6/40  5.09  2.77  2.13 12.85 16.89 .7.08  5/41  4.94  4.80 19.09 24.73 7.83  4/42  3.47  14.51 23.86 8.11  3/43  1.50  7.25 3.76  2/44  5.96 5.96  1/45  3.19  Best  X73  8.63 24.40 30.03 3.90 16/30  1.12 6.62 3.60 10.15 0.31 5.97 0.08 11.67 0.48 0.98 2.24. 6.56 2.99  combinations  X46  0.31  1.67  .  6.10 17.34 22.57 4 . 4 7 11/35  6.17  3.13  2.54 4 . 5 6  3/43  7.16  7.24  5.38  2/44  5.96 5.96  1/45  Table 24 - V a r i a n c e r a t i o v a l u e s o f independent v a r i a b l e s a t each stage i n the stepwise r e g r e s s i o n a n a l y s i s f o r f i f t e e n v a r i a b l e e q u a t i o n and f o r t h r e e s e l e c t e d v a r i a b l e s f o r a l l combinations are a l s o g i v e n f o r dependent v a r i a b l e X21 (Adj.BA) ground-data Equation i 15  Variables  XI  X2  X5  X6  X7  X13  X14  X15  X17  X19  X33  X34  X41  X73  X74  VR  0.98 0 . 9 6 3 . 4 2 6.91  8 . 4 6 0.99  7 . 4 8 0 . 9 3 1.06 7.92 3.61 4 . 3 9 0.05 19.22 2 3 . 4 4 3.05  15/31  1.30 0 . 9 4 4 . 3 3 7.42  9.26 1.24  8.00 1.12 1.51 8.14 3 . 9 4  4.71  20.66 2 4 . 5 4 3 . 3 6  14/32  1.77  3 . 4 4 6.70  9.73 1.15 10.15 2 . 6 9 1.52 7.25 3 . 0 6 3.84  19.86 23.80 3.56  13/33  1.70  2.38 5.53  8.58  9 . 0 6 1.85 1.68 6 . 4 5 1.97 2.70  18.91 2 2 . 6 4 3.74  12/34  0.80 5.74  8.17  8.28 0.29 1 . 3 6 6.90 2 . 6 4  3.22  18.56 22.48 3.85  11/35  0.99 5.57  8.06  9.04  1.31 6.87 2 . 4 2  3.02  18.77 22.85 4 . 2 9  10/36  6.30  7.13  8.05  0.89 6.06 3 . 4 3  4.55  17.86 2 1 ; 87 4 . 6 6  9/37  5.44  6.69  7.22  7.67 2.55 3.67  1 8 . 0 6 23.84 5.14  8/38  5.62  4.83  5.81  4.97  4.20  14.93 2 0 . 5 4 5.30  7/39  3.73  0.69  1.50  2.38  10.61 15.26 5.08  6/40  3.09  0.82  1.71  11.29 16.00 6 . 0 0  5/41  5.39  2.50  1 9 . 0 6 25.70 6.95  4/42  16.11 2 4 . 3 8 8.15  3/43  6.21 3.11  2/44  3.55 0.345  5.96 5 . 9 6 Best  combinations  df  3.55 3.74  1.43  f  l/45  6 . 6 8 3.86  3/43  6.58 5.03  2/44  5.96 5.96  1/45  Table 25 - V a r i a n c e r a t i o v a l u e s o f independent v a r i a b l e s a t each stage i n the stepwise r e g r e s s i o n a n a l y s i s f o r seventeen v a r i a b l e equation and f o r t h r e e s e l e c t e d v a r i a b l e s f o r a l l combinations are a l s o g i v e n f o r dependent v a r i a b l e s X73 (CF) p h o t o - d a t a . XI 17  Variables  X3  X6  X16  X19  X21  X33  X39  X41  X45  VR  df  2 . 5 4 0.30 0.21  1.01  3 . 0 9 0.13 0.003  7.62 1.01 0 . 2 5 0.79 0.73  1.50 0.23 0.10 0 . 0 6 0.20  3.67 17/29  2.62 0.33 0.23  1.11  3.21 0.15  8.04 2.41 0 . 4 4 0.83 0.78  1.59 0 . 2 4 0.10 0 . 0 6 0.22  4 . 0 4 16/30  2.73 0 . 3 6 0.21 1.16  3.41  9 . 4 2 2.43 0 . 4 4 0.80 0.74  1.65 0 . 3 4 0.09  2.74 0 . 4 5 0 . 1 9 3.86  3.54  11.39 2.78 0 . 4 3 1.21 1.49  2.87 2.75 0.15 4 . 0 3  3.72  2.80 3 . 2 8  5.07  3 . 0 0 3.54  X34  0.56  4 . 4 4 15/31  1.62 0.31 0.07  0.51  4 . 8 8 14/32  11.72 3.12 0.47 1.19 1 . 4 6  1 . 6 5 0.25  0.45  5.40 13/33  3.66  13.21 3 . 4 4 0.52 1.26 1 . 9 4  1.83 0.23  0.55  5.99 12/34  4.96  3.87  13.35 3.50 0.57 1.35 1 . 9 5  4.75  0.48  6 . 6 6 11/35  2.57 4 . 7 5  4.55  3.44  16.32 3 . 4 3 1.10 1.04 1.61  5.60  7.39 10/36  1.54 4.22  4.40  3.16  15.34 3.66 1.15  2.18  7.36  8.08  9/37  5.83  4.46  2.23  13.64 3.80 1.57  1 . 4 9 12.02  8.78  8/38  6.52  3.03  9.44  16.15 3.14 1 . 5 3  11.24  9.70  7/39  7.74  0.62 1 1 . 9 3  43.12  0.24  12.28  10.24  6/40  7.65  0 . 6 0 12.11  43.86  13.15  12.48  5/41  11.63  44.30  13.44  15.60  4/42  5.65  35.63  23.01  15.68  3/43  35.95  19.16  18.72  2/44  13.03  1/45  7.84  0.11  .  13.03 Best combinations  X46  X13  X14  X17  X38  X7  0.08  6.73  6.09  9.06  3/43  10.95  8.10  13.84  2/44  16.91  1/45  16.91  Table 26 - V a r i a n c e r a t i o v a l u e s o f independent v a r i a b l e s a t each s t a g e i n t h e stepwise r e g r e s s i o n a n a l y s i s f o r s i x t e e n v a r i a b l e e q u a t i o n and f o r t h r e e s e l e c t e d v a r i a b l e s f o r a l l combinations a r e a l s o g i v e n f o r dependent v a r i a b l e s X13 (GF) ground-data. Equation XI 16  Variables  X2  X3  X5  combinations  X7  X13  XL4  X15  Xl6  X17  X19  X21  X33  X34 X4I  VR  df  0.003 0.000 0.87 1.00 0.01 0.82 0.02  0.53 0.02 0.22 10.41  0.37 0.02 0.04 0.002 0.04  3.73 16/30  0.004  0.94 1.09 0.01 0.89 0.02  1.31 0.04 0.24 10.89  0.43 0.02 0.04 0.002 0.04  4.11 15/31  0.002  0.98 1.15 0.07 1.78 0.05  2.09 0.04 0.26 12.71  0.45 0.02 0.59  0.04  4.54 14/32  1.02 4.31 0.13 1.98 0.96  2.21 0.11 0.27 13.19  0.53 0.03 1.39  O.04  5.05 13/33  1.04 4.78 0.14 2.02 1.09  2.26 0.15 0.85 15.08  0.84  1.48  0.04  5.62 12/34  4.37 5.17 0.15 2.09 1.34  2.43 0.22 0.91 15.66  0.90  1.48  6.30 11/35  4.32 7.88  5.29 1.24  5.73 0.16 1.03 15.89  0.87  3.31  7.09 10/36  4.81 7.93  5.52 1.13 12.37  1.01 16.23  0.90  3.57  8.04  9/37  3.71 7.03  8.85  11.76  0.90 15.05  1.64  7.32  8.87  8/38  3.03 6.67  8.06  15.82  16.00  3.54  6.69  10.03  7/39  8.31  8.81  28.25  13.38  4.53  5.32  10.66  6/40  3.54  4.73  21.77  9.01  4.37  10.61  5/41  3.68  1.42  21.41  23.74  11.27  4/42  23.24  22.82  14.40  3/43  19.44  21.26  18.91  2/44  13.03  13.03  1/45  7.73  3/43  10.85  2/44  16.91  1/45  3.37  Best  X6  1.73  3.29  6.94  6.23  1.33 16.91  T a b l e 27 - V a r i a n c e r a t i o v a l u e s of independent v a r i a b l e s at each stage i n the stepwise r e g r e s s i o n a n a l y s i s f o r seventeen v a r i a b l e e q u a t i o n and f o r t h r e e s e l e c t e d v a r i a b l e s f o r a l l combinations are a l s o g i v e n f o r dependent v a r i a b l e X74 (Adj.CF) p h o t o d a t a . tEquation XI 17  Variables  X3  X6  X7  X13  XI4  X16  X17  X19  X21  X33  X34  X38  X39  X41 X45  X46  2.90 1.05 0.07  7.21 0.42 2.37 1.22 1.30  2.38 0.07 0.03  0.07  0.01 2.71 17/29  2.16 1.26 1.03 0.03  2.99 1.07 0.14  7.55 0.42 2.50 1.25 1.34  3.32 0.11 0.02  0.07  2.98 16/30  2.27 1.38  1.91  3.11 1.67 0.15  8.06 0.41 2.78 1.38 1.64  3.47 0.13 0.03  0.03  3.28 15/31  2.37 3.42 2.12  3.25 1.80 0.17  8.41 0.44 2.88 1.54 1.82  4.15 0.10  0.12  3.62 14/32  2.35 3.65 2.25  3.30 1.91  0.15  8.78 0.47 3.04 1.62 1.93  4.20  0.31  4.00 13/33  2.4-1 4.25 2.26  3.39 1.93  9.86 2.30 4.31 1.59 1.92  4.25  0.21  4.43 12/34  2.34 4.67 2.10  3.36 1.97  12.85 2.55 4.89 1.42 1.76  4.16  4.93 11/35  0.92 5.11 1.00  2.14 0.56  15.21 2.33 4.77  1.18  3.08  5.22 10/36  1.41 4.82 0.48  3.08  15.74 3.48 4.28  0.63  2.87  5.80  9/37  1.81 6.66  5.79  23.80 5.66 4.12  0.15  5.57  6.56  8/38  1.71 7.04  5.80  24.22 5.93 4.92  5.55  7.64  7/39  9.12  11.76  22.12 6.53 5.24  12.44  8.48  6/40  5.11  15.62 4.19 2.97  19.42  6.97  5/41  13.01 2.01 4.04  16.21  6.77  4/42  6.76  13.88  8.17  3/43  5.73  3.72  5.02  2/44  5.96  1/45  3.77  3/43  5.96 combinations  df  2.10 1.17 1.00 0.04  11.97  Best  VR  0.45  0.33 0.07  0.45  1.47 11.18  2/44 11.18  1/45  T a b l e 28 - V a r i a n c e r a t i o v a l u e s of independent v a r i a b l e s a t each s t a g e i n the stepwise r e g r e s s i o n a n a l y s i s f o r s i x t e e n v a r i a b l e e q u a t i o n and f o r t h r e e s e l e c t e d v a r i a b l e s f o r a l l combinations are a l s o g i v e n f o r dependent v a r i a b l e X74 ( A d j . C F ) ground-data. XI 16 Variables  X2  X3  X5  X6  X7  X1'3  XLV. X1'5  X19  X21  X33  X34  X41  VR  df  0.37 0.01 0 . 0 4 0.004  9.15 0.62 1.88 0 . 1 4 0.28 0 . 0 6 2 . 6 2  16/30  0.14 0.05 1.81 0 . 0 6 0.43 0.12  0.38 0.02 0.04  9.58 1.75 3.92 0.15 0.31 0 . 0 6 2.89  15/31  0.14 0.03 1.88 0.13 0.52  0.37  0.06  10.43 1.85 4 . 0 8 0.16 0.37 0.05 3.19  14/32  0.81 0 . 4 6  0.14  1 1 . 9 4 1.88 4.24 0.22 0.52 0.07 3.54  13/33  0.11  0.23  1 . 9 4 0.12 1.10  1.54  2.19  1.01 0.74  1.76  0.91  1 2 . 1 7 1.82 4 . 4 9 0.28 0.51 0 . 1 5 3.93  12/34  1.83  4.11  1 . 6 0 1.79  1.86  1.31  12.52 2.09 4.52 0.39  0.71  4.38  11/35  2.63  4.56  4.43 1.44  2.52  1.07  13.72 1.92 4 . 7 5  2.71  4.86  10/36  1.81  4.14  3 . 5 6 0.71  2.49  12.90 2.00 4 . 1 6  1.64  5.27  9/37  2.93  4.42  2.97  2.93  12.31 1 . 3 0 6.05  5.88  8/38  3.37  7.31  0.84  6.00  15.23 1.20 7.20  6.24  7/39  7.91  8.40  10.20  18.74 2.57 6.62  7.17  6/40  6.75  6.66  8.64  16.58  9.60  7.79  5/41  10.82  14.93  6.18  7.12  4/42  6.73  6.52  4.79  3/43  2.12  6.22  4.11  2/44  5.96  5.96  1/45  2.75 0.04  4.41  4.90  3/43  8.31  4.54  7.62  2/44  9.92  1/45  5.33  Best  X17  0.13 0.04 1.72 0.05 0.39 0.11  14.16  combinations  :xi6  9.92  2.11  T a b l e 29 - V a r i a n c e r a t i o v a l u e s o f independent  v a r i a b l e s at  each stage i n the  stepwise  r e g r e s s i o n a n a l y s i s f o r e i g h t e e n v a r i a b l e e q u a t i o n and f o r t h r e e s e l e c t e d v a r i a b l e s f o r a l l c o m b i n a t i o n s a r e a l s o g i v e n f o r dependent v a r i a b l e X19 (CC,P) p h o t o - d a t a . Equation  18  Variables  XI  X3  X7  0.16  4.41  7.74 36.12 0, 004  4.58  X34  0.78 1.09  1.54  2.50 1.93  7.69  3.05  0.81 1.15  3.12  4.22 2.66  7.97  2.14  3.06  0.71 1.31  3.31  4.43 3.33  2.15  2.99  1.58  6.10  7 . 6 2 3.36  9.44 10.68  2.61  3.23  0.97  4.49  6.26 1.85 1 0 . 5 8 2.30  3.19  0.65  3.17  4.80  8.87  2.53  8.96,  15.64 1 3 . 0 7  3.13  4.69  8.46  2.16  6.22  8.01  5.35  0.000  6.42  8.29  5.71  X16  9.38  2.95  9.56 37.87  11.68  2.56 4 . 6 9  10.00 4 0 . 4 8  14.06  2.37 4 . 5 6  15.58 53.60  20.31  3.08  1 3 . 9 6 50.13  18.32  3.27  12.25 4 9 . 0 2  16.08  2.86  11.91  49.83  X13  X33  XH  2.41  X6  16.15 52.01  16.87  10.51  16.67 53.53  17.41  2 4 . 5 9 45.41  11.37  28.96  10.85  23.93 4 4 . 8 5  29.93  10.41  9.17 25.74  11.70  9.61  0.03 1 7 . 4 8  2.06  6.08  20.45  2.65  6.31  17.41  X17  X21  4.74  X39  X41 2.06  X45 0.09  X46 6.23.  Best  combinations  8.17  7.26  15.71 32.42  30.92 43.97  VR  50 53  49.00  39.23  18/28  o  df  11.63  43.01  17/29  54.39  47.07  16/30  12.11  73.50  59.60  50.62  15/31  70.05  56.45  51.85  14/32  67.00  53.46  54.30  13/33  9.09  174.09 155.82  59.38  12/34  5.92  163.12 145.22  61.25  11/35  6 . 1 8 ! 177.40 152.78  69.30  10/36  0 . 8 0 , 152.64 133.49  67.75  9/37  19.18  ! 170.12 154.12  76.50  8/38  9.28  159.51 129.34  63.51  7/39  ; 137.54 102.85  60.11  6/40  ; 146.10 109.36  73.87  5/41  j 143.49 127.83  88.21  4/42  217.87 150.21 106.74  3/43  6.47 10.76  i  17.66  X74  50.82  0.12  38.44 16.12  X73  53.64 58.04  15.07 19.86 14.43  X38  15.41  19.36  2/44  17.66  1/45  26.18  ^3/43  31.20  2/44  43.97  1/45  T a b l e 30 - V a r i a n c e r a t i o v a l u e s o f independent v a r i a b l e s a t each s t a g e i n the stepwise r e g r e s s i o n a n a l y s i s f o r seventeen v a r i a b l e s e q u a t i o n and f o r t h r e e s e l e c t e d v a r i a b l e s f o r a l l c o m b i n a t i o n s are a l s o g i v e n f o r dependent v a r i a b l e X19 (CC,P) g r o u n d - d a t a . ^Equation XI 1 7  Variables  X2 X3  0.30 4.75 ^  ^  2.22 ^  X 5X 6  3.35  ^  2.12 6 . 3 9 2 . 2 3 7.03 2.06 7 . 0 5 2 . 5 4 8.99 4 . 9 2 1.82 6 . 9 0 5.23 1.46 6.30 4.17 5.48 2.60 6.21 3.60  X7  X13  X14  XI5  X16  1.36 2 1 . 3 0 0 . 0 0 2 0.57 0.67 1 4 . 9 9 29.70 3.80 2 2 . 2 1 0.62 2 0 . 9 5 4 0 . 9 7 3.82 3 0 . 3 2 11.91  19.82  2 1 . 2 9 4 8 . 3 5 2.79  X17  X21  X33  X34  0.38  1.55  7.34  8.64  0.40  2.41  33.01  55.91 26.26 50.70  16.65  12.49  13.94  0.88  50.82  1 . 1 4 66.50  1 0 . 5 1 11.50 0 . 6 7 2 0 9 . 1 5 1 0 . 9 6 1 2 . 0 3 13.26 217.51 9.44  28.64  9.81  33.95  8.15  10.79 12.16 9.11  7.02  10.18 8.30  33.51  7.67 1 6 . 6 9 2 1 . 6 3 8.48 4.97 1.89 0.27 0.38 1.89  33.94  2.51  8.36 27.22 0.10 3 0 . 4 7  0.83 38.98  11.49  50.17 3.02 3 2 . 5 9 51.11 1.79 3 0 . 7 3  20.25 18.12 51.77  9.63 1 0 . 6 6  X73  1 1 . 9 0 1 2 . 5 8 13.91 1.50 2 1 2 . 8 3  18.84 4 8 . 9 0 3.21 32.94 21.04  1.97  X41  29.70 9.29  38.44 16.12  214.57  VR  df  38.15 41.93 45.58  17/29  154.39  49.38  14/32  155.69  56.13  12/34  X74 39.56 51.78 57.66  51.37  150.06  68.70  150.92  71.92  188.61  119.32  56.92  148.55  91.40 96.88  152.67 190.30 217.87  122.72  150.21  53.72 65.89  83.51 , 106.74 19.36  15.41  17.66  17.66 Best combinations  8.17  30.92  7.26  15.71 32.42  43.97  15/31 13/33  6 0 . 3 1 11/35 64.75 10/36  152.27  2 3 5 . 4 0 165.06 227.86 1 6 0 . 2 8 210.51  16/30  |  26.18  21.20 43.97  9/37 8/38 7/39  6/40 5/41  4/42  3/43 2/44  1/45  . 3/43 2/44  1/45  T a b l e 31 - R e g r e s s i o n equations o f the t h r e e v a r i a b l e s s e l e c t e d f o r v a r i o u s dependent v a r i a b l e s .  No.  Dep. V a r .  In.  1 2 3 4 5 6 7 8 9 10 11 12 13  XL4 X15  X2 X2 X16 X16 X19 X19 X74 X74  U No. 1 2 3  A  5 6 7 8 9 10 11 12 13 H  a 2.611 2.4.04. 2.304. 2.84.0 -125.24.8 -28.4-27 284.851 226.365 -0.081 0.124 -0.567 0.056 0.615 0.615  Y 0.019 -0.007 0.009 0.009 275.32 279.66 52.613 78.276 0.122 0.218 1.322 0.649 0.001 0.001  X45  X46  X16 X16 X21 X21 X74 X74 X73 X73 X19 X19  b  (Photo) (Ground) (Photo) (Ground) (Photo) (Ground) (Photo) (Ground) (Photo) (Ground)  2  -0.013 -0.003 -0.004 -0.006 26.527 -59.209 36.473 -250.46 0.106 -0.079 -0.0003 0.001 0.0001 0.0001  b  3  0.005 0.003 0.013 0.010 5.061 21.192 -347.06 1.184 0.050 0.001 0.139 0.0002 -0.347 -0.347  for a l l  combinations  Var. X7 X3 X7 X7 X4.6 X7 X46 X19 X14 X15 X16 X16 X17 X17  X45  xu  X19 X19 X16 X16 SE„ E  0.768 0.229 1.033 0.919 49.349 55.034 149.334 152.166 0.682 0.660 0.407 0.419 0.104 0.104  X16 XI X23 X38 X45 X14 X19  x u X46 X21  X45  X17 X7 X7 R  0.780** 0.809** 0.684** 0.710** 0.829** 0.7818** 0.491** 0.461** 0.456** 0.508** 0.622** 0.592** 0.804** 0.804**.  n (%)  df  60.88 65.43 46.81 50.39 68.74 61.12 24.13 21.23 20.83 25.79 38.73 35.03 64.62 64.62  3/43 n  2  M  T a b l e 32  In.Var.  Best combinations  R  C o r r e l a t i o n c o e f f i c i e n t s (R) c o e f f i c i e n t s o f d e t e r m i n a t i o n (R ) percentages and standard e r r o r s o f estimate f o r a l l equations i n t h e s t e p w i s e r e g r e s s i o n a n a l y s i s of XL4, X15, X45> X 4 6 , on 14 independent v a r i a b l e s .  R ($ 2  SE  E  In.Var.  R  R $) 2  In.Var.  R  R ^) 2  S E  E  In.Var.  R  R ® 2  S E  E  X21  0.995 99.0 0.141  X3  0.992 9 8 . 4 0.572  X13  0.982 9 6 . 5 0.308  X33  0.971 94.3 0.361  X3  0.995 99.0 0.139  X16  0.992 9 8 . 4 0.564  X6  0.982 9 6 . 5 0.306  X3  0.971 9 4 . 3 0.355  X4I  0.995 99.0 0.140  X19  0.991 98.3 0.575  X21  0.982 9 6 . 5 0.299  X41  0.971 94.3 0.351  X17  0.995 99.0 0.139  X21  0.991 98.2 0.573  X33  0.982 9 6 . 5 0.296  X17  0.971 94.3 0.346  X16  0.995 98.9 0.141  X17  0.991 98.2 0.565  XI  0.982 96.5 0.295  X34  0.971 94.3 0.341  XI  0.994 98.8 0.144  X2  0.991 98.2 0.564  X41  0.981 96.3 0.294  XI  0.971 94.3 0.338  X13  0.992 98.4 0.167  X4I  0.989 9 7 . 8 0.614  X17  0.981 9 6 . 3 0.290  X13  0.970 94.1 0.336  X5  0.992 98.3 0.168  X6  0.989 9 7 . 8 0.611  X3  0.9.81 9 6 . 3 0.290  X21  0.971 94.1 0.337  X2  0.987 9 7 . 3 0.208  X7  0.986 97.2 0.674  X16  0.982 9 6 . 0 0.295  X7  0.968 9 3 . 7 0.339  X19  0.983 9 6 . 6 0.233  X34  0.985 97.1 0.681  X79  0.97  X6  0.963 9 2 . 8 0.358  X33  0.979 95.8 0.255  X33  0.976 95.2 0.861  X34  0.975 95.1 0.317  X19  0.963 9 2 . 7 0.356  X34  0.950 90.2 0.385  X13  0.973 94.7 0.898  X7  0.961 9 2 . 4 0.391  X16  0.961 9 2 . 4 0.360  X6  0.740 54.7 0.817  X5  0.943 89.0 0.127  X40  0.961 9 2 . 4 0.387  X39  0.956 91.3 0.379  X7  0.586 34.3 0.973  XI  0.731 53.4 0.259  X23  0.371 1 3 . 8 1.286  X38  0.342 1 1 . 7 1.198  0.809 6 5 . 4 0.229  X7,X16 X23  0 . 6 8 4 4 6 . 9 1.033 X 1 6  9 5 . 4 0.311  X7,X38  X7,X16 X2  0.780 6 0 . 9 0.768  X I , X2 X3  X16,X2  0.769 59.2 0.776  X2,X3  0.809 65.4 0.226  X16,X23  0.683 46.7 1.023 X l 6 , X 3 8 0.707 50.0 0.912  X2  0.614 37.7 0.948  X2  0.792 6 2 . 7 0.232  Xl6  0.608 3 7 . 0 1.100  Xl6  0.710 5 0 . 4 0.919 O.650 4 2 . 3 0.969  2 T a b l e 33 - C o r r e l a t i o n c o e f f i c i e n t s (R), c o e f f i c i e n t s of d e t e r m i n a t i o n (R ) percentages and standard e r r o r o f estimate f o r a l l equations i n the stepwise r e g r e s s i o n a n a l y s i s of X l 6 p , X l 6 g , X74P, X74g. X16 Photo In.Var.  R  X16 Ground SE  E  In.Var  R  X74 Photo R%)  S E  E  In.Var.  R  X74 Ground  R (%) 2  S E  E  In.Var.  R  R $) 2  SE^ E  X13  0.896 80.2 47.836  X17  0.858 73.5 54.362  X46  0.784 61.4  0.580  X16  0.764 58.3 0.593  X45  0.895 80.2 47.061  X13  0.858 73.5 53.478  X7  0.784 61.4  0.570  X14  0.764 58.3 0.583  X17  0.895 80.2 46.314  X5  0.858 73.5 52.638  X41  0.783 6 1 . 3  0.561  X2  0.763 58.3 0.574  XI  0.895 80.1 4 5 . 6 2 2  X41  0.857 73.5 51.909  X39  0.783 6 1 . 3 0.553  X5  0.763 58.2 O.565  X33  0.890 79.2 45.900  X7  0.856 7 3 . 3 51.267  X16  0.782 61.2  0.545  X41  0.762 58.1 0.558  X38  0.887 7 8 . 6 45.907  X73  0.849 72.0-51.775  X45  0.781 6X,0a 0.538  X33  0.761 57.9  0.551  X73  0.883 77.9  X33  0.845 7 1 . 3  51.653  X33  0.780 60.8  XI5  0.758 57.4  0.547  X4I  0.870 7 5 . 6 47.651  X15  0.836 69.8  52.256  X14  0.769 59.2 0.535  X7  0.749 56.2 0.547  X39  0.867 75.1 47.484  XI  0.831 69.1 52.188  X6  0.765 58.5 0.532  X34  0.744 55.3 0.545  X7  0.862 74.3  47.619  X2  0.831 69.1 51.590  X34  0.761 58.0  0.528  X6  0.727 52.8  0.553  XI4  0.858 7 3 . 6 47.592  X6  0.827 6 8 . 4  51.449  XI  0.760 57.8  0.523  X19  0.720 51.8  0.552  X6  O.846 7 1 . 6 48.800  X34  0.804 6 4 . 6  53.811  X3  0.748 56.0 0.527  X3  0.698 48.7  0.562  X74  0.839 70.4 49.209  X74  0.801 64.2  53.466  X13  0.678 45.9  0.577  X13  0.636 40. $ 0.599  X34  0.838 70.3 48.700  X3  0.798 63.7  53.205  X19  0.626 3 9 . 2  0.605  XI  0.501 25.1 O.664  X3  0.835 69.7  48.600  X14  0.778 60.5  54.873  X17  0.603 3 6 . 3 0.612  X17  0.397 15.8  0.696  X46  0.828 6 8 . 6 48.874  X19  0.703 49.4  61.359  X38  0.431 18.57  0.684  X21  0.342 11.7  0.704  X19  0.703 49.4  X21  0.342 11.7  0.704  45.972  61.359  5  ;•  0.532  Best combi-  X45,X46  nations  X49  X19,X46  0.828 68.6 48.874  X19  0.703 4 9 . 4 61.359  X19' U  X14,X15  X46,X45  X7,X14 0.829 68.7 49.349  X14,X19  0.782 61.1 55.034  X14  0 . 4 5 6 2 0 . 8 0.682  0.778 6 0 . 5 54.873  X14,X45 0.455 2 0 . 7 0.675  X19  0.703 4 9 . 4 61.359  X45  X21  0.508 2 5.8 0.660  X14,  0.507 2 5 . 7 0.653  X21 O.446 1 9 . 9 0.671  X14  0.425 18.1 0 . 6 7 8  T a b l e 34 - C o r r e l a t i o n c o e f f i c i e n t s (R), c o e f f i c i e n t s of d e t e r m i n a t i o n (R ) percentages and s t a n d a r d e r r o r of e s t i m a t e f o r a l l e q u a t i o n s i n the stepwise r e g r e s s i o n a n a l y s i s of X73p> X73g> X21p, X21g. X73 Ground  X73 Photo In.Var.  Best combinations  R  R ($ 2  S E  E  68.3 0 . 3 5 6  In.Var.  R  R $) 2  SE„ E  X21 Ground  X21 Photo In.Var.  R  R ($  67.6 67.6  118.811  X41  0.772 59.6  116.932  X2  0.772 59.5  2  S E  E  I n . V a r ,.  R  R ($ 2  SE„ E  X2  0.816 66.5 0.360  0.822  0.826 68.3 0.350  X34  0.816 66.5  X17  0.822  X14  0.354  X45  0.826  0.816  0.348  X13  0.821 67.5  115.188  X13  0.764 58.3 126.311  X41  0.825 68.1  X21  0.816  0.343  113.881  XI  0.754  0.825 68.1  X41  0.816 66.5 0.338  XI5  0.740  0.824 67.9  0.331  X6  0.815  66.5  X33 X34  0.820 67.2  X6 X39 X46 X33  0.340 0.335  XI  0.333  X38  0.792  X5  0.737  0.823 67.7  0.327  XI5  0.814  66.3  0.330  XI  0.764  X17  0.729 53.1  0.820 6 7 . 2 0.325  X13  0.813  0.326  X14  0.736  X33  0.721 52.0  126.377  X7  0.814  0.325  X16  0.807 65.1 0.326  X7  0.717  X34  0.698 48.8  128.870  X34  0.806  0.327  X3  0.802  64.3  0.699  48.9  130.395  X7  0.658  X19  0.797  0.330  X33  0.784 6 1 . 5 0.334  0.696 4 8 . 5  129.228  X19  0.650  X21  0.778  0.338  X19  0.751 56.4 0.351  X6 X39 X41  58.4 122.546 5 4 . 1 126.910 51.3 128.931  46.4  130.121  X14  0.631 39.8  X7  0.777  0.335  X7  0.719 51.8  0.365  X19  0.681  128.625  X3  X5  0.708 50.1 0.367  131.313  X13  0.723 52.3 0.359  X14  0.680  46.2  0.654 42.7  XI3 X6  0.602 36.3  0.773  X46  46.3  X73  0.601  136.998  0.342 11.7  X38  0.678  X17  0.474 22.5  X3  0.382 14.6  156.622  X74  X17  0.474 2 2 . 5 0.447  X74  0.342 11.7  157.490  X16  0.826  X45  68.3 0.345  66.3  64.9  63.5  60.6 60.3  59.8 0.333  46.0  0.377  X16,X19  66.5  66.5  66.2  0.326  0.377  0.447  X16,X17  X19,X46  0.803  0.681  6 4 . 5 116.621 62.7  36.2  117.761  0.352  56.9 54.7  128.343  126.420  126.589 127.840  5 4 . * 126.578  43.2 42.2  12.4  126.556  133.930 133.429 134.559 136.878 158.649 157.490  X41,X19  X45  0 . 6 2 2 3 8 . 7 0.407  X19  X19,X45  0.621 38.6 0.402  X16,X17 0.575 33.0 0 . 4 2 0  0.491 2 4 . 1 3 1 4 9 . 3 2 4 X 7 4 O.46I 2 1 . 2 152.166 X19,X46 0 . 4 4 3 19.7 1 5 1 . 9 2 1 X19,X74 0.431 18.6 1 5 2 . 9 0 6  X19  0.523 2 7 . 3 0 . 4 3 3  X19  X74  0.592 35.0 0.419 0.523 27.3 0 . 4 3 3  X74  0.342 1 1 . 7 161.985 X74  0 . 3 4 2 1 1 . 7 157.490  129. T a b l e 35 - C o r r e l a t i o n c o e f f i c i e n t s (R), c o e f f i c i e n t s o f d e t e r m i n a t i o n (R percentages and s t a n d a r d e r r o r of e s t i m a t e f o r a l l equations i n the stepwise r e g r e s s i o n a n a l y s i s o f X19p, X19g. X19 Photo  combinations  X19 Ground  R  R (fo)  X13  0.981  96.2  0.042  U5  0.981  96.2  X17  0.981  XI  E  R  R (%)  XI5  0.978  95.7  0.044  0.042  X17  0.978  95.7  0.043  96.2  0.041  X16  0.978  95.7  0.043  0.980  96.1  0.041  XI  0.978  95.6  0.043  X38  0.978  95.8  0.042  X41  0.976  95.3  0.043  X21  0.977  95.5  0.042  X3  0.976  95.2  0.043  X3  0.977  95.5  0.042  X13  0.974  95.0  0.043  X41  0.975  95.1  0.043  X2  0.973  94.7  0.044  X39  0.975  95.1  0.042  X5  0.971  94.4  0.045  X46  0.971  94.3  0.045  X33  0.969  93.8  0.046  X33.  0.970  94.2  0.045  X14  0.954  91.1  0.055  X34  0.959  91.9  0.052  X6  0.943  89.0  0.060  X6 '  0.949  90.0  0.057  X34  0.943  89.0  0.060  XL4  0.949  90.0  0.057  X21  0.943  88.8  0.059  X16  0.945  89.4  0.058  X74  0.940  88.2  0.060  X74  0.939  88.2  0.060  X73  0.684  46.8  0.126  X73  0.684  46.8  0.126  X7  0.531  28.2  0.145  X7  0.531  28.2  0.145  X16,X7 X17  0.804  64.6  0.104  X16,X7 X17  0.804  64.6  0.104  X7,X17  0.766  "58.7  0.111  X17,X7  0.766  58.7  0.111  0.703  49.4  0.121  0.703  49.4  0.121  In.Var.  Best  2  X16  In.Var  2  X16  2  S E  )  130  T a b l e 36 - M u l t i p l e r e g r e s s i o n o f dependent v a r i a b l e s X15 (CW/D), X45  (Ht/CW,P) and X46  independent v a r i a b l e s  Dep.Var.  In.Var.  a  b  l  2  R  (Ht/CW,G),  (Av.Ht/Av.CW,P) on the  t h a t made up t h e i r  b  XI4  R  2  ratios.  S E  E  df  X14  X2,X5  4.590  0.051  -0.228  0.982  96.4  0.231  2/44  X45  X23,X40  5.313  0.055  -0.282  0.957  91.7  0.404  2/44  X46  X38,X39  5.196  0.058  -0.295  0.956  91.3  0.379  2/44  131. F i g u r e 14crown w i d t h and i t  shows t h e simple l i n e a r r e g r e s s i o n o f h e i g h t on  seems t h a t t h e photo d a t a accounted f o r a g r e a t e r 2  percentage o f the t o t a l r- =62.41 p e r c e n t )  sum o f squares (Ht, ri =52.85 and A v . H t  than the ground d a t a (R =44.89 p e r c e n t )  t h r e e are a l l h i g h l y  a l t h o u g h the  significant.  F i g u r e 15 g i v e s a h i g h l y s i g n i f i c a n t crown w i d t h and d . b . h . c o r r e l a t i o n (r = 0 . 8 6 2 ) .  These two f i g u r e s confirmed the p a s t r e p o r t s  t h a t crown w i d t h and d . b . h . as w e l l as h e i g h t and crown w i d t h are h i g h l y significant.  A f r e e - h a n d curve i s a l s o f i t t e d from t h e d a t a p l o t t e d .  The c o r r e l a t i o n o f CW/D t o a d j u s t e d crowding f a c t o r i s s i g n i f i c a n t a t the %  level  ( F i g u r e 1 6 ) , and a n o n - s i g n i f i c a n t  i s found w i t h crowding f a c t o r .  only  relation  T h i s may be e x p l a i n e d by the clumping  e f f e c t o f n a t u r a l stands e . g . the a c t u a l stems p e r a c r e does not r e p r e s e n t the t r u e stems p e r a c r e , u n l e s s i t  i s a d j u s t e d t o f u l l o c c u p a t i o n of stems  p e r a c r e by t h e crown o c c u p a t i o n from stands sampled. Ht/CW r a t i o s on crowding f a c t o r and a d j u s t e d crowding f a c t o r ( F i g u r e 17) are a l l h i g h l y s i g n i f i c a n t a l t h o u g h t h e y d i d n o t account f o r much of the t o t a l sum o f s q u a r e s .  T h i s shows t h a t Ht/CW r a t i o s  are  d e f i n i t e l y a f f e c t e d by c r o w d i n g . Ht/CW r a t i o s are a l s o h i g h l y c o r r e l a t e d w i t h CW/D r a t i o ( F i g u r e 18) b u t the ground r a t i o  accounted f o r a g r e a t e r percentage o f  the t o t a l sum o f squares than the photo r a t i o s . (1961)  R e s u l t s from Smith e t . a l .  are i n d i c a t e d by F i g u r e 17 f o r comparison and i t  seems t h a t  western  hemlock has s m a l l e r r a t i o s f o r dense stands and l a r g e r r a t i o s f o r normal and open d e n s i t y  stands.  132. Figure 19  ;  shews t h a t Ht/CW r a t i o s are h i g h l y  significantly  c o r r e l a t e d w i t h b a s a l a r e a but accounted f o r o n l y a s m a l l percentage o f the v a r i a t i o n .  There i s no c o r r e l a t i o n w i t h a d j u s t e d b a s a l a r e a because  the a d j u s t e d b a s a l a r e a depends upon the crown c l o s u r e of t h e s t a n d , if  the crown c l o s u r e i s d i f f e r e n t and t h e b a s a l a r e a i s the same,  e.g.  the  s t a n d s w i t h s m a l l e r crown c l o s u r e w i l l g i v e a f a r h i g h e r a d j u s t e d b a s a l a r e a than t h e l a r g e r crown c l o s u r e s t a n d s . Ht/CW r a t i o s are shown ( F i g u r e 20) t o be s l i g h t l y  correlated  w i t h crown c l o s u r e . The ground r a t i o Ht/CW,G has a h i g h l y s i g n i f i c a n t w i t h age ( F i g u r e 2 1 ) , a l t h o u g h i t total  sum o f s q u a r e s .  c o r r e l a t e d w i t h age.  correlation  d i d not e x p l a i n a l a r g e percentage o f  Both o f t h e photo r a t i o s are n o t  the  significantly  T h i s may be due t o the d i f f e r e n c e s i n crown w i d t h  measurement on p h o t o s , which i s u s u a l l y s m a l l e r than c o n v e n t i o n a l ground measurement thus g i v i n g l a r g e r Ht/CW r a t i o s . F i g u r e 22- i n d i c a t e s the b a s a l a r e a i s h i g h l y c o r r e l a t e d w i t h crowding f a c t o r but i t w i t h a d j u s t e d crowding f a c t o r , to f u l l occupation of s i t e .  does not g i v e a s i g n i f i c a n t  because here o n l y one parameter i s  Adjusted basal area i s only s l i g h t l y  w i t h a d j u s t e d crowding f a c t o r . f u l l coverage p e r a c r e  significantly relation adjusted correlated  Here both v a r i a b l e s  are b e i n g a d j u s t e d to  (100 p e r c e n t crown c l o s u r e ) ,  t h i s may be e x p l a i n e d  by l a r g e number o f s m a l l t r e e s w i t h i n the p l o t sampled, which was n o t i n c l u d e d i n a p r i s m sweep but was counted f o r number o f stems per (any t r e e above 4 . 5 f e e t ) .  That the a d j u s t e d b a s a l a r e a i s n o t  acfe  correlated  w i t h crowding f a c t o r ,  can be s i m i l a r l y be e x p l a i n e d as above ( b a s a l a r e a  and a d j u s t e d crowding  factor).  133. CW/D r a t i o i s not c o r r e l a t e d w i t h b a s a l a r e a o r a d j u s t e d b a s a l area (Figure 2 3 ) .  T h i s means t h a t CW/D i s not a f f e c t e d by d e n s i t y o f  and can be e x p l a i n e d by the f a c t t h a t are clumpy.  stand  t h a t too many young stands were sampled  T h i s may a l s o be due to t h e t o l e r a n c e o f the  western  hemlock s p e c i e s , and t o what e x t e n t o r how l o n g can o v e r l a p o f t r e e  crowns  take p l a c e b e f o r e the growth o f crown w i d t h and d . b . h . w i l l be reduced  is  not known. F i g u r e 24- g i v e s a h i g h l y c o r r e l a t e d CW/D r a t i o w i t h a g e .  This  i s t r u e because as a t r e e grows o l d e r the crown w i d t h does not i n c r e a s e f a s t as when i t maximum.  was young and w i l l e v e n t u a l l y  However,  stop when i t  reaches  as  its  d . b . h . w i l l c o n t i n u e t o grow l o n g a f t e r a t r e e has a c q u i r e d  maximum crown w i d t h .  Therefore i t  i s o n l y n a t u r a l t h a t CW/D r a t i o  should  d e c r e a s e w i t h age. B a s a l a r e a i s h i g h l y s i g n i f i c a n t c o r r e l a t e d w i t h crown c l o s u r e (Figure 25).  For a s p e c i f i c diameter c l a s s the b a s a l a r e a w i l l i n c r e a s e w i t h  i n c r e a s e d crown c l o s u r e .  A d j u s t e d b a s a l a r e a i s not s i g n i f i c a n t  because  o n l y one parameter i s a d j u s t e d t o f u l l o c c u p a t i o n . Crown c l o s u r e a l s o i n c r e a s e s w i t h the number o f t r e e s p e r (Figure  acre  2 6 ) , t h i s can o n l y be u s e d f o r an average d . b . h . , which s h o u l d be  q u i t e s m a l l i n t h i s case because t h e r e are l a r g e r number o f young stands ( 3 0 y e a r s ) than o l d e r  stands.  F i g u r e 27 shows the crown c l o s u r e i n c r e a s e s w i t h crowding f a c t o r . The c o r r e l a t i o n i s h i g h l y s i g n i f i c a n t ,  this  can be e x p l a i n e d a g a i n as above.  154 Figure  14.  The r e l a t i o n s h i p o f height to crown width o f western hemlock.  (I)  HT / CW,P  Y = 7.06 + 0.1395 X f = 0.727  AV.HT /AV.CW.P  Y s 718 t  HT / CW,G  Y  WIDTH  SE  = 2.800  E  = 11.63 t 0.1043 X f  10 CROWN  = 2.876  E  0.1348 X  X* = 0 . 7 9 0 " (3)  SE  - 0.697"  20 (FEET)  SEE  s  3-752  135 Figure  15.  The r e l a t i o n s h i p o f crown width to diameter a t breast height.  10  D.B.H.  (INCH)  20  Figure  16.  The r e l a t i o n s h i p of crown width/diameter at breast height r a t i o to crowding f a c t o r and adjusted crowding factor.  (1)  (2)  C W / D ON ADJ. CF Y = 1.846 t l-O.I79)X f = 0.353' S E _ = 0.356 CW/D  ON  CF  Y = 1.765 t (-0.209) X f = 0.279  T  I I  1 CF  AND  SE_ = 0.365  r  2 ADJ. C F  137 Figure  17.  The r e l a t i o n s h i p o f height/crown width r a t i o to crowding f a c t o r and adjusted crowding f a c t o r .  7-  5-  O  5 _  4-  o I=  3-  2-  (1)  HT/CW,P  (2)  AV.HT/AV.CW  (3)  HT/CW,6  (4)  HT/CW,P  (5) I-  (6)  ON  ON ON  ON  AV.HT / AVCW HT/CW,6  CF  Y = 3.783 t 1.317X CF  CF ADJ. CF  ON ON  f = 0.483" S _ E = 1.213 Y « 3.949 + 1.141X  f = 0.454" SEE ' Y = 3.586 t I.064X f = 0.450" Y  ADJ. CF CF  s 3.691 t  SE  f = 0.446"  SE  3  6  = 1.240  Y = 3.870 + 0.713 X f = 0.419"  Y = 3.490 t  SE  T 2 AND  ADJ. CF  SE  0.681 X  Y* = 0 . 4 2 5 "  CF  E  1  - 1073  E  0.825 X  1  E  E  = i.157  = 1.087  138 Figure  18.  The r e l a t i o n s h i p of height/crown width r a t i o to crown width/diameter at breast height r a t i o .  CW/D  RATIO  2  139 Figure  19.  The r e l a t i o n s h i p o f height/crown width r a t i o to basal area and adjusted basal area.  7-  (1)  AVHT/AV.CW,P  (2) HT/CW.P  ON  ON  BA  Y = 3.078 t 0.010 X f - 0.650"  BA  ON  BA ON  SE  = 1.099  E  Y = 3.070 t 0.007 X f = 0.529"  (4) AV.HT/A\rXW,P  E  Y = 3.023 t 0.010 X t = 0.608"  (3) HT/CW,G  S E * 0.969  ADJ. BA  SE  = 1.0.19  E  Y = 4.199 + 0.002 X f = 0.257 S E = 1.232 E  (5)  HT/CW,P  ON  ADJ.BA  Y * 4.215 t f = 0.221  (6)  HT/CW,G  ON  ADJ.BA T  "1  100  Y = 4.041 t  BA  AND  f - 0.162  0=002 X SE  E  0.001 X SE  F  T  ADJ.BA  200  * 1.351  (SO. FEET)  = 1.185  140 Figure  20.  The r e l a t i o n s h i p o f height/crown width r a t i o to crovm c l o s u r e .  C  O  AV.HT/AVCW,P  3.416 t  Y=  2.523 X  f - 0.338* (2)  HT/CW.P  Y = 3.380 t  HT/CW.G  Y = 3222 r  T  .20  1  1  .40  .60 CROWN  CLOSURE  SE t  s 0.301'  1  .80 (CC,P)  = 1.200  E  2.542 X  t = 0.314' (3)  SE  = 1.315  E  2.II8X SE  1  E  1.00  = 1.145  141.  Figure  2 1 . The r e l a t i o n s h i p o f height/crown width r a t i o to age.  7-  cr. 5  o  I-  (1)  3-  HT/CW/3  Y = 3.439  + 0.016 X  r = 0.450  X (2)  HT / CW,P  Y = 4.222  t  0.010 X  r* = 0.237 (3)  AV.HT/AV.CW,P  Y  4.371 t f  S E - « 1.075  SE  10  30  1 70  - 0.205  AGE  1 90 (YEARS)  = 1.345  0.008 X SE  I-  -1 50  E  -  110  E  = 1.248  142. Figure  22.  The r e l a t i o n s h i p o f basal area and adjusted b a s a l area to crowding f a c t o r and adjusted crowding f a c t o r .  300-  CD 2 0 0 *  o <x o z <t CD  100-  (1)  AOJ.BA  ON  AOJXF  (2)  ADJ.BA  ON  CF  (3)  BA  Y =• 230.926 t 76.483 X SEg*157.490 f = 0.342' = 328.277 t 104.318 X Y S E =167507 Y = 0.032 Y = 119.595 t 82.43 X S E = 75.446 f = 0.485" = 150.785 t 24.849 X Y S E = 84.245 f = 0.216 E  ON  CF  E  (4)  BA  ON  ADJ.CF  E  1 CF  AND  ADJ. CF  2  143 Figure  23.  The r e l a t i o n s h i p o f crown width/diameter a t breast height r a t i o to b a s a l area and adjusted b a s a l area.  3-  5 _  2-  I(I)  CW/D  ON  ADJ. BA  Y = 1.712  t  f = 0.148 (2)  CW/D  ON  Y = 1.818  BA  t  Y = 0.268  1  __  100 BA  AND  ADJ. BA  1  200 (SQ.FEET)  (-0.0003) X SE  E  = 0.376  (-0-001) X SE  E  = 0.259  144. Figure  24.  The r e l a t i o n s h i p o f crown width/diameter at breast height r a t i o to age.  3H  O^IO  30  1  -|  50  AGE  70 (YEARS)  r  -  90  110  145. Figure  0 '  25. The r e l a t i o n s h i p o f b a s a l area and adjusted basal area to crovm c l o s u r e .  ! .20  r.40  1  1  .60 . 80 CROWN CLOSURE (CC,P>  1  —  1.00  146. Figure  26.  The r e l a t i o n s h i p o f crown c l o s u r e from a e r i a l photographs to stems per a c r e .  147. Figure  27.  The r e l a t i o n s h i p of crown closure from a e r i a l photographs to crowding f a c t o r and adjusted crowding f a c t o r .  L48. DISCUSSION Results of  analysis Each of the dependent v a r i a b l e s  Crovm w i d t h / d i a m e t e r a t b r e a s t h e i g h t  studied i s discussed here.  ratio  From T a b l e L 4 , the independent v a r i a b l e h a v i n g t h e h i g h e s t c o r r e l a t i o n w i t h CW/D r a t i o i s t o t a l h e i g h t  (r  = 0.792).  Therefore  it  i s l i k e l y t h a t t o t a l h e i g h t from the ground measurement c o u l d be used t o p r e d i c t the CW/D r a t i o . variables  The second and t h i r d most  significant  are age and d . b . h . which accounted f o r more than 50 p e r c e n t  o f the t o t a l  sum o f s q u a r e s .  The t h r e e independent v a r i a b l e s above  h i g h l y c o r r e l a t e d w i t h each o t h e r , thus i t above independent v a r i a b l e s Crown w i d t h i s  seems t h a t any one o f  are  the  c o u l d be u s e d t o determine CW/D r a t i o .  o n l y s i g n i f i c a n t at the 5 p e r c e n t l e v e l ,  t h i s may be due  l a r g e l y t o t h e l a c k of v a r i a t i o n of crovm w i d t h i n t h e s t a n d s , which was a l s o shown by the t a b l e on comparison o f v a r i o u s d e n s i t y and s t o c k i n g v a r i a b l e s by v a r i o u s age c l a s s e s  (Appendix 2 ) .  The CVJ/D r a t i o a l s o  h i g h l y s i g n i f i c a n t r e s u l t s w i t h t h e o t h e r crovm v a r i a b l e s l e n g t h , l i v e crown r a t i o ,  e.g. l i v e  crown s u r f a c e a r e a and crown volume but  o n l y accounted f o r a s m a l l percentage o f the v a r i a t i o n .  gives crown  they  Crown width/dbh  r a t i o i s not c o r r e l a t e d w i t h most o f the d e n s i t y . v a r i a b l e s  (e.g.  basal  a r e a , a d j u s t e d b a s a l a r e a and crowding f a c t o r )  except a d j u s t e d crowding  f a c t o r being s l i g h t l y c o r r e l a t e d  The main r e a s o n f o r  (r  = 0.353).  this  may be due t o t h e clumping c o n d i t i o n s e x i s t i n g i n the stands sampled, e . g . the stands v a r i e s from open to dense d e n s i t y area)  (by p r i s m sweep b a s a l  and d i f f e r e n t degree of crown c l o s u r e , i n most o f the  stands  sampled, but t h e y a l l r e p r e s e n t open-grown stands or open-density by  149. CW/D r a t i o i n d e x .  A g a i n t h i s c o u l d be r e f e r r e d t o t h e comparison t a b l e  by ages i n Appendix 2. The m u l t i p l e r e g r e s s i o n a n a l y s i s on 14 independent (Table 17)  shows t h a t t h e f i r s t  independent v a r i a b l e r e j e c t e d was age,  t h i s may be e x p l a i n e d by the f a c t t h a t ' t o t a l h e i g h t and d . b . h . correlated variables earlier.  It  variables  So here i t  age i 3 h i g h l y c o r r e l a t e d w i t h  can be seen t h a t w i t h h i g h l y  i n a m u l t i p l e r e g r e s s i o n , one may be  may a l s o be t r u e t h a t when the v a r i a b l e s  rejected  are combined age  may not p l a y such an i m p o r t a n t p a r t as i n the simple r e g r e s s i o n . d.b.h.  i s the v a r i a b l e  r e t a i n e d w i t h crown width and b a s a l a r e a of  i n d i v i d u a l t r e e as the second and t h i r d l a s t v a r i a b l e  to be r e j e c t e d .  The b e s t combinations of t h r e e independent v a r i a b l e s were d . b . h . , h e i g h t and age w i t h a h i g h l y s i g n i f i c a n t (S = 0.309) however i f  selected  correlation  o n l y two v a r i a b l e s were used i n the b e s t combina-  t i o n e . g . h e i g h t and age i t (R = 0 . 8 0 9 ) .  Here  still  gave the same c o r r e l a t i o n  coefficient  T h i s does n o t mean t h a t d . b . h . d i d not a f f e c t CW/D r a t i o  but i t may be due to t h e h i g h c o r r e l a t i o n o f d . b . h . w i t h h e i g h t and age, thus e x p l a i n i n g the same amount o f v a r i a t i o n .  As can be s e e n , i f  d.b.h.  i s a n a l y s e d w i t h h e i g h t o r age the s i g n i f i c a n c e i s h i g h (r = 0.794 and 0.765  respectively). Another a n a l y s i s o f CW/D r a t i o on crown w i d t h , d . b . h . and  crown c l o s u r e was made t o determine how w e l l t h e s e t h r e e v a r i a b l e s the CW/D r a t i o .  It  p e r c e n t of t o t a l  sum o f s q u a r e s .  variables  i s very  affect  was found t h a t crown w i d t h and d . b . h . e x p l a i n e d 89  important.  So the a c c u r a t e measurement o f  these  150. Height/crown w i d t h r a t i o , , from ground-data From T a b l e 14, a g a i n h e i g h t g i v e s the h i g h e s t ( r = 0.614-) w i t h Ht/CW,G. the d e n s i t y v a r i a b l e s crowding f a c t o r )  Here i t  significance  i s i n t e r e s t i n g t o note t h a t most o f  ( e . g . b a s a l a r e a crowding f a c t o r and a d j u s t e d  except a d j u s t e d b a s a l a r e a , were h i g h l y  significant.  But even though t h e y are h i g h l y s i g n i f i c a n t t h e percentage o f the  total  2 sum o f squares accounted f o r i s r e l a t i v e l y respectively).  The o n l y d e n s i t y v a r i a b l e  Ht/CW,G i s a d j u s t e d b a s a l a r e a (r  small (r  = 2 8 , 20, 18 p e r c e n t  t h a t i s not c o r r e l a t e d w i t h  = 0.162).  Perhaps when the  basal  a r e a i s a d j u s t e d the stands became too dense to be c o r r e l a t e d w i t h Ht/CW,G r a t i o .  So i t  can be s a i d t h a t Ht/CW,G r a t i o i s i n f l u e n c e d t o  a c e r t a i n extent by d e n s i t y and s t o c k i n g . a l s o h i g h l y s i g n i f i c a n t but e x p l a i n s t i l l  Age and l i v e crown r a t i o l e s s e r amounts o f the  variation.  Diameter at b r e a s t h e i g h t , l i v e crown l e n g t h and crown c l o s u r e are s i g n i f i c a n t at the 5 p e r c e n t  only  level.  The m u l t i p l e r e g r e s s i o n on 14 independent v a r i a b l e s shows a c o m p l e t e l y d i f f e r e n t c o n c l u s i o n from t h o s e above. variable  are  (Table  18)  Here the  r e t a i n e d was l i v e crown r a t i o , w i t h l i v e crown l e n g t h and  crown volume as the second and t h i r d l a s t v a r i a b l e s t o be r e j e c t e d .  If  these three v a r i a b l e s  is  are r e f e r r e d to T a b l e 14 o n l y l i v e crown r a t i o  h i g h l y s i g n i f i c a n t w i t h Ht/CW,G r a t i o and l i v e crown l e n g t h i s at 5 p e r c e n t l e v e l w h i l e crown.volume i s not s i g n i f i c a n t at  significant  all.  However t h e y seemed t o be b e t t e r when combined. In the b e s t combinations s e l e c t i o n o n l y l i v e crown r a t i o  was  i n c l u d e d w i t h h e i g h t and b a s a l a r e a and gave a h i g h c o r r e l a t i o n (R = 0.780)  but i f  o n l y two v a r i a b l e s  ( h e i g h t and b a s a l area) were used  the s i g n i f i c a n c e l e v e l was almost s i m i l a r t o t h a t of the t h r e e  variables  151."  (R = 0.769).  T h i s i s because l i v e crown r a t i o i s h i g h l y c o r r e l a t e d  w i t h h e i g h t and b a s a l a r e a i n d i v i d u a l l y and i t a l s o accounts f o r t h e same v a r i a t i o n as h e i g h t o r b a s a l a r e a .  When l i v e crown r a t i o i s  analysed with height o r b a s a l area the s i g n i f i c a n c e l e v e l i s a l s o high ( r = 0.720 and 0.630 r e s p e c t i v e l y ) . A n a l y s e s o f crown width, h e i g h t and crown c l o s u r e were made t o see t h e e f f e c t i v e n e s s o f t h e s e v a r i a b l e s on Ht/CW,G r a t i o . and crown w i d t h accounted  f o r 96 p e r c e n t o f t h e t o t a l sum o f squares  which i s b e t t e r t h a n those f o r CW/D (iii)  Height  Height/crown w i d t h and average from photo-data.  ratio.  height/average  crown w i d t h  ratios  From T a b l e I 4 , b a s a l a r e a has t h e h i g h e s t s i g n i f i c a n c e f o r Ht/CW,P and Av.Ht/Av.CW,P ( r = 0.609 and 0.650 r e s p e c t i v e l y ) , which i s a l s o q u i t e s i m i l a r t o Ht/CW,G ( r = 0.529) except t h a t t h e b a s a l a r e a f o r ground d a t a was n o t t h e most s i g n i f i c a n t v a r i a b l e .  Here a g a i n t h e  c o r r e l a t i o n t o d e n s i t y v a r i a b l e s i s t h e same as t h o s e f o r Ht/CW,G b u t the amount o f v a r i a t i o n accounted  f o r v a r i e s t o a c e r t a i n extent.  Crown c l o s u r e and l i v e crown r a t i o were o n l y s i g n i f i c a n t a t t h e 5 p e r c e n t l e v e l t o both Ht/CW,P and Av.Ht/Av.CW,P r a t i o s . The m u l t i p l e r e g r e s s i o n w i t h 1 4 independent 19 and 20) d i f f e r s s l i g h t l y from t h o s e o f Ht/CW,G.  variables  (Tables  F o r b o t h photo d a t a ,  Ht/GW,P and Av.Ht/Av.CW,P t h e v a r i a b l e r e t a i n e d was h e i g h t (X23(Ht,P) and X38(Av.Ht,P) r e s p e c t i v e l y ) , w i t h crown w i d t h  (X40(CW,P) and X39  (Av.CW,P) r e s p e c t i v e l y ) and l i v e crown r a t i o as t h e second  and t h i r d  l a s t v a r i a b l e s t o be r e j e c t e d . In t h e b e s t combinations  t h e t h r e e independent  variables  s e l e c t e d were l i v e crown r a t i o , b a s a l a r e a and photo h e i g h t f o r Ht/CW,P  152. r a t i o , and l i v e crown r a t i o , b a s a l a r e a and average photo h e i g h t f o r Av.Ht/Av.CW,P r a t i o .  I f two v a r i a b l e s ( b a s a l a r e a , h e i g h t and b a s a l  a r e a , average h e i g h t a r e used i n t h e b e s t combination, o f t h e t o t a l sum o f squares e x p l a i n e d i s almost s i m i l a r R  2  = 4 6 . 8 and 50.4 V s . 2 v a r i a b l e s R  2  the percentage (3 v a r i a b l e s  = 4 6 . 6 and 50.0 p e r c e n t  r e s p e c t i v e l y f o r Ht/CW,P and Av.Ht/Av.CW,P).  Here a g a i n i t i s due t o  the h i g h c o r r e l a t i o n o f l i v e crown r a t i o t o h e i g h t and b a s a l a r e a . S i m i l a r a n a l y s i s f o r Ht/CW,P and Av.Ht/Av.CW,P on t h e i r h e i g h t and crown w i d t h were made w i t h s l i g h t l y lower c o e f f i c i e n t o f determination  than t h e Ht/CW,G ( r = 92.3 and 9 1 . 4 r e s p e c t i v e l y ) .  F o r t h e above a n a l y s i s i t seems t h a t t h e ground-data (Ht/CW,G r a t i o ) i s s l i g h t l y b e t t e r than t h e p h o t o - d a t a (Ht/CW,P and Av.Ht/Av.CW,P r a t i o s ) f o r stand d e n s i t y and s t o c k i n g measurements.  153. >' ( H o w w e l l were h e i g h t , crown w i d t h and crovm c l o s u r e a c t u a l l y measured on the a e r i a l photographs? When one t a l k s about the use of a e r i a l photographs f o r mensuration p u r p o s e s , the f i r s t q u e s t i o n asked i s o f the p r e c i s i o n and a c c u r a c y o f e s t i m a t i o n s , thus t h e s e a r e two most i m p o r t a n t  variables  d e t e r m i n i n g the u s e f u l n e s s o f a e r i a l photographs i n f o r e s t r y . earlier,  it  was found t h a t the a c c u r a c y of photo measurements was  c l o s e to t h o s e o f ground measurements.  However,  found t o be h i g h l y c o r r e l a t e d w i t h i n t e r p r e t e r ; w i l l give d i f f e r e n t r e s u l t s .  Before  reviewed quite  H e i g h t e s t i m a t i o n was more  a c c u r a t e t h a n crown w i d t h e s t i m a t i o n .  accurately  As  t h e s e measurements were different  interpreter  any photo-measurement can be  e s t i m a t e d the p h o t o - i n t e r p r e t e r must f a m i l i a r i s e h i m s e l f w i t h  the e x i s t i n g ground c o n d i t i o n s o f s p e c i e s , f o r e s t t y p e , ground c o v e r and other features estimate  o f the f o r e s t s t a n d s .  Otherwise he w i l l n o t be a b l e  to  accurately. S i n c e t h e ground d a t a were gathered by the w r i t e r  c o n d i t i o n s were q u i t e c l e a r l y r e c o r d e d .  these  above  T h e r e f o r e , the a c c u r a c y o f h e i g h t ,  crown w i d t h and crown c l o s u r e a r e v e r y c l o s e t o t h o s e on the g r o u n d . However, variables  t h i s does n o t mean t h a t the i n d i v i d u a l measurements o f  these  does n o t v a r y as much as f i v e f e e t from the ground measurements.  The s t a n d a r d e r r o r o f e s t i m a t e o f crown w i d t h was v e r y s m a l l and a l s o  very  c l o s e t o the ground measurements, t h i s may be due to t h e t e c h n i q u e used by the w r i t e r ,  which was d e s c r i b e d  earlier.  154.  Height  Mean  Ground d a t a  91.51  +32.19  +4-70  Photo  91.81  +32.66  +4.77  Average photo d a t a  88.35  +32.26  +4.71  Crown Width  Mean  data  (ft.)  SD  SD  S E  M  Ground d a t a  20.83  +5.57  +0.81  Photo d a t a  19.58  +6.23  +0.91  Average photo d a t a  18.63  +6.23  +0.91  Crown C l o s u r e  Mean  (%)  Photo d a t a  57.06  SD +16.90  SE  M  +2.47  T a b l e 37 - Mean, s t a n d a r d d e v i a t i o n and standard e r r o r o f mean o f h e i g h t , crown w i d t h and crown c l o s u r e from ground and photo d a t a .  To what e x t e n t a r e CW/D and Ht/CW r a t i o s a f f e c t e d by crown c l o s u r e , s i t e , age, b a s a l a r e a and crowding f a c t o r ? From t h e d a t a a n a l y s e d , i t  can be seen t h a t CW/D r a t i o  not c o r r e l a t e d w i t h crown c l o s u r e , s i t e i n d e x , b a s a l a r e a , b a s a l a r e a and crowding f a c t o r . crowding f a c t o r  (r  It  is  adjusted  i s o n l y s l i g h t l y a f f e c t e d by a d j u s t e d  = 0.353) but i s h i g h l y c o r r e l a t e d w i t h age ( r = 0.792)  as e x p l a i n e d i n F i g u r e s 14 t o 27-'. • The ground Ht/CW,G r a t i o i s h i g h l y s i g n i f i c a n t w i t h age ( r = 0 . 4 4 6 ) , b a s a l a r e a (r a d j u s t e d crowding f a c t o r  = 0.529),  (r = 0.425).  f o r a s m a l l p e r c e n t a g e o f the t o t a l only s i g n i f i c a n t  crowding f a c t o r  ( r = 0.301)  (r = 0.450),  and  These c o r r e l a t i o n s o n l y accounted  sum o f s q u a r e s .  at the 5 p e r c e n t l e v e l  not a f f e c t e d by s i t e i n d e x and a d j u s t e d b a s a l a r e a .  Crown c l o s u r e  is  and Ht/CW,G r a t i o  is  155. The photo Ht/CW,P and Av.Ht/Av.CW,P r a t i o s a r e a l s o highlyc o r r e l a t e d w i t h b a s a l a r e a ( r = 0.608 and 0.650 r e s p e c t i v e l y ) , factor  ( r = 0.483 and 0.454)  and 0 . 4 1 9 ) .  and a d j u s t e d crowding f a c t o r  crowding  ( r = O.446  These v a r i a b l e s a g a i n o n l y accounted f o r a s m a l l percentage  o f t h e t o t a l sum o f s q u a r e s .  S i g n i f i c a n t c o r r e l a t i o n i s found w i t h  crown c l o s u r e ( r = 0.314 and 0.338 r e s p e c t i v e l y ) ,  b u t Ht/CW,P and  Av.Ht/Av.C¥,P r a t i o s a r e n o t a f f e c t e d by age and s i t e  index.  From t h e above, i t c a n be s a i d t h a t CW/D, Ht/CW,G, Ht/CW,P and Av.Ht/Av.CW,P r a t i o s a r e independent o f s i t e i n d e x , w h i l e crown c l o s u r e o n l y a f f e c t s t h e Ht/CW r a t i o s s l i g h t l y .  The i n f l u e n c e o f age c a n  o n l y be found from t h e ground (Ht/CW,G) r a t i o .  B a s a l a r e a and crowding  f a c t o r s a r e d e f i n i t e l y a f f e c t i n g Ht/CW r a t i o s .  These o b s e r v a t i o n s seem  t o i n d i c a t e t h a t Ht/CU r a t i o s a r e b e t t e r measures o f s t a n d d e n s i t y and s t o c k i n g f o r western hemlock than CW/D r a t i o . s t a t e d t h a t CW/D r a t i o i s n o t a u s e f u l v a r i a b l e  However,  i t cannot be  f o r evaluation of stocking  and d e n s i t y but i t i s d e f i n i t e l y n o t s u i t a b l e f o r t h e s e young western hemlock s t a n d s . ) How w e l l can GW/D and Ht/CW r a t i o s measure s t o c k i n g and d e n s i t y o f stands? Before t h e above q u e s t i o n can be answered, t h e concept o f n o r m a l i t y must f i r s t  be expounded but s i n c e t h i s cannot be q u a n t i t a t i v e l y  r e p r e s e n t e d , i t i s o n l y l o g i c a l t h a t c e r t a i n assumptions should be made. Here e i g h t assumptions were made w i t h most o f t h e p a s t d e f i n i t i o n s o f n o r m a l i t y t o secure a q u a n t i t a t i v e s t o c k i n g o f t h e stands s t u d i e d .  v a l u e f o r normal d e n s i t y and f u l l  156. The v a r i o u s assumptions f o r n o r m a l i t y are as f o l l o w s : (i)  Crowding f a c t o r and a d j u s t e d crowding f a c t o r are both equal t o one e . g . t h e a c t u a l o r a d j u s t e d number o f t r e e s i s e q u a l t o t h e normal number o f t r e e s ,  from the normal y i e l d t a b l e ,  on a p e r a c r e  basis  (Czarnowski 1 9 6 1 ) . (ii)  CW/D r a t i o  (iii)  i s equal to one as determined by Smith  et.al.(I96l).  Ht/CW r a t i o s from ground and photo-measurements are e q u a l t o  five  (Smith e t . a l . i 9 6 l ) . (iv)  B a s a l a r e a i s 237 s q . f t . / a c r e  (v)  (Smith e t . a l . 1 9 6 1 ) .  A d j u s t e d b a s a l a r e a i s 307 s q . f t . / a c r e d e r i v e d from the second assumption t h a t a d j u s t e d crowding f a c t o r i s equal t o one. because a d j u s t e d b a s a l a r e a has the l a r g e s t  significant  It  is  correlation  w i t h a d j u s t e d crowding f a c t o r . A l l t h e assumptions a r e a p p l i e d t o F i g u r e s 14 t o 1 7 , 20 and 21 f o r quantitative  v a l u e s which are t a b u l a t e d i n T a b l e 3 8 .  Assumption one - crowding f a c t o r i s one: CW/D r a t i o i s 1 . 5 5 ,  Ht/CW,G  i s 4 . 6 5 , Ht/CW,P and Av.Ht/Av.CW,P r a t i o s are 5.1 and b a s a l a r e a 200 s q . f t / a c r e . 338 s q . f t . / a c r e .  There i s a l s o a non s i g n i f i c a n t a d j u s t e d b a s a l a r e a of These datas w i l l be shown d i a g r a m a t i c a l l y i n F i g u r e 2 8 .  When CF = 1 and the CW/D = 1 . 5 5 two s i t u a t i o n s may a r i s e . widths are t h e same and the d . b . h . if  is  If  t h e crown  are a l s o the same ( F i g u r e 28 (c))  but  t h e crownd widths are changed and the d . b . h . a l s o changed ( F i g u r e 28  (4))  t h e CW/D r a t i o can s t i l l  proportion.  be the same i f  The ground Ht/CW r a t i o i s 4 . 6 5  the change i s i n the same and the photo Ht/CW  ratios  a r e 5.1, here a g a i n two p o s s i b l e c o n d i t i o n s may a l s o a r i s e t h a t i s t h e h e i g h t s are the same ( F i g u r e 28 ( 4 ) ) ,  if  the ground measured crown widths  157. a r e d e f i n i t e l y l a r g e r than t h e photo crown w i d t h s but i f t h e h e i g h t s are d i f f e r e n t t h e same.  ( F i g u r e 28 ( c ) ) t h e n t h e crown widths o f both c o u l d be  However, i f t h e crown w i d t h s a l s o d i f f e r then  s i t u a t i o n arose  another  ( F i g u r e 28 (A)) so t h e stand may be l i k e any one o f t h e s e .  B a s a l a r e a i s 200 s q . f t . / a c r e and a d j u s t e d b a s a l a r e a i s 338 s q . f t . / a c r e but b o t h t h e s e v a l u e s a r e u n r e a l i s t i c because t h e former used number o f stems o f incomplete  crown c l o s u r e o r a c t u a l number t o determine crowding  f a c t o r and f o r t h e l a t t e r o n l y b a s a l a r e a was a d j u s t e d w i t h o u t a d j u s t i n g the crowding  factor.  Assumption two - a d j u s t e d crowding f a c t o r i s one. CW/D r a t i o i s 1 . 6 7 , Ht/CW,G i s 4 . 1 8 , Ht/CW,P i s 5.0, Av.Ht/Av.CW,P i s 6.0,  b a s a l a r e a i s 175 s q . f t / a c r e and a d j u s t e d b a s a l a r e a i s 307 s q . f t . /  acre.  Even though t h e r a t i o s change, t h e p a t t e r n s a r e s i m i l a r t o t h o s e  d e s c r i b e d above.  The b a s a l a r e a decreases  and t h e a d j u s t e d b a s a l a r e a i s a l s o lowered The  from 200 t o 175 s q . f t / a c r e from 338 t o 307 s q . f t / a c r e .  b a s a l a r e a here i s u n r e a l i s t i c because o n l y t h e crowding f a c t o r was  adjusted.  The p o i n t where t h e a d j u s t e d b a s a l a r e a and a d j u s t e d crowding  f a c t o r meets, r e p r e s e n t s t h e t r u e b a s a l a r e a o f t h e e x i s t i n g  stand.  Assumption t h r e e - CW/D r a t i o i s one. Ht/CW,G i s 5.90, Ht/CW,P i s 6.02 and Av.Ht/Av.CW,P i s 6 . I 4 w i t h no v a l u e s are g i v e n f o r b a s a l areas and crowding f a c t o r s as t h e y a r e n o t s i g n i f i c a n t w i t h CW/D r a t i o .  The type o f stand e x i s t i n g here i s t h e same as those  d e s c r i b e d above ( F i g u r e 28 ( 4 ) ( c ) ( A ) ) a l t h o u g h t h e h e i g h t r a t i o s i n different proportions.  vary  158. Assumption f o u r - Ht/CW,G r a t i o CW/D r a t i o i s 1 . 3 7 ,  is  five.  crowding f a c t o r i s 1 . 3 5 , a d j u s t e d crowding f a c t o r  i s 2.25 and b a s a l a r e a i s 260 s q . f t / a c r e .  If  the Ht/CW,G r a t i o  c o n s t a n t the CW/D r a t i o may a l s o be equal ( F i g u r e 28 ( l ) ) d.b.h.  is  where  held  height  and crown w i d t h are e q u a l and p r o p o r t i o n a l t o each o t h e r .  However when h e i g h t d . b . h . Ht/CW r a t i o  and crown w i d t h v a r y  and CW/D r a t i o may s t i l l  ( F i g u r e 28(A))  be the same.  With t h e same Ht/CW,G  r a t i o the crowding f a c t o r and a d j u s t e d crowding f a c t o r v a r y as much, and i t  is  s u r p r i s i n g t o f i n d t h a t both are s t i l l  c o r r e l a t e d w i t h Ht/CW,G r a t i o .  the  almost t w i c e  highly  Only b a s a l a r e a o f 260 s q . f t / a c r e  is  r e c o r d e d because a d j u s t e d b a s a l a r e a i s n o t s i g n i f i c a n t xd.th Ht/CW,G r a t i o . Assumption f i v e - Ht/CW,P r a t i o i s  five.  CW/D r a t i o i s I . 4 6 , crowding f a c t o r i s 0 . 9 6 , a d j u s t e d crowding f a c t o r i s 1.59 and b a s a l a r e a i s 200 s q . f t / a c r e . Assumption s i x - Av.Ht/Av.CW,P Cw/D r a t i o  i s 1.54,  ratio is  five.  crowding f a c t o r i s 0 . 9 5 , a d j u s t e d crowding f a c t o r  i s 1.59 and b a s a l a r e a i s 200 s q . f t / a c r e . It  can be seen from the above t h a t the v a l u e s are almost  therefore i t  i s o n l y r e a s o n a b l e t o put them t o g e t h e r .  are b a s i c a l l y the same as t h a t of ground r a t i o  identical  The stands p r e s e n t  (Ht/CW,G), t h e o n l y  d i f f e r e n c e i s t h a t the stands here are not as dense from t h e o f crowding f a c t o r ,  a d j u s t e d crowding f a c t o r and b a s a l  indication  area.  Assumption seven - b a s a l a r e a i s 237 s q . f t / a c r e . CW/D r a t i o i s 1 . 5 5 , Ht/CW,G r a t i o i s 4 . 8 3 , Ht/CW,P r a t i o i s Av.Ht/Av.CW,P r a t i o i s  5.35 and crowding f a c t o r i s  1.45.  5.33,  159. Assumption e i g h t - a d j u s t e d b a s a l a r e a i s 307 s q . f t / a c r e . CW/D r a t i o  i s 1.62,  Ht/CW,G r a t i o i s 4.4O,  Ht/CW,P r a t i o i s  4.78,  Av.Ht/Av.CW,P r a t i o i s 4.80 and a d j u s t e d crowding f a c t o r i s  1.00.  The v a l u e s secured by t h e s e two b a s a l a r e a assumptions are n e a r l y same a l t h o u g h assumption seven gave l a r g e r v a l u e s f o r a l l than assumption e i g h t .  the  variables  T h i s means t h a t normal b a s a l a r e a shows a denser  s t a n d than a d j u s t e d b a s a l a r e a but i t may a l s o mean t h a t the sampled are a l i t t l e  the  below n o r m a l .  stands  The stands here are s i m i l a r t o those  i n assumption t h r e e . From t h e above assumptions i t photo r a t i o s  (Ht/CW,P and Av.Ht/Av.CW,P)  ground r a t i o  (Ht/CW,G).  i s p o s s i b l e t o say t h a t  the  are always l a r g e r than the  The CW/D and Ht/CW r a t i o s f o l l o w a v e r y s i m i l a r p a t t e r n f o r the e i g h t assumptions (Table 3 8 ) .  Therefore i t  i s l o g i c a l t o say  t h e s e r a t i o s t h u s measured stand d e n s i t y and s t o c k i n g v e r y w e l l . ;  i t must be n o t e d t h a t than Ht/CW r a t i o s ,  all  that However,  t h e r e are more n o n - s i g n i f i c a n t v a l u e s i n CW/D r a t i o s  so t h e Ht/CW r a t i o i s b e t t e r than t h e CW/D r a t i o  d e n s i t y and s t o c k i n g measurements.  for  T a b l e 38 - The q u a n t i t a t i v e v a l u e s secured from F i g u r e s 16-27 by the assumptions and t h e i r means. Variable i n assumption CF  CF  Adj.CF  1.00  Adj.CF  1.00  CW/D  CW/D  Av.Ht/ Av.CW,P  Basal area  Adj. basal area  4.65  5.00  5.01  200  338  1.67  4.18  5.00  6.00  175  307  1.00  5.90  6.02  6.14  5.00  1.35  2.25  1.37  Ht/CW,P  0.96  1.59  1.46  Av.Ht/ Av.CW,P  0.95  1.59  1.54  Basal area  1.45 area  Ht/CW,P  l_5_i  Ht/CW,G  Adj.basal  Ht/CW,G  eight  260  5.00  200 5.00  200 237  1_5_5  4.83  5.33  5.35  1.00  1.00  1.62  4.40  4.78  4,80  Mean  1.115  1.486  1.470  4.827  5.188  5.383  212  317.3  Mean o f significant values  1.142  1.486  1.408  4.910  5.270  5.500  219.5  307  307  The v a l u e s u n d e r l i n e d are based on n o n - s i g n i f i c a n t r e g r e s s i o n a p p r o x i m a t i o n o n l y .  161.  Figure  28.  The b a s i c crown width/diameter a t breast height and:height/crown width r a t i o s being achieved by v a r y i n g the d.b.h., crown width, and height o f trees.  HT.  HT=25'  HT=50'  = 25*  CW.= 5  D=5"  (A)  CW HT CW/D  (2)  K  ±  H T / O W  ?fc  (B)  t  CW  =  DBH  =  DBH  *  HT  =  H T  #  C W / D  *  C W / D  *  H T / C W  3 «  CW  CONT.  HT CW/D  H T / C W  /  DBH  t 4  CW  DBH  H T / C W  9*  OR  =  OR  =  162.  /V\ (C)  cw  CW  =  DBH  DBH  =  HT  HT  jt  CW/D  CW/D  =  HT / CW  HT/CW  *  A  Av i \  K (D)  (4) CW  CW  DBH  DBH  HT  HT  CW/D HT/CW  *  OR  CW/D HT/CW  *  OR  163. CONCLUSION A e r i a l photographs have been used f o r f o r e s t r y purposes f o r many y e a r s and the uses are 'expanding g r a d u a l l y . p r o g r e s s e d to such a stage t h a t a e r i a l  The development has  photographs have f o r the  few y e a r s became an e s s e n t i a l t o o l f o r f o r e s t managements.  past  This  trend  w i l l p r o b a b l y c o n t i n u e and improve as b e t t e r t e c h n i q u e s are found f o r more e f f i c i e n t use o f a e r i a l p h o t o g r a p h s . The f o l l o w i n g c o n c l u s i o n s c o u l d be drawn from the d a t a analysed. 1.  The models p r e s e n t e d and d a t a a n a l y s e d h e r e i n can be used t o improve p h o t o - i n t e r p r e t a t i o n and photo-mensuration of s t o c k i n g and d e n s i t y .  2.  The agreement between t h e t h e o r e t i c a l and a c t u a l models was p o o r , p r i m a r i l y because o f t h e extreme i r r e g u l a r i t y  3.  of natural  stands.  The p r e c i s i o n o f h e i g h t measurements on a e r i a l photographs conformed w i t h those o f p a s t r e p o r t s . was +4.77 f e e t .  Standard e r r o r o f mean  The p r e c i s i o n o f h e i g h t measurements was  t o t h o s e from the ground samples, b u t i t was not as  similar  accurately  measured. 4.  Crown w i d t h was a l s o e s t i m a t e d as p r e c i s e l y as those on the ground. Standard e r r o r o f mean was +0.91 f e e t .  A g a i n , t h e a c c u r a c y was n o t  as good as the ground measurements. 5.  Crown c l o s u r e e s t i m a t e from a e r i a l photographs was a l s o precise.  6.  Standard e r r o r of mean was +2.47 per  quite  cent.  A number o f stand d e n s i t y and s t o c k i n g v a r i a b l e s were used and were found t o be h i g h l y s i g n i f i c a n t l y a s s o c i a t e d w i t h each o t h e r as below:  164  (a)  Crowding f a c t o r was h i g h l y c o r r e l a t e d w i t h Ht/CW r a t i o s photo (Ht/CW,P and Av.Ht/Av.CW,P) w i t h b a s a l a r e a , but i t  (b)  on  and ground (Ht/CW,G), and a l s o  was n o t a f f e c t e d by CW/D r a t i o .  A d j u s t e d crowding f a c t o r was a l s o h i g h l y c o r r e l a t e d w i t h Ht/CW ratios  and a d j u s t e d b a s a l a r e a , but i t  was o n l y s l i g h t l y  related  t o CW/D r a t i o . (c)  Crown width/diameter b r e a s t h e i g h t r a t i o was h i g h l y  significantly  c o r r e l a t e d w i t h Height/crown w i d t h r a t i o s  Ht/CW,P and  Av.Ht/Av.CW,P)  (Ht/CW,G,  but o n l y s l i g h t l y c o r r e l a t e d w i t h a d j u s t e d crowding  factor, while i t  i s n o t a f f e c t e d by b a s a l a r e a and a d j u s t e d b a s a l  area. (d)  Height/crown w i d t h r a t i o s  (Ht/CW,G,  Ht/CW,P and  Av.Ht/Av.CW,P)  a l l had h i g h l y s i g n i f i c a n t c o r r e l a t i o n w i t h the same v a r i a b l e s (crowding f a c t o r ,  a d j u s t e d crowding f a c t o r ,  CW/D r a t i o ,  and b a s a l  a r e a p e r a c r e ) however t h e y o n l y each accounted f o r a s m a l l percentage o f the sum o f s q u a r e s . (e)  B a s a l a r e a per a c r e was h i g h l y c o r r e l a t e d w i t h a l l  the  three  Ht/CW r a t i o s and the crowding f a c t o r . 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Vezina,  P.E.,  1963b. More about the crown c o m p e t i t i o n f a c t o r . C h r o n . 39 : 313-317.  Vezina,  P.E.,  1964.  Walters, J . ,  J.  Walters, J . ,  and J .  For.  An a n a l y s i s o f measures o f d e n s i t y i n even-aged balsam f i r and j a c k p i n e s t a n d s . F o r . C h r o n . 40(4) : 474-487.  Soos, and I.W. Ker, 1961. I n f l u e n c e o f crown c l a s s and s i t e q u a l i t y on growth t o b r e a s t h e i g h t o f Douglas f i r , western hemlock and western r e d c e d a r . U n i v . B r i t . C o l . , F a c . F o r . , Research Note No.37. 4pp» Soos, 1962. The v e r t i c a l and h o r i z o n t a l o r g a n i s a t i o n o f growth i n some c o n i f e r s o f B r i t i s h Columbia. Univ. B r i t . C o l . , F a c . F o r . , Research Note No.51.  23pp. Walters, J . ,  and J .  Walters, J . ,  and A. Kozak, 1964. The e c c e n t r i c i t y o f diameter a t b r e a s t h e i g h t o f Douglas f i r , western hemlock and western red cedar. Univ. B r i t . C o l . , Fac. F o r . Res. Note No.44. 4pp.  Walters,  J.,  Wang, Y . M . ,  Soos, 1963. Shoot growth p a t t e r n s o f some B r i t i s h Columbia c o n i f e r s . F o r . Sci.9(1) : 73-84.  1964.  Some o b s e r v a t i o n s on the j u v e n i l e growth o f western hemlock i n p l a n t a t i o n . Univ. B r i t . C o l . , Fac. F o r . , Res. Paper No.61. 12pp.  1965.  Use o f a s e r i e s o f a e r i a l photographs t o e s t i m a t e growth o f t r e e s and stands. U n i v . B r i t . C o l . , Fac. F o r . , u n p u b l i s h e d t h e s i s f o r MF degree..  143pp.  Ward,  1964.  W.W.,  L i v e crown r a t i o  and stand d e n s i t y irti:young,  even-aged r e d oak stands. Warrack, G . C . ,  1959.  R.W.,  1943.  : 56-65.  Crown diamension, i n i t i a l diameter and diameter growth i n a j u v e n i l e s t a n d o f Douglas f i r . F o r .  Chron.35(2) Wellwood,  F o r . Sci.10(1)  : 150-153.  Trend towards n o r m a l i t y o f s t o c k i n g f o r secondgrowth l o b l o l l y p i n e s t a n d s . J o u r . For.41 :202-209.  175. Wile, B.C.,  I960.  Crovm s i z e and stem diameter i n r e d spruce and balsam f i r . 9pp.  Willingham,  J.W.,  1957.  D e p t . F o r . C a n a d a . , Pub.No.1056.  E s t i m a t i o n o f f o r e s t management i n v e n t o r y from a e r i a l p h o t o g r a p h i c measurements. S c i . 3 ( 3 ) i 270-274.  Wilson, F.G.,  194-6.  W i l s o n , R.,  1948.  data  For.  N u m e r i c a l e x p r e s s i o n o f s t o c k i n g i n terms o f  height.  J o u r . F o r . 4 4 : 758-761.  P h o t o - i n t e r p r e t a t i o n a i d f o r timber  J o u r . F o r . 4 6 : 41-»44«  and A . H . A l d r e d , 1967.  survey.  Wittgenstein,  L.S.,  Worley, D . P . ,  and G.H. L a n d i s , 1954. The a c c u r a c y o f h e i g h t measurements w i t h p a r a l l a x i n s t r u m e n t s on 1:12,000 p h o t o g r a p h s . Photogram. Eng. 20 : 823-829.  Worley, D.P.,  and H.A. Meyer, 1954. Measurements of crown diameter and crown c o v e r and t h e i r a c c u r a c y f o r 1:12,000 photographs. Photogram. Eng.21 : 372-375.  photos.  Tree volumes from l a r g e - s c a l e  Photogram. E n g . 33(1)  : 69-73.  176. APPENDIX 1  I l l u s t r a t e diagrams o f the t h e o r e t i c a l stand d e n s i t i e s These f i g u r e s ( A , B , C , D and E)  were drawn w i t h s i m i l a r  increase  o f crown w i d t h and d . b . h . but w i t h d i f f e r e n t number o f t r e e s w i t h i n  each  f i g u r e to show the degree o f crowding from open, open-normal, n o r m a l , normal-dense, and dense d e n s i t i e s .  From the f i g u r e s , i t  can be seen  c l e a r l y how a stand t r e n d towards n o r m a l i t y and may even grow p a s t n o r m a l i t y to dense d e n s i t y . F i g u r e A shows t h a t the t r e e s a r e v e r y wide a p a r t and t h e i r p r o g r e s s from open to normal stand d e n s i t y i s v e r y slow, t h a t i s t h e y w i l l not form a c l o s e d stand u n l e s s the crown w i d t h i s spread wide enough t o cover the d i s t a n c e between them.  The chances of t h i s type of stand t r e n d i n g  towards dense stand d e n s i t y i s almost n i l a l t h o u g h i t that i t  does r e a c h such a s t a g e .  (vii),  normal stand d e n s i t y ( v i i i )  is  shown i n the f i g u r e  The open stand d e n s i t y i s from ( i ) and dense stand d e n s i t y a t  (ix)  and  F i g u r e B has t w i c e as many t r e e s as f i g u r e A and t h e r e f o r e t a k e s l e s s time f o r i t  to r e a c h n o r m a l i t y ( v i ) ,  dense stand d e n s i t y ( v i i ) F i g u r e C has f i g u r e B.  to ( i x ) ,  to  it  and s t i l l l e s s time to  and open s t a n d d e n s i t y ( i )  to  (x).  reach  (v).  times as many t r e e s as f i g u r e A and 2% times as  Thus the i n c r e a s e i n s t o c k i n g and d e n s i t y i s f a r more r a p i d t h a n  t h e above two.  Open s t a n d d e n s i t y ( i )  and dense stand d e n s i t y  (vi)  to  to ( i v ) ,  normal stand d e n s i t y  (v),  (ix).  F i g u r e D has 8 times as many t r e e s as f i g u r e A, 4 t i m e s as  5  f i g u r e B and l g times as f i g u r e C . density i s  s t i l l faster.  T h e r e f o r e the t r e n d towards dense stand  Open s t a n d d e n s i t y ( i )  and ( i i ) ,  normal stand  177.  density  (iii)  and dense stand d e n s i t y  (iv)  to  (vi).  F i g u r e E shows a c o m p l e t e l y d i f f e r e n t c o n d i t i o n , o f a r e l e a s e d s i t u a t i o n from f i g u r e D. density  (v)  it  density  (vii).  it  the r e l e a s e i s stand density  and then t o dense stand  and ( x ) .  (ii)  and dense stand d e n s i t y ( i v ) .  t o normal stand d e n s i t y ( v i i i ) (ix)  (vi)  i s r e l e a s e d t o open-normal d e n s i t y  w i l l be t o normal-dense ( i i i )  It  i s a model  When r e l e a s e d t o open-stand  w i l l advance towards n o r m a l i t y If  it  the  trends  However,  if  the t r e n d s w i l l be t o dense  can a l s o be seen t h a t t h e c l e a r  l e n g t h i s h i g h e r than those i n the o t h e r f i g u r e s .  bole  \QO A. c  FIG.  A  FiG.  E  APPENDIX 2  179..  Comparisons o f the v a r i o u s d e n s i t y and s t o c k i n g v a r i a b l e s shown below f o r d i f f e r e n t age c l a s s . Model No.  1— 2 3 4 5 6 7 8  9 10.  11-  12 13 14 15 16 17 18 192021  22  2324 25  26 _ 2728 29 30 31 32  33  3435 36 37 38 39 40 -  4142 43  44^  45 46 47-  Age cjlass 30 II  n n it ii it tt rt tt it it tt tt tt it tt tt tt 60 tt tt it it it it 90 it ti it it it tt tt tt n tt tt II  tt 120 tt it II  tt tt tt  BA 50 60 60 70 70 110 120 140  140 150 200 230 230 240 250 250 330 340  340  110 130 140 140 210 220 240 110 120 120 130  140 210 230 230 240 260 280 280 310 370  60  90 130 140 140 180 230  Adi.BA  CW/D  Ht/CW.G  125 150 1200 280 200  2.21  2.11  2.34 1.90 1.98 2.04  2.50 2.43 2.48 2.95 2.38 3.12 5.08 3.70 3.25 2.94 5.09 5.39 3.69 5.92 4.05  222  185 311 280 188 267 329 329 353 313 294 508 486 425  222 236 215 280  420 338 343  222  171 400 289 255 350 288 368 384  400 431 350 564 493 120 171 274 280 280 514 418  2.22  1.98 1.64 1.52 2.16 1.92 1.38  1.61 1.91  1.32 1.71  1.15 1.82 1.81 1.18 1.76 i;97  1.83 1.53 1.68 2.10 1.32 1.71  1.22 1.69 1.13  1.41 1.45 1.27 1.35 1.23  7.22  1.54  1.15 1.08 1.02 1.15  4.11 6.71  6.65  5.39 4.78 4.21 8.01  2.66 2.49 2.90 3.59 2.51  3.36  5.59 4.12 3.82  3.66 5.77  5.72 4.79 6.38 4.42 8.01 6.71 4.98 6.16 3.40  3.24 4.56  4.41  4.22  4.41  4.41 5.77  1.06  1.16  2.93 2.87 3.74 3.19 3.50 5.90 3.79 4.23  3.36 4.74 4.65 4.38 4.50 3.86 4.10 4.25 5.36 4.04 5.91 4.37 3.84  4.85 6.94  1.14  2.66  2.80  5.88 5.33  1.40  1.50  2.78  Ht/CW,P  5.10  4.60 5.77  5.13 5.50 6.24 6.10 6.27 4.08 4.10 3.79  1.26  Av.Ht/ Av.CW.P  6.00  4.66  6.42  5.31  4.27  4.33  4.98 6.01 5.79 4.15 6.68 4.53 3.92  4.32 5.67 5.23 5.46 6.38 6.80 7.32 3.96 4.13 3.80 5.28 4.75 7.07 5.18  are  CF  0.155 0.141 0.105 0.125 0.136  O.364  0.392  0.350 0.528 1.326 0.606 0.490 0.816 1.156 2.219  0.500  1.378 0.731 0.350 0.417  0.860  4.97  0.750 1.375  4.54 4.75 4.54 5.30 5.52 4.15 4.08 4.41  1.373 0.786 1.214 0.775 0.886 0.786 0.753  3.88  4.25 5.71 5.23 5.65  6.38  6.80 5.30 3.96 4.04 3.87 6.28 4.68 7.95 5.18  0.444 1.000  2.000  0.353 0.883 0.896 0.707 1.512  1.667  1.417 0.238 0.690 0.580 1.436 0.256  0.749 0.682  Adi.CF  0.388 0.352 2.105 0.500 0.390 0.808  0.603  0.778 1.056 1.658 0.808 0.700 1.165 1.652 2.743 0.588 2.121 1.044 0.438 0.925 1.565 1.155 2.750 0.889 1.538 1.961 1.748 1.734 2.585 1.970  1.430  1.254 2.500 0.562 1.403  1.379  1.088 1.891 3.030 1.890 0.476 1.314 1.220 2.870 0.513 2.139 1.241  APPENDIX 2 Model No. Photo Data Date o f Photo RF Focal length Flying height 'Plot size E l e v a t i o n of p l o t Height photo Average h e i g h t Crown w i d t h Average crown width Ht/CW Av.Ht/Av.CW Brown c l o s u r e Ground Data Age c l a s s Site class S i t e index B.A. SPA Height Crown width D.B.H. Average DBH LCL CW/DBH Ht/CW NSPA CF Adj.CF Adj.BA Adj.SPA Mortality  1  July,1965 1:15,350 1:16,025 12" 17,200' l/5 a c r e 1850' 1175 42.6 43.1 39.2 42.6 16.0 15.4 14.1 2.80 2.78 40  16.0 2.66 2.66 40  30 30 poor d r y poor wet 105 50 450 40 19 7.5 3.4  40  2.21 2.11 2900 0.155 0.388 125 1125 150  3  2  100 60 450 45 18 7.7 3.3 27 2.34 2.50 3200 0.141 0.352 150 1125  -  4  6  5  7  8  9  1:16,300  1:16,300  1:16,700  1:15,325  1:15,950  1:16,075  1:16,650  900 54.1 51.9 21.7  830 63.3 58.8 21.8  500 57.4 55.0 16.0  1875 39.2 a.5 15.6  1250 53.7 51.5 16.0  1125 59.8 55.5 10.7  550 85.7 76.2 20.8  17.7 2.49 2.13 5  20.5 2.90 2.87 25  14.7  13.0 2.51 3.19 45  14.7 3.36 3.50 65  9.4 5.59 3.90 45  20.1 4.12 3.79 50  30 medium 125  60  250 55 23 11.9 3.8 49 1.90 2.43 2375 0.105 2.105 1200 5000  -  30 good seepage  3.59  3.74 35  30 poor d r y  30 medium  30 poor wet  70 250  30 very good 130 70 300  25 12.6 4.1  20 7.8 3.9  130 110 800 38  16  120 120 1000 53 17 8.6 3.7 40 1.98 3.12 2550 0.392 0.603 185 1538 150  140 140 700 61 12 7.2 4.1 48 1.64 5.08 2000 0.350 0.778 311 1556  140 62  62  1.98 2.48 2000 0.125 0.500 280 1000  -  59  49  2.04  2.95  2200 0.136 0.390 200 857 2050  7.2 3.9 38 2.22 2.38 2200 0.364 0.808 222 1778 150  -  30 very good 160 140  950  85 23 15.1 4.4 62 1.52 3.70 1800 0.528 1.056 280 1900 200  M o d e l No. Photo Data Date o f Photo RF Focal length F l y i n g height Plot size Elevation of plot H e i g h t photo Average h e i g h t Crown w i d t h Average crown width Ht/CW Av.Ht/Av.CW Crown c l o s u r e Ground Data Age c l a s s Site class S i t e index B.A. SPA Height Crown w i d t h D.B.H. Average DBH LCL CW/DBH Ht/CW NSPA CF AdJ.CF AdJ.BA Ad j ; . SPA Mortality  10  11  J u l y , 1965 1:16,050 1:15,425 12" 17200' 1/5 acre 1150 1775 51.2 56.3 51.2 47.7 15.4 13.4 12.1 3.82 4.23 80 30 good seepage 125 150 3150 52 16 7.4 3.8 37 2.16 3.25 2375 1.326 1.658 188 3938 1000  12  13  14  15  16  17  18  1:15,950  1:16,650  1:16,050  1:16,075  1:16,650  1:16,075  1:15,925  1250 53.7 53.7 9.3  71.5 69.2 12.5  550  1150 51.2 46.9 10.7  1125 68.3 64.1 10.7  550 85.7 76.2 19.4  1125 64.1 64.1 8.0  1275 53.7 47.0 8.0  11.6 3.66 4.11 75  8.0 5.77 6.71 70  10.4 5.72 6.65 70  8.7 4.79 5.39 70  13.4 6.38 4.78 80  18.1 4.42 4.21 85  8.0 8.01 8.01 65  8.0 6.71 5.88 70  30  30  30 very good 150 230 1550 70 13 8.1 4.2 57 1.61 5.39 1900 0.816 1.165 329 2214 350  30 good seepage 100 240 3700 48 13 6.8 3.3 34 1.91 3.69 3200 1.156 1.652 353 5286 650  30 poor wet 160 250 3950 71 12 9.1 4.4 61 1.32 5.92 1800 2.219 2.743 313 4938  poor dry 90 200 2000 53 18 9.4 3.1 33 1.92 2.94 3300  0.606  0.808 267 2667 250  medium 120 230 1250 56 11 8.0 3.7 45 1.38 5.09 2550 0.490 0.700 329 1786 800  -  30 very good 160 250 900 89 22 12.9 4.4 40 1.71 4.05 1800 0.500 0.588 294 1059 1550  30 poor wet 155 330 2500 65 9 7.8 4.3 50  1.15  7.22 1850 1.378 2.121 508 3923  -  30 medium 110 340 1900 51 9.5 5.5 3.5 25 1.32 5.10  2600  0.731  1.044  486 2714 1850  Model No. Photo Data Date of Photo RF Focal length Flying height Plot size Elevation of plot H e i g h t Photo Average Height Crovm w i d t h Average crovm width Ht/CW Av.Ht/Av.CW Crown c l o s u r e Ground d a t a Age c l a s s Site class S i t e index B.A. SPA Height Crown width D.B.H. Average DBH LCL CW/DBH Ht/CW NSPA CF .Adj.CF Adj.BA Adj.SPA Mortality  19  20  J u l y , 1965 1:16,325 1:15,850 12" 17,200' 1/5 a c r e 1350 875 67.7 129.9 65.5 123.3 13.6 21.1 12.3 4.98 5.33 80 30 good seepage  140  340 700 69 15 8.3 4.1 39 1.81 4.60 2000 0.350 0.438 425 875 700  19.2 6.16 6.42 45 60 medium 135 110 200 127 22 18.6 10.4 72 1.18 5.77 480 0.417 0.925 222 444 350  21  1:16,025  22  1:16,250  23  1:16,400  24  1:16,325  1175 72.7 68.2 21.4  950 107.5 105.3 24.4  800 108.9 108.9 21.9  875 108.0 103.5 24.5  16.1 3.40 55  23.1 4.41 4.56 65  20.5 4.97 5.31 50  24.5 4.41 4.22 50  60  60  4.24  poor dry 92 130 800 74 22 12.5 6.9 49 1.76 3.36 930 0.860 1.565 236 1455 550  medium 155 140 300 109 23 11.7 11.4  63  1.97  4.74  400  0.750 1.155 215 462 150  60 good seepage 155 140 550 107 23 12.2 11.4 67 1.83 4.65 400 1.375 2.750 280 1100 250  60  poor wet 140 210 200 105 24 15.7 10.6 81 1.53 4.38 450 0.444 0.389 420 400 250  25  26  27  1:16,250  1:16,400  1:16,025  950  800 90.9 88.7 19.1  1175 127.2 123.0 28.0  23.1  20.5 4.75 4.33 70  24.7 4.54 4.98 45  98.6 98.6 21.7  4.54  4.27  65  60 medium 140 220  450  99 22 13.1 10.6  60 1.68 4.50 450  1.000  1.538  338 692 450  60 good seepage 130 240 700 93 20 12.9 9.9  60  2.10  3.36  510 1.373 1.961 343 1000 500  90 good seepage  125  110 250 123  30  22.7 13.2 98 1.32 4.10 318 0.786 1.748 222 556 150  Model No. Photo Data Date o f photo RF Focal length F l y i n g height Plot size Elevation of plot Height photo Average h e i g h t Crown w i d t h Average crown width Ht/CW Av.Ht/Av.CW Crown c l o s u r e Ground d a t a Age c l a s s Site class S i t e index 8.A. SPA Height Crown w i d t h D.B.H. Average DBH LCL CW/DBH Ht/CW NSPA CF Adj.CF Adj.BA Adi.SPA Mortality  28  29  J u l y , 1965 1:15,975 :1:16,225 12" 17,200' 1/5 a c r e 975 1225 84.8 134.2 133.1 80.5 16.0 24.3  13.4 5.30 6.01 70  90 poof. "dry 80 120 850 85 20 11.7 8.2 65 1.71 4.25 700 1.214 1.734 171 1214 500  23-0 5.52 5.79 30 90 very good 145 120 200 134 25 20.5 15.0 89 1.22 5.36 258 0.775 2.585 400 669 50  30  1:16,125  31  1:15,925  32  1:16,125  33  1:15,825  1075 100.5 100.5 24.2  1275 131.6 124.9 21.2  1075 118.6 109.6 26.9  1375 71.8 67.4 18.5  24.2 4.15 4.15 45  26.7 6.08 4.68 55  24.2 4.41 4.53  17.2 3.88 3.92 80  90 poor wet 110 130 350 101 25  14.3 11.6  51 1.69 4.64 395 0.886 1.970 289 778 200  90 medium 125 140 250 130 22 19.5 13.2 71 1.13 5.91 318 0.786 1.430 255 455  400  60  90 poor wet 100 210  350  118 27 19.2 10.5 80 1.41 4.37 465 0.753 1.254 350 583 300  90 poor dry 80 230 1400 73 19 13.1 8.2 58 1.45 3.84 700 2.000 2.500 288 1750 1050  34  1:16,075  35  1:16,025  1125 136.3 127.3 32.1  1175 152.4  4.25  29.5  25.4 5.71  4.32  62.5  5.67 62.5  90 medium 135 230 100 147 32 25.3 14.2 76 1.27 4.41 283 0.353 0.562 368 159 200  144.0 26.7  90 very good 135  240  250 150  26  19.3 14.2  95 1.35 5.77 283  0.883 1.402 384 397  36  1:16,025  1175 118.8 118.8 22.7 22.7 5.23 5.23  65  90 good seepage 120 260 300 118 23 18.7 12.7 53 1.23 5.13 335 0.896 1.379 400 462 300  Model No. Photo Data Date o f photo RF Focal length F l y i n g Height Plot size Elevation of plot Height photo Average h e i g h t Crown w i d t h Average crown width Ht/CW Av.Ht/Av.CW Crown c l o s u r e Ground d a t a Age c l a s s Site class S i t e index B.A. SPA Height Crown w i d t h D.B.H. Average DBH LCL CW/DBH Ht/CW NSPA CF £dj..CF Adj.BA A a £ . SPA Mortality  37  38  J u l y , 1965 1:15,925 1:16,050 12" 17,200« 1/5 acre 1150 1275 135.0 102.1 130.6 102.1 16.0 23.9 23.9 5.65 5.46  65  90 very good 135 280 200 132  24  19.0 14.2 54 1.26 5.50 283  0.707  1.088 431 308 100  16.0 6.38 6.38 80 90 medium 105 280 650  106.  17 11.3 11.1 51 . 1.50 6.24 430 1.512 1.891 350 813 700  39 1:16,025  40  41  42  43  44  45  1:15,750  1:16,025  1:16,025  1:16,175  1:16,075  1:15,950  1175 127.2 127.2 18.7  1450 93.7 87.1 15.8  1025 96.2 96.2 24.3  675 127.9 127.9 31.7  1025 118.7 109.8 30.7  1125 109.2 102.4 17.4  1250 162.0 148.6 34.6  18.7 6.80 6.80 55  11.9 5.30 7.32 75  24.3 3.96 3.96 50  31.0  28.9 3.37 3.80 47.5  19.4 6.28 5.28 50  31.3 4.68 4.75 50  90 good seepage 130 310 500 122 20 17.5 13.7 84 1.14 6.10 300 1.667 3.030 564 909 200  90 poor dry 85 370 900  94 15 12.9 8.7 52 1.16 6.27 635 1.417 1.890 493 1200 900  120 poor wet 90  60  100 98 24 15.6 11.2 80 1.54 4.08 420 0.238 0.476 120 200  4.04 4.13  52.5  120 good seepage 110 90 200 127 31 27.0 13.9 71 1.15  4.10  290 0.698  1.314 171 381 200  120 poor wet 100 130 200 119 32 23.6 12.6 86  1.40  3.79 345 0.580  1.220 274 421  120 poor dry 95  140  550 108 18 16.7 11.9 68 1.08 6.00 383 1.436 2.87 280 1100 500  120 very good  140  140 50 165 34 33.2 17.7 98 1.02 4.35 195 0.256 0.513 280 100 150  Model No. Photo Data Date o f photo RF Focal length Flying height Plot size E l e v a t i o n of p l o t Hiehgt photo Average h e i g h t Crown width Average crown w i d t h Ht/CW Av.Ht/CW Crown c l o s u r e Ground Data Age c l a s s Site class S i t e index B.A. SPA Height Crown w i d t h D.B.H. Average DBH LCL CW/DBH Ht/CW NSPA CF  ad'i.cF  Adi.BA Adj.SPA Mortality  46 J u l y , 1965 1:16,025 12" 17,200' 1/5 acre 1175 127.2 123.0 16.0 17.4 7.95 7.07 35 120 good seepage 115 180 200 125 18 17.0 14.6 95.  1.06  6.94 267 0.749 2.139 514 571 300  47  1:16,025  1175 152.4 152.4 29.4 29.4 5.18 5.18 55 120 very good 130 230 150 149 32 27.8 16.6 89 1.15 4.66 220 0.682  1.2a as 273  -  186  MODEL  Note;  I  ( i ) ' X ' on the model represents the p o i n t from which the ground stereogram was taken. ( i i ) The p l o t center i s i n the c e n t r a l o f the square on the a e r i a l photographs  •  (stereogram).  187.  MODEL  2  188  MODEL  3  MODEL  4  189.  190.  MODEL  5  191.  192.  MODEL  7  193.  MODEL  8  194. MODEL  9  195.  MODEL  1 0  196.  MODEL  II  198.  MODEL  13  199  MODEL  14  MODEL  15  201.  MODEL  16  202.  203. MODEL  18  204.  MODEL  19  205.  MODEL  20  206.  MODEL  21  207.  MODEL  22  208.  MODEL  23  209.  MODEL  24  MODEL  25  210.  211.  MODEL  26  212. MODEL  27  213  MODEL  28  214.  MODEL  29  MODEL  30  MODEL  3!  217.  MODEL  32  MODEL  33  218.  219.  MODEL  34  MODEL  35  220.  MODEL  36  221.  222.  MODEL  37  MODEL  38  223.  224.  MODEL  39  225.  MODEL  40  226. MODEL  41  MODEL  43  228.  229.  MODEL  44  230.  MODEL  45  MODEL  46  231.  232.  MODEL  47  (l)  APPENDIX 3. Ground stereograms at 20 f e e t from the edge of the f o r e s t with photo-base from 2incb.es to one f o o t .  233.  234 (2)  Ground stereograms at 40 f e e t from the edge o f the f o r e s t with photo-base from 2 inches to one f o o t .  235 APPENDIX 4.  Mosaic of the University Research Forest,Haney.  UNIVERSITY OF BRITISH COLUMBIA RESEARCH FOREST, HANEY, B-CScales |" _ 1^20' || Date of Photography-July 17,1965 Prepared by Fourth Year Photogrammetry Class, Faculty of Forestry, U- B-COctober, 1965  o  (14 l *  c  

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